This article was downloaded by: [Moskow State Univ Bibliote]On: 10 February 2014, At: 00:04Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Journal of Intelligent Transportation Systems:Technology, Planning, and OperationsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/gits20

A Dynamic Programming Approach for Optimal SignalPriority Control Upon Multiple High-Frequency BusRequestsWanjing Ma a , Yue Liu b & Xiaoguang Yang aa Key Laboratory of Road and Traffic Engineering of the Ministry of Education , TongjiUniversity , Shanghai , P.R. Chinab Department of Civil Engineering and Mechanics , University of Wisconsin at Milwaukee ,Milwaukee , Wisconsin , USAAccepted author version posted online: 24 Sep 2012.Published online: 22 Nov 2013.

To cite this article: Wanjing Ma , Yue Liu & Xiaoguang Yang (2013) A Dynamic Programming Approach for Optimal SignalPriority Control Upon Multiple High-Frequency Bus Requests, Journal of Intelligent Transportation Systems: Technology,Planning, and Operations, 17:4, 282-293, DOI: 10.1080/15472450.2012.729380

To link to this article: http://dx.doi.org/10.1080/15472450.2012.729380

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Journal of Intelligent Transportation Systems, 17(4):282–293, 2013Copyright C©© Taylor and Francis Group, LLCISSN: 1547-2450 print / 1547-2442 onlineDOI: 10.1080/15472450.2012.729380

A Dynamic Programming Approachfor Optimal Signal Priority ControlUpon Multiple High-FrequencyBus Requests

WANJING MA,1 YUE LIU,2and XIAOGUANG YANG1

1Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai, P.R. China2Department of Civil Engineering and Mechanics, University of Wisconsin at Milwaukee, Milwaukee, Wisconsin, USA

This article presents a priority signal control model for multiple bus requests. The proposed model aims to generate theoptimal priority serving sequence to maximize the utilization of available green times by buses, but not to incur excessivecongestion for other vehicular traffic. This study first depicts the serving sequence for multiple priority requests as amultistage decision process and explicitly models three bus priority strategies under the constraints of minimum green time,acceptable degree of saturation, and length of priority window. Further, it formulates a dynamic programming model tooptimize the serving sequence for multiple priority requests as well as the corresponding signal timing plans under variouslevels of bus occupancy, schedule deviation, and traffic demand. A rolling time horizon approach is employed to solve theproposed model in real time. Comparative analysis results have shown that the proposed dynamic programming modeloutperforms the first-come-first-serve policy in terms of reducing bus delays, improving schedule adherence, and minimizingthe impacts on other vehicular traffic. Computational performance analysis has further demonstrated the potential of theproposed model and algorithm to be applied in real-time bus priority control system.

Keywords Dynamic Programming; Multiple Priority Requests; Traffic Control; Transit Signal Priority

INTRODUCTION

Contending with traffic congestion has long been one ofthe pressing issues during the process of urbanization. An in-creasing number of researchers have recognized that providingreliable public transportation service is one of the most effectivestrategies to relieve traffic congestion. Compared with the con-siderable amount of time and resources invested by agenciesto improve transit infrastructure, transit signal priority (TSP)is one of the most promising and low-cost options. With TSP,buses can request the green phase of traffic signals to claim theright of way and proceed unimpeded through an intersection.

The research is funded by Program for Young Excellent Talents in TongjiUniversity. The research is also supported by a project of National NaturalScience Foundation of China (number 51178345).

Address correspondence to Yue Liu, Assistant Professor, Department ofCivil Engineering and Mechanics, University of Wisconsin at Milwaukee, Mil-waukee, Wisconsin, USA. E-mail: liu28@uwm.edu

Properly designed transit signal priority strategies will signif-icantly reduce the travel times and improve the reliability oftransit systems. Therefore, transit signal priority strategy hasbecome a key component in urban traffic control systems.

Since Wilbur Smith Associates and the Bureau of Traffic Re-search in the Los Angeles Department of Transportation firstconducted the bus preemption experiment and indicated the ef-fect of signal preemption in reducing bus travel times (WilburSmith and Associates, Westinghouse Airbrake Co., & Instituteof Public Administration, 1968), many studies have developedTSP strategies and documented their benefits of implementa-tion, including design of transit signal control logic for isolatedintersections (Balke, Urbanik, & Conrad et al., 2000; Chang &Vasudevan, 1996; Cima & Corby, 2000; Garrow & Machemehl,1998; Hunter, Kloos, & Daneher, 1995; Yagar & Han, 1994),evaluation and comparison of transit signal priority strategiesusing simulation or field experiments (Banerjee, 2001; Duerr,2000; Furth & Muller, 2000; Janos & Furth, 2001; Nash &Sylvia, 2001), optimization of transit signal priority strategies

282

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 283

for coordinated signalized arterials (Duerr, 2000; Lee, Abdul-hai, Shalaby, & Chung, Liu & Chang, 2011; Ma, Yang, & Liu,2010; Meenakshy, 2005; Mirchandani & Lucas, 2004; Yao et al.,2009), and conditional priority strategies that provide preemp-tion only to buses behind schedule (Ghanim, Dion, & Abu-Lebdeh, 2009; Lin, 2002; Ngan, Sayed, & Abdelfatah,2004).In summary, TSP strategies developed in those studies can beclassified into three categories: passive priority strategy, ac-tive priority strategy, and real-time priority strategy (Baker &Dale, 2003). Passive priority operates continuously regardlessof whether transit is present or not and does not require a tran-sit detection/priority request generation system (Skabardonis,2001; Yagar, 1993), Active priority strategies provide prior-ity treatment to a specific transit vehicle following detection,or a priority request by the vehicle/system (Furth & Muller,2000; Garrow & Machemehl, 1998; Ngan et al., 2004; Ya-gar & Han, 1994). Adaptive/real-time TSP strategies providepriority while simultaneously trying to optimize given perfor-mance criteria. The criteria may include person delay, tran-sit delay, vehicle delay, and/or a combination of these criteria(Balke et al., 2000; Chang & Vasudevan, 1996; Ma et al., 2010;Meenakshy, 2005).

