Research Article Optimization Based High-Speed …downloads.hindawi.com › journals › ddns › 2014 › 934369.pdfResearch Article Optimization Based High-Speed Railway Train Rescheduling

Research ArticleOptimization Based High-Speed Railway Train Reschedulingwith Speed Restriction

Li Wang12 Wenting Mo3 Yong Qin1 Fei Dou2 and Limin Jia1

1 State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China2 School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China3 IBM China Research Lab 2F Diamond A Zhong Guan Cun Software Park Beijing 100193 China

Correspondence should be addressed to Limin Jia jialmvipsinacom

Received 16 August 2013 Revised 17 October 2013 Accepted 6 November 2013 Published 12 January 2014

Academic Editor Wuhong Wang

Copyright copy 2014 Li Wang et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A decision support framework with four components is proposed for high-speed railway timetable rescheduling in case of speedrestrictionThe first module provides the speed restriction informationThe capacity evaluationmodule is used to evaluate whetherthe capacity can fulfill the demand before rescheduling timetable based on deduction factor method The bilayer reschedulingmodule is the key of the decision support framework In the bilayer rescheduling module the upper-layer objective is to make anoptimal rerouting plan with selected rerouting actions Given a specific rerouting plan the lower-layer focuses on minimizing thetotal delay as well as the number of seriously impacted trains The result assessment module is designed to invoke the reschedulingmodel iteratively with different settings There are three prominent features of the framework such as realized interaction withdispatchers emphasized passengersrsquo satisfaction and reduced computation complexity with a bilayer modeling approach Theproposed rescheduling model is simulated on the busiest part of Beijing to Shanghai high-speed railway in China The case studyshows the significance of rerouting strategy and utilization of the railway network capacity in case of speed restriction

1 Introduction

China is extensively developing the infrastructure of high-speed railway The target is to cover its major economicareas with a high-speed railway network which consistsof four horizontal and four vertical lines in the followingseveral years The network scale is much larger than anyother existing ones in the world In the network Beijing-Shanghai high-speed line connects Beijing (the capital ofChina) and Shanghai (the biggest economic centre of China)and it goes through Yangtze River Delta region (the bestdeveloped area in China) Thus people describe it as theNorth-South Aorta of China As designed trains of differentspeeds will be operated in a mixed way on the network witha minimum headway of 3 minutes In other words it has thecharacteristics of high train speed high train frequency andmixed train speed (HHM)

A basic train timetable essentially provides the arrivaltime of trains at stations and the corresponding departuretime from the stations Based on the timetable the dwell

time of trains at the stations (which is 0 if they do notstop) and the departure order of trains from the trainscan be derived During daily operation disturbances to thetimetable are inevitable whichmay be caused by emergencieslike natural disasters accidents or maintenance requestsIn case of the disturbance dispatchers must adopt properemergencymanagement strategies to ensure operation safetyConsequently they need to reschedule the timetable to avoidconflict and recover to the original timetable Drivers willthen adjust the train speed and dwell time according to thenew arrival and departure time given in the rescheduledtimetable

In the context of transportation operation the timetablerescheduling problem is famous of its NP hardness Whatis worse it is very hard to find a generalized reschedulingalgorithm suitable for all kinds of emergency cases because ofvarious railway infrastructure and various emergency man-agement actions Except adjusting arrivaldeparture time allthe actions taken for rescheduling are called rerouting actions

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2014 Article ID 934369 14 pageshttpdxdoiorg1011552014934369

2 Discrete Dynamics in Nature and Society

in this paper including cancelling trains merging trains andmaking a detour

Setting speed restriction is one of the most commonstrategies used by dispatchers facing emergency cases Withfixed departure order of trains at all the stations andunchanged time interval between consecutive departures thethroughput of a railway section over a period of time willdecrease in case of speed restriction In other words trainsmay be delayed or even cancelled The impacted numberof trains is decided by the size of the restricted sectionthe time period in restriction and the restricted speed OnJune 20 2010 the southern part of the existing Beijing-Shanghai line experienced speed restriction for heavy rainstorm As announced 18 trains departing from Shanghaiwere cancelled thereby more than 20000 passengers beingaffected Also the rest in-service trains were more or lessdelayed Considering the high train speed and high trainfrequency of high-speed lines the impact of speed restrictionwould be more serious than on existing lines (in this paperthe existing nonhigh speed railway line is called existing linefor short) On the other hand high-speed lines are morepassenger-oriented than existing lines where punctuality isextraordinarily important Thus it is significant to builda responsive and effective decision support mechanism tohandle the timetable rescheduling in case of speed restrictionfor high-speed lines However there are two challengesto achieve this goal One is the interaction between therescheduling algorithm and the dispatchers Since the dis-patchers have rich experience their advice and decision onthe rescheduling strategies are highly valuable The other oneis the HHM characteristics of the high-speed network

In this paper we investigate the design and imple-mentation of a decision support mechanism for timetablerescheduling in case of speed restriction as mentioned aboveNote that the three prominent features of this mechanism arerealized interactionwith dispatchers emphasized passengersrsquosatisfaction and reduced computation complexity with a bi-layer modeling approach In the rest of the paper relatedresearch work is discussed in the section of The LiteratureReview The next section describes the decision supportmechanism in detail including the mathematical modelingA case study on the busiest part of Beijing-Shanghai high-speed line is given in the section of Case Study The lastsection concludes the whole paper and gives directions forfuture research

2 The Literature Review

The timetable rescheduling problem has been widely inves-tigated by researchers Some related works are reviewedalthough they are quite different from our work from modelcreation to solving method

Some researchers take the rerouting cancellation andother complicated strategies into consideration Reference[1] developed a detailed model based on the identificationof possible route conflicts with high accuracy using theblocking time theory when the objective is to minimizeadditional running times In presence of disturbances analgorithm detects the infeasible train routes and solves

each conflict locally based on train priorities Reference[2] regarded the train rescheduling problem as a constraintoptimization problem using passengersrsquo dissatisfaction as theobjective criterion Then an efficient algorithm combiningPERT and metaheuristics has been addressed Experimentsshow that it works quite fast and it supports versatilemethodsof rescheduling including cancellation change of train-setoperation schedule and change of tracks DrsquoAriano et alhave developed a real-time dispatching system called ROMA(railway traffic optimization by means of alternative graphs)to automatically recover disturbances ROMA is able toautomatically control traffic evaluating the detailed effects oftrain [3] and local rerouting actions [4] while taking intoaccount minimum distance headways between consecutivetrains and the corresponding variability of train dynamics[5ndash7] In order to handle large time horizons within a linearincrease of computation time the temporal decompositionapproaches which decompose a long time horizon intotractable intervals to be solved in cascade with the objectiveof improving punctuality have been proposed in [8]

To speed up trains rescheduling computation time somedecomposition ormultilayermethods are adopted Reference[8] proposed the temporal decomposition approach thatdecompose a long time horizon into tractable intervalsReference [9] proposed a bilayer optimization model withina simulation framework to deal with the high-speed railway(HSR) line planning problem It can reduce computationcomplexity and an optimal set of stop-schedules can alwaysbe generated with less calculation time Reference [10] pre-sented an optimization method for fast construction of timetables which can be used for dispatching or long term opera-tion planning This method contains two steps constructingand iterative improving Constructing step uses branch-and-bound method to construct the first solution takinginto account only restricted amount of possible decisionsImproving step adopts the genetic algorithm as an iterativeimproving method These several levels of optimizationmethod can help reduce the calculation effort

Furthermore [11 12] addressed the problem of solvingconflicts in railway traffic due to disturbancesThe problem isformulated as a problem of reschedulingmeets and overtakesof trains and has been dealt with in a two-level process Theupper level handles the order of meets and overtakes of trainson the track sectionswhile the lower level determines the startand end times for each train and the sections it will occupyReference [13] dealt with analyzing dispatchersrsquo decisionprocess in intertrain conflict resolutions and developing aheuristic algorithm for rescheduling trains by modifyingexisting meetpass plans in conflicting situations in a single-track railway A systemrsquos approach is used in construction ofthe heuristic algorithm which is based on inter-train conflictmanagement Reference [14] introduced an optimizationmodel based on improved symmetric tolerance approachwhich could reschedule the timetable timely due to unex-pected interference with little cost and risk Reference [15]investigated the train re-scheduling problem by optimizationand simulation in order to obtain an exact or approximatesolution The model aims at maximizing the number ofpassengers transported and is solved by heuristic procedure

Discrete Dynamics in Nature and Society 3

based on backtracking algorithm The model and DSS areimplemented in Asturias of the Spanish National RailwayCompany in 1998 Reference [16] proposed a model and asolution method for the dispatching of trains on a single-track line Their model mainly addresses the operationalproblem of dispatching trains in real time but can also serveat the strategic level to evaluate the impacts of timetableor infrastructure changes on train arrival times and traindelaysThe formulation is a nonlinearmixed integer programthat incorporates lower and upper limits on train velocitiesfor each train on each segment The objective function onlyseeks to minimize a combination of total train tardiness andfuel consumption Based on the driverrsquos safety approachingbehavior and pedestrian safety crossing behavior Wang et al[17] and Guo et al [18] proposed an intelligent drivingshaping model with multiruled decision-making mechanismin the urban traffic environment

Despite the effort devoted to solve the sophisticatedrescheduling problem neither of them proposes the closedloop bilayer feedback approach This approach is able tosimulate the scheduling process of dispatchers Also itpermits the dispatchers adding their experiences into therescheduling process so as to improve the usability of the real-time rescheduling

3 Decision Support Mechanism (DSM) forTimetable Rescheduling

Note that the railway lines considered in this paper are alldouble-track passenger lines with automatic blocking

In order to handle daily operation tasks there is usuallya train operation system for dispatchers In emergenciesdispatchers issue action commands through this system tosignal systemThere are 4 components in the proposed DSMas shown in Figure 1

The speed restriction action as the first part is the inputcoming from the train operation system It contains thefollowing information

(i) Restricted section is a part of the line where speed oftrains is restricted

(ii) Restricted period is the start and end times of a speedrestriction

(iii) Applied train type is different trains may be restrictedto different speeds according to their type

(iv) Speed limitation is the maximum speed a train thatcan run at

Given the speed restriction information the line capacityevaluation module is used to evaluate whether the capacitycan fulfill all the trains scheduled in the original timetablein limited service hour Then the speed and capacity infor-mation are transferred to the third module In the bilayerrescheduling model the upper-layer objective is to makean optimal rerouting plan with selected rerouting actionsGiven a specific rerouting plan the second layer focuses onminimizing the total delay as well as the number of seriouslyimpacted trains Thereafter if the rescheduling result is

acceptable the new timetable generated from the DSM willbe fed back into the train operation system Otherwise thebilayer rescheduling will be executed in a loop till the newtimetable is acceptable so that it can be disseminated todrivers

31 Line Capacity Evaluation As mentioned in the Intro-duction section the line throughput may drop dramaticallyduring the restricted period As a result it may not be ableto fulfill all the trains scheduled in the original timetablein limited service hour If the capacity was not enough forthe demand the result of timetable rescheduling would bemeaningless Thus a module is used to evaluate whether thecapacity can fulfill the demand before rescheduling timetableWith the evaluation result the dispatcher canmake a decisionon train canceling according to rules and their experience

During the past several years analytical [19ndash21] andsimulation methods [22] are used to calculate the capacityof railway lines (either single-track or double-track) Amongthose methods [23] is widely used in Europe which can becategorized as a simulation method It stated that railwaycapacity depends on both infrastructure and the timetableTherefore the capacity calculation according to UIC 406requires an actual timetable Some timetabling softwaressuch as RailSys have already implemented such calculationmethods However this approachmay cost long computationtime and may not obtain a feasible timetable

In this paper we use deduction factormethod [24] whichis popular in recent years in China railway to calculate theline capacity The deduction factor method is an analyticalmethod for calculating the capacity of high-speed rail linewith various types of trains This method considers thecapacity occupancy of different trains and normalizes theminto one kind of trains in order to obtain the theoretical valueof capacity

If there is only one kind of trains without stopovers onhigh-speed rail line capacity of high-speed rail line withhigh-speed trains without stopovers can be obtained by

119899max =

1440 minus 119905maintenance minus 119905inefficacy

119868

(1)

where 1440 is the total number of minutes in a day and119905maintenance denotes the maintenance window time In thispaper 119905inefficacy is the capacity which cannot be used Forinstance we have to ensure that all the trains arrive todestination before the maintenance operation starts Hencegiven the speed of trains the last train must depart from thefirst station before a specific time after which we cannot sendmore trains In other words some capacity is wasted This isthe concept behind the calculation of capacity inefficacy Inaddition 119868 is the headway between consecutive trains Thisparameter is the so-called safety distance which is deter-mined by the number of blocks between each consecutivetrain So it can be obtained by train speed and blockingdistance

On the contrary if there are various trains with differentspeed on the rail line (1) cannot precisely obtain the linecapacity as different kinds of trains may take up different


Train operation system

Speed restriction Bilayer rescheduling

Is the capacity enough for fulfill demand

Line capacity evaluation

Arrivaldeparture time adjustment Is the rescheduling

result acceptable

Result assessment

New timetable

Yes

No

bullMerge trainsbullMake a detourbullCancel trainsbullAdvance departure time

Rerouting management

Figure 1 Architecture of the decision support mechanism

I

tdifference Iarrival

Ideparture

Figure 2 Deduction factor for single-quasihigh speed trains with-out stopovers with regard to high-speed trains without stopovers

capacity For example as shown in Figure 2 quasihigh-speedtrainswill take upmore ldquoareardquo in the timetableThe deductionfactor for single quasihigh-speed trains without stopoverswith regard to high-speed trains without stopovers can beobtained by

120576nostopquasihigh =

119868departure + 119905diffenence + 119868arrival minus 119868

119868

(2)

Different deduction factors need to be calculated accordingto train operation mode which are beyond the scope of thispaper After obtaining all kinds of deduction factors averagededuction factor can be obtained according to the ratio ofdifferent situationsThen the normalized line capacity can becalculated

InChina there are two types of trains onmost high-speedlines (high-speed trains and quasi-high-speed trains) In thissituation two kinds of deduction factors are used for capacitycalculation One arises fromhigh-speed trains with stopoverswith regard to high-speed trains without stopoversThe other

one arises from the speed difference of two types of trains Adetailed example will be given in the Case Study section

32 Bilayer Rescheduling As shown in Figure 1 the resched-uling consists of three components that are executed in aloop From the optimization perspective the reschedulingproblem is decomposed into two layersThefirst layer decidesthe rerouted trains and the second layer adjusts the arrivaland departure times of the rest of the trains The detaileddescriptions of the components are given below

33 Rerouting Management The first step in reschedulingis to decide the rerouting actions to avoid extensive delayresulted from decreased capacity