Despite the promising progress in previous studies, insuffi-cient research has been done to design priority signals in re-sponse to multiple high-frequency bus requests from conflictingmovements at an intersection, which is very common in cities ofdeveloping countries (e.g., China). With the increasing invest-ment in transit systems in those cities (e.g., promotion of theBus Rapid Transit systems, development of more transit lines,construction of exclusive bus lanes, etc.), the transit networkhas become more complex, consisting of different levels of buslines, and the service frequency of buses has been significantlyincreased. It is quite normal for an intersection to have more thanone bus arriving at one or more approaches in a signal cycle.Furthermore, each bus priority request has its own characteris-tics, resulting in the variation of signal priority efficiency withdifferent serving sequences. For example, providing priority fora bus with high occupancy and a larger schedule deviation maybe better than doing that for a bus with fewer passengers.

In a review of the literature, most previous studies have em-ployed the first-come-first-serve (FCFS) policy to schedule mul-tiple priority requests or assumed that buses are only presenton the major roads and in peak directions (Meenakshy, 2005).However, for intersections with a high bus demand in conflict-ing movements, transit priority strategies become even morecomplicated because they need to determine not only the typeof priority over the automobile traffic, but also the priority ofeach conflicting transit movement (Skabardonis, 2001). In a re-cent study, Head, Gettman, and Wei (2006) have modeled thetraditional core ring, barrier, and phase logic as a precedencegraph, and have shown that the first-come-first-serve policy forserving priority requests may result in extra delays. However,most of those studies have focused on optimizing one cycle withlimited priority requests and do not capture the real-world op-

erational characteristics of multiple bus requests in detail, suchas schedule deviation, bus occupancy, delay at cross streets,and so on. Most importantly, the impact of the serving se-quence on the other vehicular traffic has not been discussedand the methodology to provide priority in consecutive cyclesfor sequential bus requests has not been sufficiently addressedeither.

To effectively address the above critical research issues, thisstudy will:

1. Design a new transit signal priority control framework thatcan provide efficient bus priority control for multiple busrequests.

2. Formulate a dynamic programming model to yield theoptimal serving sequence and corresponding signal tim-ings for multiple bus priority requests with various occu-pancy and schedule deviations under different traffic demandlevels.

3. Apply a rolling horizon scheme to solve the proposed modelin real time.

4. Demonstrate the effectiveness of the proposed model withan illustrative case study, and perform sensitivity analyses ofcritical affecting factors on model performance.

THE CONTROL FRAMEWORK

The proposed control framework aims to provide efficientpriority control for multiple bus requests, as well as to minimizethe overall negative impacts on the control system. It consists oftwo critical modules: minimization of system disturbance andoptimization of the serving sequence. The interrelation amongthe two modules as well as their principal components is illus-trated in Figure 1 (the focus of this article is highlighted withgray color).

System Disturbance Minimization

Less or improper consideration of other vehicular traffic is theprimary reason accounting for failure or discontinuity of manyearly TSP programs (Hunter, 2000). To deal with this problem,this study has proposed the system disturbance minimizationmodule to maintain an acceptable level of saturation degree (ornegative impact) for each vehicular movement. Under such aconstraint, transit signal priority will not result in oversaturatedmovements at the signalized intersection. This module assignsthe required minimum green time to a traffic movement basedon its volume and the threshold value of saturation degree. Thethreshold values of saturation degree could be fixed values givenby system operators or dynamically determined by the urbantraffic control system.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

284 W. MA ET AL.

Figure 1 The proposed control framework.

Serving Sequence Optimization

With the constraints from the system disturbance minimiza-tion module as the input, a dynamic programming model isproposed to generate the optimal signal timings and serving se-quence for a set of bus priority requests in a cycle. Realizing theimportance of improving the transit system reliability rather thanjust reducing bus delays at intersections, the proposed modelminimizes the weighted bus delays at the intersection consider-ing both bus occupancy and schedule deviation. The proposedmodel is further integrated with a rolling horizon approach forreal-time operation.

It should be noted that the framework assumes the availabil-ity of an optimal signal plan for the general traffic demand ineach cycle and threshold values of the saturation degree. Suchparameters could be fixed or time dependent.

A DYNAMIC PROGRAMMING APPROACH

Notation

To facilitate the model presentation, key notations and pa-rameters used hereafter are summarized in Table 1.

Serving Bus Priority Requests—A Multistage DecisionProcess

Usually the signal optimizer provides priority to a bus requestat either the end of the previous phase green time or the startof next phase green time. Based on this operational feature,we model the serving sequence optimization as a multiple-stagedecision problem. As dynamic programming (DP) is one of mostefficient methods for solving multiple-stage decision problems,in this study we formulate a dynamic programming model tosolve for the optimal serving sequence for a set of bus priorityrequests. Figure 2 depicts the stages (s1, s2, s3, and s4) of theDP model in an example cycle with four phases. Each decisionstage is associated with a signal phase. For a given cycle, there isa maximum available amount of time (i.e., the priority windowshown in Figure 3) for providing priority between two stagesconstrained by the background signal plan and the minimumrequired green times.

Furthermore, a priority request can be served by differentstrategies: green extension, red truncation, and phase insertion.Figure 3 illustrates an example of a bus priority requested atstage 1 being served by three different strategies at differentstages.

State Transfer Functions

All related signal parameters should be updated in case apriority request is selected at a stage, including a priority strat-egy implemented in the stage, ending time of the green signal,starting time of the next stage, priority window of the next stage,and priority status of all requests.

Update Required Minimum Green Time of Phase i

The degree of saturation for critical movement in phase i ofcycle k is given by:

xi,k = Ckqi,k/

Qi gi,k(1)

In Eq. 1, traffic volume can be obtained from loop detectors orother kinds of detection in the real-world implementation.

Given the maximum acceptable limit of saturation degree(xmax

i ), one can update the minimum required green time with:

gRi,k = Ckqi,k

/xmax

i Qi(2)

Update Priority Strategies

The actual priority strategy used in the stage i can be updatedwith the following equation:

P Si,k =⎧⎨⎩

1 bpm = i

−1 bpm = i + 1

0 bpm �= i and bp

m �= i + 1∀um

i,k = 1 (3)

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 285

Table 1 Notation and parameters.

Sets, parameters, and variablesPk Set of signal phases in cycle kNp Number of signal phasesi, j Index of phases or stages, i = i, 2, . . . . . . Np, j = i, 2, . . . . . . Np

m, n Index of each bus priority requestsk Index of cycleBk Set of bus priority requests in cycle kN k

b Number of priority requests received at cycle kB N

i,k Set of bus priority requests that are not served before the start of phase i in cycle kBS

i,k Set of bus priority requests served at phase i in cycle kCk Length of cycle k (s)Qi Saturation flow rate of phase iqi,k Traffic volume of critical movement (with maximum flow ratio in phase i) phase i in cycle k

(vehicles)xi,k Saturation degree of phase i in cycle kxmax

i Threshold value of saturation degree of phase iIi, j Inter-green time from phase i to phase j (s)gi,k Length of green time of phase i in cycle k (s)gR

i,k Required minimum green time of phase i in cycle k (s)gi,min Minimum green time of phase i (s)gi,max Maximum green time of phase i (s)W S

i,k Starting time of priority window at phase i in cycle k (s)W S

i,k = gSi,k + gR

i,kW E

i,k Ending time of priority window at phase i in cycle k (s)W E

i,k = gEi+1,k − gR

i+1,kbt

m,k Arrival time of bus priority requests m; it was represented by the cycle operating time whenthe bus arriving at stop line (s)

bsdm,k Schedule deviation of bus priority request bm (s)

bpm The phase number for request m

bnumm,k Number of passengers of bus priority request m

tin Length of green time insertion in bus phase (s)dm,k Delay of bus request m passing intersection in cycle k (s)d0

m,k Delay of bus request m without passing intersection in cycle k (s)bSm

i,k A binary variable to indicate the status of request m of phase i in cycle k;

bSmi,k =

{1 i f the priori t y request isserved0 else

Decision VariablesgS

i,k Starting time of phase i in cycle k (s)gE

i,k Ending time of phase i in cycle k (s)P Si,k An decision variable determining the priority strategy selected at phase i in cycle k

P Si,k =⎧⎨⎩

1 greenextension−1 redtruncation0 phaseinsertion

umi,k A binary decision variable of strategy selected at phase i in cycle k for request m;

umi,k =

{1 provide priori t y f or request mat phasei0 else

Legend

Green timeIntergreen time

phase 1 phase 2 phase 3 phase 4

s s

s

s

Nkg ,1 kg ,2

W W

mimg ,1 mimg ,2

kg ,3 kg ,3 4,3I

Figure 2 Parameters used in the model.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

286 W. MA ET AL.

Original

Truncation Time

Priority Window2

Insert Time2

Insert Time1

Priority Window1

Red Truncation

Phase Insertion

Green Extension

Bus Arrival Time

phase1 phase2 phase3 phase4

Legend

Green timeIntergreen time

Figure 3 Bus priority control strategies.

where P Si,k = 1 indicates that the green extension strategy isselected for request m in phase i; P Si,k = −1 means the redtruncation strategy is selected for request m in phase i +1; andP Si,k = 0 means the phase insertion strategy is selected forrequest m in neither phase i nor phase i + 1.