If the capacity is not enough it will be necessary to reducethe demand In this paper the following rerouting actions areconsidered for capacity releasing

(i) Merging trains means to merge two trains into onesubject to two constraints First only trains of certaintype can be merged to prevent the merged trainfrom exceeding the maximum train length Secondtrain 119860 and train 119861 can be merged only if 119878119878

119860

sube 119878119878119861

or 119878119878119861

sube 119878119878119860

where 119878119878119860

and 119878119878119861

denote the stoppingstation set of 119860 and 119861 respectively Although onetrain number will disappear after merging the pas-sengers who bought the tickets of the correspondingtrain will be noticed to get onboard to the mergedtrain and are guaranteed to be able to get off at theirdestinations by the second merging constraint Thusthe impact on the passengers of this rerouting actionmay be ignored

(ii) Making a detour means to drive trains off the high-speed line and use the intercity line or existing linewhen residual capacity is available


(iii) Cancelling means to cancel trains When a trainis cancelled not only the tickets must be refundedbut also the reputation would be damaged So thisrerouting action is of the lowest priority

Note that the calculated capacity is the upper bound of thereal capacity Theoretically if the capacity is larger than thedemand all the trains can travel from the origin to thedestination in the service hour Nonetheless the capacitymaynot be fully utilized due to sparse departure from the originstation Thus advancing departure time is another reroutingaction which can be taken when the capacity is not fullyutilized

The optimization at this layer aims at finding an optimalrerouting plan with the minimum cost The cost is associatedwith the impacts of the above rerouting actions onpassengersincluding the refundable paid by railway company and theextra transfer taken by passengersThis reflects the passenger-oriented principle in the high-speed railway

34 ArrivalDeparture Time Adjustment Given the rerout-ing plan the trains remaining to run on the high-speedline are known Thereafter the optimization objective isto minimize the weighted delay of these trains where theweights correspond to their priorities The objective canbe achieved by adjusting the arrivaldeparture time tofromstations In practice the speed of trains running between twoconsecutive stations the dwell time of trains at stations andthe departure order of trains from stations may need to bechanged according to the arrivaldeparture time adjustment

The advantages of bilayer decomposition can be inter-preted from different angles From the system perspective itfacilitates the interaction with dispatchers They are enabledto explicitly control the rerouting actions From the problemsolving perspective it effectively reduces the complexity ofoptimization Long computation time is usually a cursefor rescheduling problems because of the large numberof decision variables which prevents the application ofoptimization-based automatic timetable rescheduling algo-rithms being used in real world

35 Decision Tree-Based Result Assessment A decision treeis mined from an evaluation rule set for reschedulingresult assessment purpose A rule defines the conditionsfor accepting or rejecting a rescheduled timetable The ruleset is generated from the dispatchersrsquo experience on theacceptability of a rescheduled timetable Basically extensivedelay and long delay of single trains are not acceptable topassengers in high-speed lines Table 1 gives an example ofthe evaluation rules where 120579

1

= 30mins and 1205792

= 60minsOverlapping or redundancy may exist in the rule set as

the rules are generated from experience Greedy algorithmcan be used to search for the smallest decision tree based ona given rule set [23] In a decision tree each node is a testfor an attribute each branch corresponds to test results andeach leaf assigns a decision For illustration purpose Figure 3shows the smallest decision tree obtained from the rules givenin Table 1

4 Mathematical Modeling ofthe Bilayer Rescheduling

Mixed integer linear programming (MILP) is used to modelthe proposed bilayer rescheduling

41 Input Data The numerical inputs are described asfollows

inis119901

inie119901

initial start and end times of interval paccording to original timetable119911119901

the minimum size of interval p If p is thepossession of a station 119889

119901

stands for the minimumdwell time of the train associated with p Otherwiseit stands for the minimum running time of the train119891119896

the minimum separation time of two intervals onstation k that is end time of an interval and start timeof the subsequent intervalℎ119908119896

the headway of section k that is start time of aninterval and start time of the subsequent interval119892119894

the length of train i Only if 119892119894

= G train i can bemerged G is a constant input

119888cancel119894

119888detour119894

and 119888merge119894119895

the cost of canceling traini detouring train i and merging train i to train jrespectively

119888delay119894

the cost per time unit delay for train I119908119894

delay tolerance for train I

ℎ119901

1 if interval 119901 is a planned stopwhere 119901 isin Itv

0 otherwise(3)

Δ119862 the total residual capacity of alternative lines120575 theminimal number of trains to be applying rerout-ing actions which is obtained from line capacityevaluation module119872 a very big integer for example 100000

Some sets are defined in Table 2 for modeling Note that thesegment between two stations is called ldquosectionrdquo while thestation segment is called ldquostationrdquo for short

42 Model of Rerouting Management Layer

421 Decision Variables

119902119894

=

1 if train 119894 is canceledwhere 119894 isin Trn0 otherwise

119898119894119895

=

1 if train 119894 is merged to train 119895

where 119894 119895 isin Trn 119892119894

= 119892119895

= 119866

0 otherwise

(4)


Table 1 Example of evaluation rules

Percentage of trains being delayedmore than 120579

1


2

Number of delayedhighpriority trains Acceptable (outcome)

le80 ge50 ge8 Nole20 mdash mdash Yesle50 mdash le15 Yesmdash le50 le15 Yes

Table 2 Sets defined for modeling

Set name Description Size Indexof set

Trn All the trains 119879 119894

Seg All the segments 119878 119896

Stn sube Seg All the stations 119873 mdashSec sube Seg All the sections SminusN mdash

Itv All the intervals where an interval is the possession of a segment by a train with specified start and endtimes mdash p

Itv119894

sube Itv The ordered set of intervals for train 119894 according to the original timetable mdash mdashItvstn119894

sube Itv119894

The ordered set of intervals associated with stopping at stations for trains 119894 mdash mdashItv119896

sube Itv The ordered set of intervals for segment 119896 according to the original timetable mdash mdashTrk119896

All the tracks of station 119896 119871119896

119897

Remarks (1) for the ease of understanding we use p as the index for every interval-related set (ie Itv Itv119894 Itvstn119894

and Itv119896) In each of the interval-related sets

p + 1 indicates the first subsequent interval of p and 119901 indicates all the subsequent intervals of p

Note that if train 119894 is merged to train 119895 the train numberof 119894 will no longer exist

119900i =

1 if train 119894 makes a detour with existinglinewhere 119894 isin Trn

0 otherwise(5)

422 Objective Functions

(i) To minimize the rerouting cost

Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints

(ii) Cancelled trains cannot make detour

119902119894

+ 119900119894

le 1 119894 isin Trn (7)

(iii) If a train is eligible to be merged it can be mergedto (with) at most one other train The merged traincannot be cancelled

sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894

le 1 119894 isin Trn

sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)

(iv) The number of detoured trains cannot exceed theresidual capacity of alternative lines

sum

119894isinTrn119900119894

le Δ119862 (9)

(v) The minimal number of the trains that being appliedrerouting actions

sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)

43 Model of ArrivalDeparture Time Adjustment Layer

431 The Decision Variables The decision variable are de-scribed as follows

119904119901

119890119901

start time and end time of interval 119901119889119901

delay of interval 119901 which is defined as the differ-ence between the departure time after adjustment andthe planned departure time in the original timetable

119887119894

=

1 if train 119894 reaches its final considered stop witha delay larger than 119908

119894

where 119894 isin Trn0 otherwise


Percentage of trains being delayed more than


Number of delayed high priority trains

No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80

Figure 3 Illustration of the smallest decision tree obtained from Table 1

120578119901119897

=

1 if interval 119901 uses track 119897where 119901 isin Itv119896

119897 isin Trk119896

and 119896 isin Stn0 otherwise

120572119901119901

1 if interval 119901 occurs before 119901 as in theinitial timetablewhere 119901 119901 isin Itv

119896

119896 isin Seg0 otherwise

120573119901119901

=

1 if interval 119901 is changed to occur after 119901

where 119901 119901 isin Itv119896


(11)


(i) To minimize the delay cost

Minimize sum

119894isinTrn(119888

delay119894

sdot sum

119901isinItvstn119894

119889119901

) (12)

(ii) Tominimize the number of trains exceeding delay tol-erance

Minimize sum

119894isinTrn119887119894

(13)

433 Constraints

(i) Interval restrictions are as follows

119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)

The real departure time cannot be earlier than the originaldeparture time

119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)

(ii) Track restrictions

sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)

(iii) Connectivity restrictions are as follows

119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)

For each station if two intervals use the same track at leastone of 120572 and 120573 is forced to be 1

120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)

One train can enter a station after the preceding train whichuses the same track leaves it

119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)

For each section at least one of 120572 and 120573 is forced to be 1because there is only one track

120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)

Headways for each section are as follows

119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)

(iv) Auxiliary restrictions are as follows

119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study

TheproposedDSM is simulated on the busiest part of Beijing-Shanghai high-speed line between Nanjing (Ning for short)and Shanghai (Hu for short) In the rest of this paper ldquoHu-Ning Partrdquo is used to represent this part of the Beijing-Shanghai high-speed line As shown in Figure 5 besidesBeijing-Shanghai high-speed line there are two other linesconnecting Hu andNing which are Hu-Ning inter-city high-speed line and existing Beijing-Shanghai line Since all of


them are double-track lines we only consider the directionfrom Ning to Hu without loss of generality All the MILPmodels are solved by IBM ILOG CPLEX 122

As shown in Figure 4 there are seven stations on theHu-Ning Part Nanjing South Zhenjiang West ChangzhouNorth Wuxi East Suzhou North Kunshan South andHongqiao (Shanghai) A specific section is the railway partbetween two consecutive stations for example Nanjing-Zhenjiang Section is the railway part between Nanjing SouthStation and Zhenjiang West Station that is regarded asthe 1st section on the Hu-Ning Part The lengths of thesix sections starting from Nanjing-Zhenjiang Section are65110m 61050m 56400m 26810m 31350m and 43570mrespectively Its daily service starts at 630 am and ends at1130 pm The planned timetable is obtained from Beijing-Shanghai High-speed Line Timetable Planning Lab BeijingJiao TongUniversity As currently planned there are 60 trainsin the initial timetableThe trains from Beijing-Shanghai lineare called self-line trains while those from Riverside lineare called cross-line trains Fourteen high-speed trains fromBeijing-Shanghai line take 119871 and 119863119869 as the train numberprefix 38 quasi-high-speed trains from Beijing-Shanghai linetake 119866 as the train number and 8 quasi-high-speed trainsfrom Riverside line take 119870 as the train number As in realityself-line trains have higher priority than cross-line trains Asfor self-line trains the high-speed trains have higher prioritythan the quasi-high speed trainsThe costs per time unit delayfor the three kinds of trains are set to 5 3 and 1 respectivelyThe costs of three kinds of rerouting strategies for trains(canceling train detouring train and merging train) are setbased on the trainrsquos priority and its delay timeDelay tolerancefor trains is set to 30min The minimum separation time ontrack possession in each station is set to 1min

In Figure 5 the high-speed line inter-city line and exist-ing line are represented by NH NH

119894119888

and NH119890

respectivelyCorrespondingly the capacities are 119862 119862

119894119888

and 119862119890

and thedemands are 119863 119863

119894119888

and 119863119890

The unit of both capacity anddemand is the number of trains Suppose there is a speedrestriction on NH resulting in that the capacity of NHreduces to 119862

1015840 NH119894119888

and NH119890

are in normal service withknown residual capacity Δ119862

119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890

respectively Before rescheduling the timetable in case ofspeed restriction 1198621015840 needs to be evaluated

Although there are two different train speeds on theBeijing-Shanghai Part in the planned timetable which arehigh-speed (350 kmhr) and quasi-high speed (300 kmhr)the speed of trains will become uniform when the speedrestriction is lower than 300 kmhThus in the two deductionfactors mentioned at the end of Line Capacity Evaluationsection only the stopover of trains needs to be considered butnot the meeting of the trains The deduction factor for singlehigh-speed train with stopovers with regard to high-speedtrain without stopovers can be obtained by the followingequation [24]

120576highstop

=

119868 + 119879

119868

(23)

where 119868 denotes the minimum headway between consecu-tive trains and 119879 denotes the minimum stopping time at

stationsThen the average deduction factor formultiple high-speed trains can be obtained by the equation below [24]

120576high = 120572high

+ 120572highstop

120576highstop

(24)

where 120572high denotes the ratio of high-speed trains without

stopovers and 120572highstop denotes the ratio of high-speed trains

with stopovers Given equations (1) (23) and (24) the capac-ity of high-speed rail line with trains of uniformed speed withstopovers can be obtained by the following equation

1198621015840

=

119899max120576high

=


120576high119868 (25)

where the headway 119868 is calculated by (Number of blocks lowast

Length of block + Length of Train)Trainrsquos average speed [24]In the case study 119879 is 3minutes Since the capacity of the

sections with the most stopovers restrains the capacity of thewhole line 120572high

= 1643 120572highstop= 2743 are calculated

in these sections As planned 119905maintenance = 6 hours (000 AMto 600 AM) 119905inefficacy asymp disV is related to the total distancedis (284 km in this case) and the restricted train speed VThe lower the restricted speed is the longer the inefficacywill be The capacity of the Hu-Ning Part in various speedrestrictions is calculated by (23)ndash(25) and the results areshown in Table 3

In the case study demand 119863 = 43 It can be seen fromTable 3 that 1198621015840decreases as the speed restriction gets lowerBut it never gets smaller than 119863 which means the demandof Hu-Ning Part can always be fulfilled even when the speedis restricted down to 50 kmhr The reason why the demandis so small may be that the obtained timetable is designed forthe first step operation of the Beijing-Shanghai line at whichtime of the high-speed network in blueprint has not formedyet

Since 1198621015840

ge 119863 holds in all the speed restriction casesrerouting actions will not be taken at the first place as statedin the Rerouting Management section The arrivaldeparturetime adjustment optimization is executed and the results aregiven in Table 4 where 120578

1

denotes the number of trains witha delay not less than 30mins 120578

2

denotes the number of trainswith a delay not less than 60mins 120582 denotes the number oftrains entering the last section beyond service hour and 120574

denotes the number of delayed self-line trains The values inbrackets are the results with no rescheduling

It can be seen fromTable 4 that no trainwill be delayed formore than 30mins when the speed restriction takes place in1st section or 1st and 2nd sections and the speed limitation ishigher than 100 kmhr There is a finding that the delay of 1stand 2nd sections speed restriction is more serious than thatof 1st section speed restriction in terms of all the metricsTheresults suggest that the longer the restricted distance is or thelower the speed limitation is the more serious the delay willbe In addition it can be seen from the results that both thetotal delay time and the number of delayed trains obtainedwith the proposed approach are less than those obtainedwithout rescheduling

As proposed in the Decision Tree-based Result Assess-ment section a decision tree is used to evaluate the resched-uled timetable In the case study it is assumed that the