Determine Stage Green Ending Time

The actual ending time of the stage i green signal dependson the selected priority strategy, the arriving time of the priorityrequest served in the related priority window, the starting andending time of the priority window, and the inter-green time(amber and all-red), given by:

gEi,k=

⎧⎨⎩

btm P Si,k = 1

max[(

btm − Ii,i+1

), W S

i,k

]P Si,k = −1

gE∗i,k P Si,k = 0

,∀umi,k=1 (4)

As shown in Eq. 4, the ending time of stage i should be equal tothe arrival time of the bus priority request m if the green exten-sion strategy is selected; if the red truncation strategy is selected,the ending time should be the maximum value of the startingtime of the priority window at stage i and the difference betweenthe arrival time of the corresponding requests and the inter-greentime; otherwise, if the phase insertion strategy is selected, theending time of stage i is equal to gE∗

i,k , which is determined by

the location of the insertion phase for the priority request in thepriority window given by Eq. 5. In order to offset the travel timeuncertainty, the arriving time of the priority request should beplaced at the center of the insertion phase if possible or at leastcovered by the insertion phase. The inter-green time should alsobe considered.

gE∗i,k =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

W Si,k bt

m ≤ W Si,k + tin+Ii,b

pm

+Ibpm, i+1

2

btm − tin+Ii,b

pm

+Ibpm ,i+1

2 W Si,k + tin+Ii,b

pm

+Ibpm ,i+1

2 < btm

≤ W Ei,k − tin+Ii,b

pm

+Ibpm ,i+1

2

W Ei,k − (

tin + Ii,bpm

+ Ibpm ,i+1

)W E

i,k − tin+Ii,bpm

+Ibpm ,i+1

2 < btm

≤ W Ei,k − Ibp

m ,i+1

(5)

In Eq. 5, gE∗i,k will be equal to the starting time of the priority

window of stage i (W Si,k) if the arrival time of the served request

is earlier than the starting time of the priority window plus halfof the total insertion time (green time and inter-green time); ifthe total insertion time can be covered by the priority window,then gE∗

i,k will be the arrival time of the served request minus

half of the total insertion time (btm − tin+Ii,b

pm

+Ibpm ,i+1

2 ); and if thearrival time of the served request is later than the ending timeof the priority window subtracted by half of the total insertiontime, gE∗

i,k will be the ending time of the priority window minusthe total insertion time (W E

i,k − (tin + Ii,bpm

+ Ibpm ,i+1)).

Update Starting Time of the Next Green Timeand Priority Window

The starting time of the green signal at stage i + 1 can beupdated by the following equation based on the ending time of

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 287

the previous stage and the priority strategy used:

gSi+1,k =

{gE

i,k + Ii,i+1 P Si,k = ±1gE

i,k + tin + Ii,bpm

+ Ibpm ,i+1 P Si,k = 0

(6)

As shown in Figure 3, the length of the priority window is gov-erned by the earliest ending time of the previous phase and thelatest starting time of the next phase. Priority requests arrivingat the stop line before the ending time of the priority windowcan be served.

Given gSi+1,k from Eq. 6, the starting time of the next priority

window can be updated with:

W Si+1,k = gS

i+1,k + gRi+1,k (7)

Update Green Time

The green time of phase i can then be updated by the follow-ing equation based on the updated ending time of phase i fromEq. 4:

gi,k = gEi,k − gS

i,k (8)

Update Priority Request Status

One can update the status of priority requests with Eq. 9.Note that buses requesting the same stage and arriving in thesame priority window, or arriving at the normal green time ofstage i, will receive priority at the same time.

bSmi,k =

{bSm∗

i,k umi,k = 0

1 m = n and uni,k = 1

∀m ∈ B Ni,k (9)

In Eq. 9, bSmi,k = 1means the priority status should be changed

to 1 if the request is selected to be served in stage i (m =n and un

i,k = 1); bSm∗i,k is a binary variable indicating the status

of the bus request that is not selected to be served in stagei, which is determined by the requesting phase number (bp

m),the arriving time of the request (bt

m), and the priority strategies(P Si,k) used in stage i, given by:

bsm∗i,k =

⎧⎨⎩

1(bp

m = i and btm ≤ gE

i,k

)or

0

(bp

m = bpn and un

i,k = 1 and bsm∗∗i,k

else

)(10)

In Eq. 10, bSm∗i,k should be set to 1 if it requests to be served

in phase i and arrives before the ending time of phase i, or itrequests to be served in the same phase with the selected requestn and arrives in the corresponding priority window.

Here, bSm∗∗i,k indicates whether the priority status of request

m can be set to 1 if request n is selected in stage i (uni,k = 1) with

both of them requesting the same phase (bpm = bp

n ), and can becalculated with:

bSm∗∗i,k =

⎧⎨⎩

btm ≤ bt

n P Si,k = 1bt

m ≤ gSi+1,k P Si,k = −1

gEi,k ≤ bt

m ≤ gSi+1,k P Si,k = 0

(11)

In Eqs. 10 and 11, bSm∗∗i,k = (bt

m ≤ btn)means the priority status

of request m should be changed to 1 (bSm∗i,k = 1) if the arrival of

request m is earlier than that of request n (request n is selected toprovide priority) when the green extension strategy is used underthe situation of bp

m = bpn and un

i,k = 1; bSm∗∗i,k = (bt

m ≤ gSi+1,k)

means the priority status of request m should be changed to1 (bSm∗

i,k = 1) if the arrival of request m is earlier than thestarting time of the next phase when the red truncation strategyis used under the situation of bp

m = bpn and un

i,k = 1; andbSm∗∗

i,k = (gEi,k ≤ bt

m ≤ gSi+1,k) means the priority status of

request m should be changed to 1 (bSm∗i,k = 1) if the arrival

time of request m is between the ending time of phase i and thestarting time of the next phase when the phase insertion strategyis used under the situation of bp

m = bpn and un

i,k = 1.