300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159

Figure 4 The planned timetable of Hu-Ning Part

Table 3 Capacity of Hu-Ning part in speed restrictions

Restricted speed(kmhr) 119905inefficacy (hr) 119868 (min) 119899max 120576

highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168

Table 4 Evaluation results on the rescheduled timetable

Restricted section(s) Speed limitation (kmh) 1205781

1205782

120582 120574 Total delay (min) Calculation time(s)

1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669

1st and 2nd sections

300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567

All (1stndash6th) sections

300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane

Jing-Huspeed-high line

Jing-Hu existing line

Nanjing(Ning)

Hu-Ning intercity line

Hu-Ning Part inspeed restriction


Shanghai(Hu)

Figure 5 The railway network around Nanjing (Ning)

decision tree only comprises of one node which is 120582 = 0In other words only if all the trains can enter the last sectionin service hour the rescheduled result can be accepted Withthis single-node decision tree the unaccepted results areidentified in Table 4 including 1st section-50 kmhr 1st and2nd sections-80 kmhr 1st and 2nd sections-50 kmhr allsections-100 kmhr all sections-80 kmhr and all sections-50 kmhr The results imply that 1198621015840 is not fully utilized

As proposed in DSM if a result is not accepted withresult assessment it goes back to the rerouting managementmodule In the case study two rerouting strategies areconsidered for 119862

1015840

ge 119863 One is to mergedetourcancelsome trains represented by RS-1 The other one is to advancedeparture time represented by RS-2

(i) RS-1 In the optimization model of the reroutingmanagement layer we assume residual capacitiesΔ119862119894119888

= 3 and Δ119862119890

= 2 Advanced departure time isnot allowedHence the calculatedmaximumcapacityis not applicable with this strategy The strategy RS-1is testedwith theminimum rerouted number of trains120575 increasing from 1 to 13

(ii) RS-2The departure time is allowed to be advanced byrelaxing the second constraint of interval restrictionsin the time adjustment-layer optimization model

The comparison results are shown in Table 5It can be seen from Table 5 that detouring trains strategy

has a high priority merging trains strategy has a mediumpriority and canceling trains strategy has a low priorityaccording to the costs respectively The K-trains (K101 K103K105 K107 K109 K111 K113 and K115) and G-trains (G149G151 G153 G155 G157 and G159) take a detour or arecancelled because that the K-trains are cross-line trains thathave lower 119888

detour and 119888cancel than other trains and the G-

trains that depart fromNanjing South after 8 pm have a lower119888detour and 119888

cancel than other trains The detoured train G151is replaced by L9 when the speed limitation is lower than80 kmh and the speed restriction takes place in all sectionsThis may be explained that 119888detourand 119888

cancel are related notonly with the train priority but also with the speed limitationand L9 departs after G151 from Nanjing South

In addition there is a finding that the results of RS-2outperform RS-1 in terms of all the metrics Although theresults obtained by using RS-1 are better than those before

rerouting management shown in Table 4 the improvementis not big The difference may be only resulted from thereduction of trains Consequently half of the results are stillnot acceptable based on the decision tree In contrast usingRS-2 results is significant improvement for all the scenariosNot only all the rescheduled timetables are acceptable thevalues of all the metrics lower down considerably Thecomparison result implies that to increase the utilization ofline capacity is more helpful than to reduce demand whenthe train departure is sparse

6 Conclusion and Future Work

This paper proposed a DSM for dispatchers to deal withtimetable rescheduling in case of extensive speed restric-tion The main contributions include the following (1) Thererouting optimization is incorporated into the timetablerescheduling with a bilayer optimization model (2) the linecapacity calculation is innovatively used in solving timetablerescheduling problem to guide the selection of rerout-ing actions and parameters (3) dispatchers are effectivelyinvolved into the iterative timetable rescheduling so that theirvaluable experience can be leveraged while most researchwork on timetable rescheduling focuses on the optimizationmodel itself

The proposed decomposition into two optimization lay-ers including rerouting management and arrivaldeparturetime adjustmentmakes the timetable rescheduling optimiza-tion problem solvable even in a complex setting with anacceptable computation time In addition interposition andguidance of dispatchers are introduced into the optimizationprocedurewith the decomposition resulting in amore practi-cal approach for real-world application Despite these advan-tages the optimality of the original timetable reschedulingoptimization problem may be sacrificed in a sense due to thedecomposition The timetable rescheduling usually involvesmultiple objectives of which the optimal solutions constitutea Pareto-front When making the decision on which trainsto be rerouted in the rerouting management layer there isno way of considering the potential delay that each trainwill induce into the timetable So it is possible that a goodsolution is lost with rerouting an improper train therebylosing the corresponding Pareto-optimal point Fortunatelythe arrivaldeparture time adjustment layer guarantees to findthe global optimal solution Hence a Pareto-optimal solutionwill be found in the end In summary the optimality issacrificed in the sense that some Pareto-optimal solution ismissed This is acceptable because it is hard to say that oneobjective is more important than another in daily operation

The proposed mechanism methods and models aresimulated on the busiest part of the Beijing-Shanghai high-speed rail lineTheproposedDSMshowed good performancein the sense that the costs of delay and rerouting can bebalanced and optimized iteratively Additionally a significantfinding from the case study is that the most important step isto increase the utilization of the rail line in case of extensivespeed restriction


Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359


There remain some interesting areas to explore aroundthe proposed DSM Firstly the speed restriction is set per dayper section how to make the setting more flexible is an issueSecondly the rolling-stock rebalancing is yet to be consideredtogether with the timetable rescheduling Moreover theproposedDSM is designed for decision support purpose Ourultimate goal is to design and develop a real-time decisionsupport framework in the future

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work has been supported by National Natural ScienceFoundation of China (61074151) National Key TechnologyResearch and Development Program (2009BAG12A10) andNational High Technology Research and Development Pro-gram of China (2012AA112001)

References

[1] J Jacobs ldquoReducing delays by means of computer-aidedldquoon-the-spotrdquo reschedulingrdquo Computers in Railways IX WITSouthampton UK vol 15 pp 603ndash612 2004

[2] T Norio T Yoshiaki T Noriyuki H Chikara and M Kunim-itsu ldquoTrain rescheduling algorithm which minimizes passen-gersrsquo dissatisfactionrdquo Transactions of Information ProcessingSociety of Japan vol 46 no 2 pp 26ndash38 2005

[3] ADrsquoArianoD Pacciarelli andM Pranzo ldquoAbranch and boundalgorithm for scheduling trains in a railway networkrdquo EuropeanJournal of Operational Research vol 183 no 2 pp 643ndash6572007

[4] A DrsquoAriano F Corman D Pacciarelli and M PranzoldquoReordering and local rerouting strategies to manage traintraffic in real timerdquo Transportation Science vol 42 no 4 pp405ndash419 2008

[5] A DrsquoAriano and T Albrecht ldquoRunning time re-optimizationduring real-time timetable perturbationsrdquo inComputers in Rail-ways X J Allan C A Brebbia A F Rumsey G Sciutto S Soneand C J Goodman Eds pp 531ndash540 WIT Southampton UKJuly 2006

[6] A DrsquoAriano M Pranzo and I A Hansen ldquoConflict resolutionand train speed coordination for solving real-time timetableperturbationsrdquo IEEE Transactions on Intelligent TransportationSystems vol 8 no 2 pp 208ndash222 2007


[8] A DrsquoAriano and M Pranzo ldquoAn advanced real-time traindispatching system for minimizing the propagation of delaysin a dispatching area under severe disturbancesrdquo Networks andSpatial Economics vol 9 no 1 pp 63ndash84 2009

[9] L Wang L-M Jia Y Qin J Xu and W-T Mo ldquoA two-layer optimizationmodel for high-speed railway line planningrdquoJournal of Zhejiang University SCIENCE A vol 12 no 12 pp902ndash912 2011

[10] S Wegele and E Schnieder ldquoDispatching of train operationsusing genetic algorithmsrdquo in Proceedings of the 9th InternationalConference on Computer-Aided Scheduling of Public Transport(CASPT rsquo04) San Diego Calif USA 2004

[11] J Tornquist and J A Persson ldquoTrain traffic deviation handlingusing tabu search and simulated annealingrdquo in Proceedings ofthe 38th Annual Hawaii International Conference on SystemSciences p 73 January 2005

[12] J Tornquist and J A Persson ldquoN-tracked railway traffic re-scheduling during disturbancesrdquo Transportation Research PartB vol 41 no 3 pp 342ndash362 2007

[13] I Sahin ldquoRailway traffic control and train scheduling based oninter-train conflict managementrdquo Transportation Research PartB vol 33 no 7 pp 511ndash534 1999

[14] L Wang Y Qin J Xu and L Jia ldquoA fuzzy optimizationmodel for high-speed railway timetable reschedulingrdquo DiscreteDynamics in Nature and Society vol 2012 Article ID 827073 22pages 2012

[15] B Adenso-Dıaz M Oliva Gonzalez and P Gonzalez-TorreldquoOn-line timetable re-scheduling in regional train servicesrdquoTransportation Research Part B vol 33 no 6 pp 387ndash398 1999

[16] A Higgins E Kozan and L Ferreira ldquoOptimal scheduling oftrains on a single line trackrdquoTransportation Research Part B vol30 no 2 pp 147ndash158 1996

[17] W Wang Y Mao J Jin et al ldquoDriverrsquos various informationprocess and multi-ruled decision-making mechanism a fun-damental of intelligent driving shaping modelrdquo InternationalJournal of Computational Intelligence Systems vol 4 no 3 pp297ndash305 2011

[18] H Guo W Wang W Guo X Jiang and H Bubb ldquoReliabilityanalysis of pedestrian safety crossing in urban traffic environ-mentrdquo Safety Science vol 50 no 4 pp 968ndash973 2012

[19] E R Kraft ldquoJam capacity of single track rail linesrdquo Proceedingsof the Transportation Research Forum vol 23 no 1 pp 461ndash4711982

[20] B Szpigel ldquoOptimal train scheduling on a single track railwayrdquoOperational Research vol 72 pp 343ndash352 1972

[21] D Jovanovic and P T Harker ldquoTactical scheduling of railoperationsThe SCAN I systemrdquoTransportation Science vol 25no 1 pp 46ndash64 1991

[22] N Welch and J Gussow ldquoExpansion of Canadian NationalRailwayrsquos line capacityrdquo Interfaces vol 16 no 1 pp 51ndash64 1986

[23] UIC leaflet 406 Capacity UIC Paris France 2004[24] H Yang Theory of Railway Transportation Planning China

Railway Publishing House 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


in this paper including cancelling trains merging trains andmaking a detour

Setting speed restriction is one of the most commonstrategies used by dispatchers facing emergency cases Withfixed departure order of trains at all the stations andunchanged time interval between consecutive departures thethroughput of a railway section over a period of time willdecrease in case of speed restriction In other words trainsmay be delayed or even cancelled The impacted numberof trains is decided by the size of the restricted sectionthe time period in restriction and the restricted speed OnJune 20 2010 the southern part of the existing Beijing-Shanghai line experienced speed restriction for heavy rainstorm As announced 18 trains departing from Shanghaiwere cancelled thereby more than 20000 passengers beingaffected Also the rest in-service trains were more or lessdelayed Considering the high train speed and high trainfrequency of high-speed lines the impact of speed restrictionwould be more serious than on existing lines (in this paperthe existing nonhigh speed railway line is called existing linefor short) On the other hand high-speed lines are morepassenger-oriented than existing lines where punctuality isextraordinarily important Thus it is significant to builda responsive and effective decision support mechanism tohandle the timetable rescheduling in case of speed restrictionfor high-speed lines However there are two challengesto achieve this goal One is the interaction between therescheduling algorithm and the dispatchers Since the dis-patchers have rich experience their advice and decision onthe rescheduling strategies are highly valuable The other oneis the HHM characteristics of the high-speed network

In this paper we investigate the design and imple-mentation of a decision support mechanism for timetablerescheduling in case of speed restriction as mentioned aboveNote that the three prominent features of this mechanism arerealized interactionwith dispatchers emphasized passengersrsquosatisfaction and reduced computation complexity with a bi-layer modeling approach In the rest of the paper relatedresearch work is discussed in the section of The LiteratureReview The next section describes the decision supportmechanism in detail including the mathematical modelingA case study on the busiest part of Beijing-Shanghai high-speed line is given in the section of Case Study The lastsection concludes the whole paper and gives directions forfuture research

2 The Literature Review

The timetable rescheduling problem has been widely inves-tigated by researchers Some related works are reviewedalthough they are quite different from our work from modelcreation to solving method

Some researchers take the rerouting cancellation andother complicated strategies into consideration Reference[1] developed a detailed model based on the identificationof possible route conflicts with high accuracy using theblocking time theory when the objective is to minimizeadditional running times In presence of disturbances analgorithm detects the infeasible train routes and solves

each conflict locally based on train priorities Reference[2] regarded the train rescheduling problem as a constraintoptimization problem using passengersrsquo dissatisfaction as theobjective criterion Then an efficient algorithm combiningPERT and metaheuristics has been addressed Experimentsshow that it works quite fast and it supports versatilemethodsof rescheduling including cancellation change of train-setoperation schedule and change of tracks DrsquoAriano et alhave developed a real-time dispatching system called ROMA(railway traffic optimization by means of alternative graphs)to automatically recover disturbances ROMA is able toautomatically control traffic evaluating the detailed effects oftrain [3] and local rerouting actions [4] while taking intoaccount minimum distance headways between consecutivetrains and the corresponding variability of train dynamics[5ndash7] In order to handle large time horizons within a linearincrease of computation time the temporal decompositionapproaches which decompose a long time horizon intotractable intervals to be solved in cascade with the objectiveof improving punctuality have been proposed in [8]

To speed up trains rescheduling computation time somedecomposition ormultilayermethods are adopted Reference[8] proposed the temporal decomposition approach thatdecompose a long time horizon into tractable intervalsReference [9] proposed a bilayer optimization model withina simulation framework to deal with the high-speed railway(HSR) line planning problem It can reduce computationcomplexity and an optimal set of stop-schedules can alwaysbe generated with less calculation time Reference [10] pre-sented an optimization method for fast construction of timetables which can be used for dispatching or long term opera-tion planning This method contains two steps constructingand iterative improving Constructing step uses branch-and-bound method to construct the first solution takinginto account only restricted amount of possible decisionsImproving step adopts the genetic algorithm as an iterativeimproving method These several levels of optimizationmethod can help reduce the calculation effort