The Control Model

In order to explicitly consider the occupancy and scheduleadherence of buses in the optimization process, this study hasadopted the control objective of minimizing the total weightedbus delay (by the number of passengers and the schedule devi-ation) in the proposed DP model. The objective consists of twocomponents: total delay for served priority requests and totaldelay for nonserved priority requests.

Total Delay for Served Priority Requests

We denote fk(i) as the total delay for bus priority requestsserved from stage i (including stage i) to the last stage, a recur-sive formulation for fk(i) is given by:

fk(i) = di,k + fk(i + 1) (12)

where di,k is the total weighted delay of priority requests servedin stage i in cycle k, and can be calculated with:

di,k =∑

bnumm,k ∗ di

m,k ∗ bsdm,k ∀m ∈ BS

i,k (13)

In Eq. 13, bnumm,k represents the number of passengers on the

bus priority sending request m and bsdm,k represents the schedule

deviation of the bus sending priority request m. Informationabout bnum

m,k and bsdm,k is assumed to be obtainable from the bus

operation system via the radiofrequency identification (RFID)and the automatic passenger count technology; di

m,k representsthe delay for request m and can be determined according to therequest arriving time and the priority strategy, given by:

dim,k =

⎧⎨⎩

0 bpm,k = i

gSi+1,k − bt

m,k bpm,k = i + 1

max (0, gEi,k − bt

m,k) else(14)

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

288 W. MA ET AL.

Total Delay for Nonserved Priority Requests

Buses sending priority requests that are not served in thecurrent cycle will proceed during normal green times of therequesting phase in the next cycle (k + 1). Then the total delay,denoted as fk (0), can be calculated with:

fk (0) =∑

bnumn,k ∗ d0

n,k ∗ bsdn,k (15)

where bnumn,k represents the number of passengers on the bus send-

ing the priority request n; bsdn,k represents the schedule deviation

of the bus sending the priority request n; and d0n,k represents

the delay for request n that is not served in cycle k and can becalculated with:

d0n,k = ck − bt

n +bp

n∑i=1

(gi,k+1 + Ii,i+1) ∀n ∈ B NN k

b ,k ∩ BSN k

b ,k(16)

In Eq. 16, ck − btn represents the delay of request n arriving but

not served in cycle k (∀n ∈ B NN k

b ,k∩ BS

N kb ,k

);bp

n∑i=1

(gi,k+1 + Ii,i+1)

represents the delay of requests in cycle k+ 1 before they canbe served in the normal green time of the requesting phase.

The Objective Function

Given the cycle k of analysis, Eq. 17 represents the objectiveof the control model to minimize the total weighted delay of allbus priority requests:

min fk (1) + fk (0) (17)

Constraints

Equations 2–11, representing the state transfer functions, arethe principal constraints for the control model. Moreover, thefollowing are the constraints for limiting the impact of the transitsignal priority on other vehicular traffic and common restrictionsfor the signal control parameters:∑

m∈BSi,k

umi,k ≤ 1 (18)

gRi,k ≤ gi,k ≤ gi,max (19)

gi min ≤ gRi,k ≤ gi,k (20)

Equation 18 requires that only one priority treatment can beimplemented at each phase; Eq. 19 requires that the green timefor each phase should satisfy the required minimum green time,but not exceed the maximum green time; and Eq. 20 requiresthat the required minimum green time for each phase shouldsatisfy the minimum green time, but not exceed the backgroundgreen time for providing priority for buses.

A ROLLING HORIZON APPROACH FOR REAL-TIMEOPERATION

The proposed control model is based on the bus arrivals in aforegone cycle. However, such information is usually unknownat the beginning of a cycle and bus priority requests are alsounpredictable. In order to take into account the latest bus ar-rival and vehicular demand information, this study has appliedthe following rolling horizon scheme to facilitate the proposedmodel to operate in real time:

1. The horizon length is set to be the cycle length.2. The optimal service sequence and signal control plans are op-

timized over successive cycles, but implemented only withina phase in that cycle.

3. Once the plan is implemented, the state of bus priority re-quests and traffic demand information within the system areupdated using real-time measurements, and the optimizationprocess starts all over again for the next cycle with the controlhorizon shifted forward by one phase.

As shown in Figure 4, the optimal serving sequence for cy-cle k (consists of phases g1,k ,g2,k . . .gNp,k) is optimized basedon the detected bus priority requests (priority request set Bk)and vehicular demand information, but is only implemented forthe first phase (g1,k). Then the priority request set (Bk+1) is up-dated with requests that have not been served in cycle k plusthe new requests arriving in g1,k , and the optimization processstarts all over again for a new cycle k + 1 (consisting phasesg2,k ,g3,k . . .gNp,k, gi,k+1). The optimization process will continueuntil the end of the control period.

cycle k (g1,k+g2,k+g3,k+g4,k)

cycle k+1 (g2,k+g3,k+g4 ,k+g1,k+1)

cycle k+2 (g3,k+g4,k+g1 ,k+1+g2,k+1)

Horizon k:

Horizon k+1:

Horizon k+2:

Figure 4 The rolling horizon scheme.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 289

BRTBRT

B2 B3B12

B11

Phase I Phase II Phase III

BRT

BR

TB

RT

BRT

BRT

N

Huaide Road

Qinye Road

Figure 5 Layout of the study intersection (color figure available).

CASE STUDY

Experiment Design

To illustrate the applicability and efficiency of the proposedmodel, this study has selected a signalized intersection at HuaideRoad, a major Bus Rapid Transit (BRT) corridor of Changzhoucity in China, for the case study. Figure 5 shows the layout ofthe intersection that has exclusive bus lanes in operation at allapproaches.

This study has employed VISSIM, a widely used micro-scopic simulation package, to evaluate the model performanceas its component object model interface (i.e., VISSIM-COM,an external module that enables communication and dynamicobject creation between the simulation environment and exter-nal processes), which has been successfully used in the liter-ature to evaluate the transit signal priority operation (Ghanimet al., 2009). A flowchart for integrating the proposed optimiza-tion process and the simulation environment is developed and

Start VISSIM-COM Save Simulated Traffic ConditionsSave Signal Control TimingsSave Transit Related Data

Call DP Model For Serve SequenceOptimization andReturn Signal Plan

Save New Signal TimingParameters

Continue with thesimulation

Call VISSIM Simulation

For k=1, i=1, Simulation

Y

N

start

Time to Call DP?

Environment

Interface

Figure 6 Flow chart of simulation evaluation using VISSIM (color figureavailable).

shown in Figure 6. Each simulation runs 2 h, and to overcomethe stochastic nature of the microscopic simulation system, anaverage of 20 simulation runs has been used.

Three traffic demand levels (70%, 100%, and 130% of thebase volumes in Table 2) are designed in the simulation testcorresponding to the volume-to-capacity ratios at 0.5, 0.7, and0.9. The operation of three transit routes is simulated to evaluatethe proposed model’s efficiency in handling multiple bus priorityrequests at intersections.

Key parameters in the simulation test are given as:

1. The mean headway is 2 min for each bus route.2. A bus stop is set at upstream of each intersection approach

with a normal distribution for the bus dwelling time (mean= 40 s, standard deviation = 40 s).

3. The bus occupancy and schedule deviation are simulated bytwo normal distributions, one with a mean of 30 s and astandard deviation of 120 s, and the other with a mean of 30passengers and a standard deviation of 30 passengers.

4. Bus and vehicle detectors have been installed 100 m beforethe stop line at each exclusive bus lane.

The proposed model will then be evaluated through the fol-lowing steps:

Table 2 Basic traffic volumes for simulation.

Approach Direction Vehicle type Volume (veh/h)

SB Left Car 138Through Car 1242

Bus 12EB Left Car 846

Bus 28Right Car 258

NB Through Car 1170Bus 18

Right Car 1098

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

290 W. MA ET AL.

0

10

20

30

40

50

60

70

80

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Pro

bab

ility

(%)

Time consuming (ms)

Number of Request =1Number of Request =2Number of Request =3Number of Request =4

Figure 7 Time consuming of the dynamic programming model (color figureavailable).

Step 1. Evaluate the computing efficiency of the proposed modelunder various scenarios of bus priority requests.

Step 2. Compare the model performance with the following twocontrol strategies. (To ensure a fair comparison, we generatethe background signal timing plans for all control strategiesusing the same optimization scheme.)

Control a: Fixed-time control without TSP: implement fixedsignal timing plans optimized offline without transit signal pri-ority; and

Control b: FCFS TSP: control with the normal first-come-first-service (FCFS) active TSP treatments offering red trunca-tion, green extensions, and phase insertion.

Step 1: Computing Efficiency of the Proposed Model

Figure 7 shows the distribution of computing times of the pro-posed model under different scenarios of bus priority requests. Itcan be observed that the proposed model is computation friendlyas it only takes less than 35 ms for the model to run the worstscenario with 4 bus priority requests (successive buses). Sucha property enables the proposed model to be applicable in areal-time traffic control system.

Step 2: Comparative Analysis of Model Performance

Delay Reduction for Buses and Other Vehicular Traffic

Table 3 summarizes the comparison results between the pro-posed model and other two control strategies under differentscenarios. The following findings can be reached:

1. The proposed model can outperform control strategies (a)and (b) under all demand scenarios in terms of reductionin bus delays (10–30% over control (a), and 7–23% over

Table 3 Comparison results of model performance.

Average delay (s/veh)

Intersection Traffic Control Control Proposed Improvement over control Improvement over controlapproaches demand (v/c) (a) (b) model (a) (%) (p value)∗ (b) (%) (p value)∗