Furthermore [11 12] addressed the problem of solvingconflicts in railway traffic due to disturbancesThe problem isformulated as a problem of reschedulingmeets and overtakesof trains and has been dealt with in a two-level process Theupper level handles the order of meets and overtakes of trainson the track sectionswhile the lower level determines the startand end times for each train and the sections it will occupyReference [13] dealt with analyzing dispatchersrsquo decisionprocess in intertrain conflict resolutions and developing aheuristic algorithm for rescheduling trains by modifyingexisting meetpass plans in conflicting situations in a single-track railway A systemrsquos approach is used in construction ofthe heuristic algorithm which is based on inter-train conflictmanagement Reference [14] introduced an optimizationmodel based on improved symmetric tolerance approachwhich could reschedule the timetable timely due to unex-pected interference with little cost and risk Reference [15]investigated the train re-scheduling problem by optimizationand simulation in order to obtain an exact or approximatesolution The model aims at maximizing the number ofpassengers transported and is solved by heuristic procedure


















119899max =


119868

(1)









result acceptable

Result assessment

New timetable

Yes

No




I


Ideparture





119868

(2)








119860

sube 119878119878119861

or 119878119878119861

sube 119878119878119860

where 119878119878119860

and 119878119878119861










1

= 30mins and 1205792






inis119901

inie119901



119901






119888cancel119894

119888detour119894

and 119888merge119894119895


119888delay119894



ℎ119901


0 otherwise(3)





119902119894

=


119898119894119895

=


where 119894 119895 isin Trn 119892119894

= 119892119895

= 119866

0 otherwise

(4)




1


2









Itv119894


sube Itv119894




119897





119900i =


0 otherwise(5)



Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints


119902119894

+ 119900119894

le 1 119894 isin Trn (7)


sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894


sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)


sum

119894isinTrn119900119894

le Δ119862 (9)


sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)



119904119901

119890119901



119887119894

=


119894






No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























119899max =


119868

(1)









result acceptable

Result assessment

New timetable

Yes

No




I


Ideparture





119868

(2)








119860

sube 119878119878119861

or 119878119878119861

sube 119878119878119860

where 119878119878119860

and 119878119878119861










1

= 30mins and 1205792






inis119901

inie119901



119901






119888cancel119894

119888detour119894

and 119888merge119894119895


119888delay119894



ℎ119901


0 otherwise(3)





119902119894

=


119898119894119895

=


where 119894 119895 isin Trn 119892119894

= 119892119895

= 119866

0 otherwise

(4)




1


2









Itv119894


sube Itv119894




119897





119900i =


0 otherwise(5)



Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints


119902119894

+ 119900119894

le 1 119894 isin Trn (7)


sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894


sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)


sum

119894isinTrn119900119894

le Δ119862 (9)


sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)



119904119901

119890119901



119887119894

=


119894






No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















result acceptable

Result assessment

New timetable

Yes

No




I


Ideparture





119868

(2)








119860

sube 119878119878119861

or 119878119878119861

sube 119878119878119860

where 119878119878119860

and 119878119878119861










1

= 30mins and 1205792






inis119901

inie119901



119901






119888cancel119894

119888detour119894

and 119888merge119894119895


119888delay119894



ℎ119901


0 otherwise(3)





119902119894

=


119898119894119895

=


where 119894 119895 isin Trn 119892119894

= 119892119895

= 119866

0 otherwise

(4)




1


2









Itv119894


sube Itv119894




119897





119900i =


0 otherwise(5)



Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints


119902119894

+ 119900119894

le 1 119894 isin Trn (7)


sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894


sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)


sum

119894isinTrn119900119894

le Δ119862 (9)


sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)



119904119901

119890119901



119887119894

=


119894






No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1

= 30mins and 1205792






inis119901

inie119901



119901






119888cancel119894

119888detour119894

and 119888merge119894119895


119888delay119894



ℎ119901


0 otherwise(3)





119902119894

=


119898119894119895

=


where 119894 119895 isin Trn 119892119894

= 119892119895

= 119866

0 otherwise

(4)




1


2









Itv119894


sube Itv119894




119897





119900i =


0 otherwise(5)



Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints


119902119894

+ 119900119894

le 1 119894 isin Trn (7)


sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894


sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)


sum

119894isinTrn119900119894

le Δ119862 (9)


sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)



119904119901

119890119901



119887119894

=


119894






No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1


2









Itv119894


sube Itv119894




119897





119900i =


0 otherwise(5)



Minimize sum

119894isinTrn(119888

cancel119894

119902119894

+ 119888detour119894

119900119894

+ 119888merge119894119895

sum

119895isinTrn119898119894119895

) (6)

423 Constraints


119902119894

+ 119900119894

le 1 119894 isin Trn (7)


sum

119894=119895

119898119894119895

= 0 119894 119895 isin Trn

sum

119895isinTrn119898119894119895

+ 119902119894


sum

119894isinTrn119898119894119895

+ 119902119895


119898119894119895

+ 119898119895119894

le 1 119894 119895 isin Trn(8)


sum

119894isinTrn119900119894

le Δ119862 (9)


sum

119894isinTrnsum

119895isinTrn119898119894119895

+ sum

119894isinTrn119902119894

+ sum

119894isinTrn119900119894

ge 120575 (10)



119904119901

119890119901



119887119894

=


119894






No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













No

NoYes

Yes No Yes

1205791

1205792

le15 gt15lt50 ge50

le20

le50 le80gt80


120578119901119897

=


119897 isin Trk119896


120572119901119901


119896


120573119901119901

=


where 119901 119901 isin Itv119896


(11)



Minimize sum

119894isinTrn(119888

delay119894

sdot sum


119889119901

) (12)


Minimize sum

119894isinTrn119887119894

(13)

433 Constraints


119890119901

ge 119904119901

+ 119911119901

119901 isin Itv (14)


119890119901

ge inie119901

119901 isin Itv ℎ119901

= 1

119890119901

minus inie119901

= 119889119901

119901 isin Itv(15)


sum

119897isinTrk119896

120578119901119897

= 1 119901 isin Itv119896

119896 isin Stn (16)


119890119901

= 119904119901+1

119901 isin Itv119894

119901 = last (Itv119894

) 119894 isin Trn (17)


120578119901119897

+ 120578119901119897

minus 1 le 120572119901119901

+ 120573119901119901

119901 119901 isin Itv119896

119901 lt 119901 119897 isin Trk119896

119896 isin Stn(18)


119904119901

minus 119890119901

ge 119891119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Stn

119904119901

minus 119890119901

ge 119891119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Stn(19)


120572119901119901

+ 120573119901119901

= 1 119901 119901 isin Itv119896

119896 isin Sec (20)


119904119901

minus 119904119901

ge ℎ119908119896

120572119901119901

minus 119872(1 minus 120572119901119901

) 119901 119901 isin Itv119896

119896 isin Sec

119904119901

minus 119904119901

ge ℎ119908119896

120573119901119901

minus 119872(1 minus 120573119901119901

) 119901 119901 isin Itv119896

119896 isin Sec(21)


119889last(Itv119894) minus 119908119894

le 119872119887119894

(22)

5 Case Study






119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119894119888

and NH119890


119894119888

and 119862119890


119894119888

and 119863119890


1015840 NH119894119888

and NH119890


119894119888

= 119862119894119890

minus 119863119894119890

and Δ119862119890

= 119862119890

minus

119863119890



120576highstop

=

119868 + 119879

119868

(23)



120576high = 120572high

+ 120572highstop

120576highstop

(24)




1198621015840

=

119899max120576high

=


120576high119868 (25)







Since 1198621015840


1


2






300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










300000Hongqiao

250000Kunshannan

Suzhou Bei200000

Wuxi Dong

150000

Changzhou Bei

100000

Zhen Jiangxi50000

Nanjing Nan

Stat

ions

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

DJ503G321

G323G325

G311

G313

G301

G303

G305

G101

G103

G105

L1

K115

K101DJ505

L15

G109

G107

G111G115

G113

K103G117

G119

G121

G123

L3 G127

G125

K105L17

G129L19

G133

G131K107

K109

L5G137

G135 L11

K111

G141

DJ509

G139

DJ507L7

L13

G145G143

G147K113 G151

G153

L9

G149

G155

G157G159




highstop120576high

1198621015840

300 NA 23 469 23 182 257200 1 2 510 25 194 262100 2 22 436 236 185 23580 3 27 333 21 169 19750 6 24 300 225 178 168



1205782


1st section

300 0 (0) 0 (0) 0 (0) 1 (14) 381 (231) 483200 0 (0) 0 (0) 0 (0) 25 (52) 9821 (2596) 524150 0 (0) 0 (0) 0 (0) 47 (52) 38481 (8102) 1869100 0 (0) 0 (0) 0 (0) 52 (52) 115881 (16058) 92280 23 (60) 0 (0) 0 (0) 52 (52) 174331 (20176) 66350 40 (0) 20 (60) 1(1) 52 (52) 350131 (377523) 669


300 0 (0) 0 (0) 0 (0) 4 (52) 7 (4144) 522200 0 (0) 0 (0) 0 (0) 47 (52) 38313 (50828) 813150 0 (0) 0 (0) 0 (0) 52 (52) 112528 (126498) 619100 60 (60) 0 (0) 0 (1) 52 (52) 264014 (277905) 52880 18 (0) 42 (60) 1(1) 52 (52) 377615 (391199) 58150 0 (0) 60 (60) 3(3) 52 (52) 718028 (732087) 567


300 0 (0) 0 (0) 0 (0) 15 (52) 5405 (9363) 513200 11 (46) 0 (0) 0 (0) 52 (52) 135995 (143596) 37150 51 (0) 9 (60) 0 (1) 52 (52) 306595 (314171) 372100 0 (0) 60 (60) 2(3) 52 (52) 647695 (655322) 42780 0 (0) 60 (60) 4(5) 52 (52) 903595 (911178) 36750 0 (0) 60 (60) 11 (15) 52 (52) 1671615 (167876) 414


Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Riverside

high-speed lane



Nanjing(Ning)




Shanghai(Hu)




1015840



= 3 and Δ119862119890
















Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table5Re

schedu

lingresults

comparis

onon

different

reroutingstrategies

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

RS-1 120575

=1

5

1stsectio

n50

G157G159K1

13K

105K1

0335

200

5032176

825

1stand

2nd

sections

80G153G155G157G159K1

1314

410

48348491

677

50G153G155G157G159K1

130

550

4866

0888

675

All(1stndash

6th)

sections

100

G151G153G155G157G159

055

047

597105

489

80G153L9G

155G157G159

055

047

83007

488

50G153L9

G155G157G159

055

647

153370

3494

120575=

6

1stsectio

n50

G141-D

J507

G157G159K1

13K

105K1

0334

200

49316098

698

1stand

2nd

sections

80G141-D

J507

G153G155G157G159K1

1314

410

47342473

561

50G141-D

J507

G153G155G157G159K1

130

540

47649193

581

All(1stndash

6th)

sections

100

G141-D

J507

G151G153G155G157G159

054

046

586653

388

80G141-D

J507

G153L9G

155G157G159

054

046

815353

456

50G141-DJ507

G153L9

G155G157G159

054

646

1506

193

386

120575=

7

1stsectio

n50

DJ505-G

103G141-D

J507

G157G159K1

13K

115K1

0335

180

48309801

666

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G153G155G157G159K1

1313

400

46336255

555

50DJ505-G

103G141-D

J507

G153G155G157G159K1

130

530

46636615

527

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

053

045

575048

362

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

053

045

799483

366

50G141-DJ507

G151G153L9

G155G157

G159

053

545

1478983

355

120575=

8

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143

G157G159K1

09K

115K1

0135

170

47303726

677

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

1312

400

45330273

527

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

130

520

45625073

533

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G151G153G155G157G159

K113

052

045

564896

365

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151

052

044

785066

403

50DJ505

-G103G141-DJ507

G151G153L9

G155G157

G159

052

544

145032

355

120575=

9

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K

103

3417

046

298388

605

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

1113

380

45322795

436

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

050

510

45612898

475

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153G155G157G159

K113

051

044

555245

367

80DJ505-G

103G141-D

J507

G153L9G

155G157G159

G151K1

130

510

4477065

367

50DJ505

-G103G141-DJ507

G151

L9G

155G157G159

G149G153

051

443

142353

352


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

10

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

01K

115K1

03K1

1333

170

46292353

475

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109

1337

045

3164

76414

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

1110

500

45599668

439

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

130

500

43543483

284

80DJ505-G

103G141-D

J507

G151G159L9G

155G157

G153G149K1

130

500

43756233

289

50DJ505

-G103G141-DJ507

G149G151G153L9

G157

G155G159K113

050

343

1395

90

281

120575=

11

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111

3217

046

2866

5442

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

15K1

11K

109K1

1312

370

45310678

383

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

05K

111K1

130

490

4558769

394

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115

049

043

533231

325

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K113G

153G151

049

042

742316

339

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

G159G149K113

049

242

1369

19324

120575=

12

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

0931

170

4628076

419

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

01K1

11K

109K1

13K

115

1236

045

303618

386

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113

048

045

576336

364

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151L9G

155G157G159

G153K1

13K

115K

109

048

043

52248

288

80DJ505-G

103G141-D

J507

G145-G143

G149G155G159L9G

157

K101K

113G

153G151

048

042

726558

264

50DJ505

-G103G141-DJ507

G145-G143

G149G151G153L9

G157

K105K113G155G159

048

242

134138

253


Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table5Con

tinued

Rerouting

strategy

Restr

icted

section(s)

Speed

limitatio

n(kmh)

Mergedtrains

Detou

redtrains

Cancelledtrains

1205781

1205782

120582120574

Totald

elay

(m)

Calculation

time(s)

120575=

13

1stsectio

n50

DJ505-G

103G141-D

J507

G145-G143G129-G131

G157G159K1

05K

115K1

03K1

13K

111K1

09K

107

3116

046

274158

377

1stand

2nd

sections

80DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

11K

109K1

13K

115K1

0112

350

4529720

341

50DJ505-G

103G141-D

J507

G145-G143

G153G155G157G159K1

03K1

05K

109K1

11K

113K1

150

470

45564745

346

All(1stndash

6th)

sections

100

DJ505-G

103G141-D

J507

G145-G143

G151G153L9G

155G157

K115K

109K1

13K

101G159

047

043

510986

239

80DJ505-G

103G141-D

J507

G145-G143

G149G151L9G

157G159

K115K

101K1

13G

153G155

047

042

712041

319

50DJ505

-G103G141-DJ507

G145-G143

G151G153L9

G155G157

K115K105K113G149G159

039

239

1084

19295

RS-2

1stsectio

n50

mdashmdash

mdash0

10

10118

63

6547

1stand

2nd

sections

80mdash

mdashmdash

01

011

17403

1873

50mdash

mdashmdash

22

011

35273

6753

All(1stndash

6th)

sections

100

mdashmdash

mdash3

10

528061

1322

80mdash

mdashmdash

05

047

96373

1808

50mdash

mdashmdash

012

049

251274

56359





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Optimization Based High-Speed …downloads.hindawi.com › journals › ddns › 2014 › 934369.pdfResearch Article Optimization Based High-Speed Railway Train Rescheduling