SB bus 0.5 19.8 17.8 13.8 30.3 (0.00) 22.7 (0.00)SB other 44.6 47.9 48.1 −7.8 (0.00) −0.4 (0.013)NB bus 18.2 15.6 12.1 33.8 (0.00) 22.8 (0.00)NB other 46.8 50.6 48.7 −4.2 (0.05) 3.8 (0.00)WB bus 23.1 22.8 17.4 24.4 (0.00) 23.5 (0.00)WB other 45.6 48 46.5 −1.9 (0.11) 3.1 (0.01)Bus average 20.4 18.7 14.4 29.1 (0.00) 23.0 (0.00)Other average 45.7 48.8 47.8 −4.6 (0.00) 2.2 (0.00)SB bus 0.7 23.3 21 18.7 20.0 (0.00) 11.1 (0.00)SB other 48 51.8 53.2 −10.9 (0.00) −2.6 (0.04)NB bus 23.1 21.1 17.6 23.8 (0.00) 15.9 (0.00)NB other 52 54.5 50.1 3.7 (0.05) 8.0 (0.00)WB bus 25.7 24.9 20.2 21.4 (0.00) 18.8 (0.00)WB other 50 53.2 53.3 −6.0 (0.00) 0.3 (0.13)Bus average 24.0 22.3 18.8 21.6 (0.00) 15.6 (0.00)Other average 50.0 53.2 52.2 −4.4 (0.00) 1.9 (0.09)SB bus 0.9 25.1 22.7 21.3 15.0 (0.00) 6.0 (0.00)SB other 51.5 54.1 56.7 −10.1 (0.00) −4.9 (0.00)NB bus 26.1 24 21.6 17.3 (0.00) 10.0 (0.00)NB other 58.3 60.6 57.2 1.9 (0.03) 5.5 (0.00)WB bus 27.6 25.7 23.8 13.6 (0.00) 7.3 (0.00)WB other 55.5 59.2 61.5 −10.8 (0.00) −3.9 (0.05)Bus average 26.3 24.1 22.2 15.4 (0.00) 7.9 (0.00)Other average 55.1 58.0 57.5 −4.3 (0.00) 0.8 (0.10)

Note. NB, northbound; SB, southbound; WB, westbound.∗Statistically significant at the 95% confidence level.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 291

control (b)). The improvements are statistically significantat the 95% confidence level as indicated by the paired t-testresults (p values < 0.05). The overall intersection averagebus delay can be reduced by more than 15% over control (a),and 7.9% over control (b). The results clearly demonstratethe efficiency of the proposed model to handle multiple buspriority requests.

2. Control plans generated by the proposed model will not incura large increase of delay for other vehicular traffic at the inter-section. More specifically, the proposed model under low andmedium traffic situations can reduce delay of other vehiculartraffic; for a congested situation, increase in traffic delaysfor other vehicular traffic is less than 11% compared with afixed-time control, and 5% compared with the FCFS policy.

Reduction in Bus Schedule Deviation

This study also investigates the performance of the proposedmodel in reducing bus schedule deviation. Two performance in-dices, average bus schedule deviation and weighted bus scheduledeviation (weighted by number of passengers on every bus), are

Figure 8 Reduction in bus schedule deviation (color figure available).

a: average bus delay

b: average vehicular traffic delay

-10

-5

0

5

10

15

20

25

x=1 x=0.97 x=0.95 x=0.93 x=0.91

Red

ucti

on c

ompa

red

wit

h F

CF

S (%

)

v/c=0.5 v/c=0.7 v/c=0.9

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

x=1 x=0.97 x=0.95 x=0.93 x=0.91

Incr

ease

com

par

ed w

ith

FC

FS

(%)

v/c=0.5 v/c=0.7 v/c=0.9

Figure 9 Impacts of x on bus delay and vehicle delay compared with FCFS(color figure available).

used for evaluation. As shown in Figure 8a, control with the pro-posed model yields much lower average bus schedule deviationthan the other two control strategies for all demand scenarios(30–70% reduction compared with control (a), and 21–43%compared with control (b)). Also indicated in Figure 8b is theeven more significant reduction in weighted average bus sched-ule deviation with the proposed model. Such findings demon-strate the effectiveness of the proposed model in improving thebus schedule adherence.

Impact of the Maximum Allowable Degree of Saturation

To assist traffic engineers in best applying the proposedmodel under different traffic demand situations, this sectionhas further investigated the impacts of the maximum allowablesaturation degree (denoted as x) on the control efficiency.

Figure 9a shows the reduction of bus delay by the proposedmodel compared with the FCFS control under various demandscenarios and different values of x. It can be observed that withthe decrease of x, bus delay by the proposed model will decrease.When the traffic demand is high (larger v/c ratio), a lower valueof x may even cause the proposed model to yield higher bus

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

292 W. MA ET AL.

delay than the FCFS control (negative part in Figure 9a). That isbecause the higher the x, the shorter is the priority window usedfor providing priority in the proposed model. In contrast, thedecrease of x will make the proposed model generate a lowerdelay for other vehicular traffic, as shown in Figure 9b. Suchfindings indicate that there is a threshold value of x for eachscenario at which the proposed model can yield acceptable busdelay savings without incurring excessive congestion for othervehicular traffic. Traffic engineers need to carefully select thevalue of x to balance the operational efficiency between thebuses and other vehicular traffic.

CONCLUSIONS AND RECOMMENDATIONS

This article presents a bus priority signal control model formultiple bus requests. The proposed model aims to maximize theuse of available green times by buses, but not to incur excessivecongestion for other traffic. The proposed model is capable ofcapturing the critical operational characteristics such as impactof bus requests with various occupancy and schedule deviations,different traffic demand levels, and various priority strategies.The model produces detailed output information including theoptimal serving sequence of multiple bus priority requests andthe corresponding signal timings. A rolling time horizon ap-proach is employed to solve the proposed model with real-timeinformation as input.

Performance evaluation of the proposed model using VIS-SIM shows that it can reduce bus delays and improve transitschedule adherence compared with the fixed-time and FCFScontrol without significantly increasing the delay for other ve-hicular traffic. The results further show that the proposed modelis able to effectively serve multiple priority requests and bal-ances the operational efficiency between the buses and othervehicular traffic if the critical degree of saturation is properly se-lected. Computational performance analysis has further demon-strated the potential of the proposed model and algorithm to beapplied in real-time bus priority control system.

Note that this article has presented preliminary evaluationresults for the proposed model. More extensive experiments orfield tests will be conducted to assess the effectiveness of theproposed model under various vehicular demand patterns, busvolume levels, location of bus stops, geometry configurationsof intersections, and the type of traffic control (actuated or co-ordinated control). The selection of the maximum allowablesaturation degree also deserves to be studied further. Moreover,the effectiveness of the proposed model could be further im-proved if a bus delay model was incorporated that can considerthe impacts of existing queues in front of the buses.

REFERENCES

Balke, K., Urbanik, D., & Conrad, L. (2000). Development and eval-uation of intelligent bus priority concept. Transportation ResearchRecord, 1727, 12–19.

Banerjee, F. (2001). Transit priority system evaluation report. LosAngeles, CA: City of Los Angeles Department of Transportation.

Baker, R. J., & Dale, J. J. (2003). An overview of transit signal priority.Washington, DC: ITS America.

Chang, G.L., & Vasudevan, M. (1996). Modeling and evaluationof adaptive bus preemption control with and without automaticvehicle location systems. Transportation Research, 30A(4), 251–268.

Cima, B., & Corby, M. (2000). Transit signal priority: A comparison ofrecent and future implementations. Paper presented at ITE AnnualMeeting, Nashville, TN.

Duerr, P. (2000). Dynamic right-of-way for transit vehicles: Integratedmodeling approach for optimizing signal control on mixed trafficarterials. Transportation Research Record, 1731, 31–39.

Furth, P., & Muller, T. (2000). Conditional bus priority at signalizedintersections: Better service with less traffic disruption, Transporta-tion Research Record, 1731, 23–30.

Garrow, M., & Machemehl, R. (1998). Development and evaluation oftransit signal priority strategies. Austin, TX: Center for Transporta-tion Research, University of Texas, Austin.

Ghanim, M., F., & G. (2009). Integration of signal control and transitsignal priority optimization in coordinated network using geneticalgorithms and artificial neural networks. Paper presented at TRBAnnual Meeting, National Research Council, Washington, DC.

.L., Gettman, D., & Wei, Z. (2006).Hunter, C. (2000). Guidelines for the successful implementation of

transit signal priority on arterials. Washington, DC: University ofWashington.

Hunter, K., Kloos, W., & Danaher, A. (1995). Bus priority at traffic sig-nals in Portland: The Powell Boulevard pilot project, TransportationResearch Record, 1503, 29–33.

Janos, M., & Furth, P. (2001). Bus priority with highly interruptibletraffic signal control: Simulation of San Juan’s Avenida Ponce deLeon. Transportation Research Record, 1811, 157–165.

Lee, J., Abdulhai, B., Shalaby, A., & Chung, E. H. (2005). Real-time optimization for adaptive traffic signal control using geneticalgorithms. Journal of Intelligent Transportation Systems, 9(3),111–122.

Lin, W. (2002). Quantifying delay reduction to buses with signal pri-ority treatment in mixed-mode operations. Transportation ResearchRecord, 1811, 100–106.

Liu, Y., & Chang, G. L. (2011). An arterial signal optimization modelfor intersections experiencing queue spillback and lane blockage.Transportation Research, Part C, 19(1), 130–144.

Ma, W., Yang, X. G., & Liu Y. (2010). Development and evaluationof coordinated and conditional bus signal priority approach. Trans-portation Research Record, 2145, 49–58.

Meenakshy, V. (2005). Robust optimization model for bus priority un-der arterial progression. PhD dissertation, University of Maryland,Washington, DC.

Mirchandani, P. B., & Lucas, D. E. (2004). Integrated transit pri-ority and rail/emergency preemption in real-time traffic adaptivesignal control. Journal of Intelligent Transportation Systems, 8(2),101–115.

Nash A., & Sylvia, R. (2001). Implementation of Zurhich’s transitpriority program. San Jose, CA: Mineta Transportation Institute,College of Business, San Jose State University.

Ngan, V., Sayed, T., & Abdelfatah, A. (2004). Impacts of various trafficparameters on transit signal priority effectiveness. Journal of PublicTransportation, 7(3), 71–93.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014

OPTIMAL SIGNAL PRIORITY CONTROL 293

Skabardonis, A. (2000). Control strategies for transit priority. Trans-portation Research Record, 1727, 20–26.

Wilbur Smith and Associates, Westinghouse Airbrake Co., & Instituteof Public Administration. (1968). Study of evolutionary urban trans-portation, Vols. I, II, and III. Washington, DC: U.S. Department ofHousing and Urban Development.

Yagar, S. (1993). Efficient transit priority at intersections. Transporta-tion Research Record, 1390, 10–15.

Yagar, S., & Han, B. (1994). A procedure for real-time signal controlthat considers transit interference. Transportation Research, 28B(4),315–331.

Yao, D., Su, Y., Zhang, Y., Li, L., Cheng, S., & Wei, Z. (2009). Controlstrategies for transit priority based on queue modeling and surro-gate testing. Journal of Intelligent Transportation Systems, 13(3),142–148.

intelligent transportation systems vol. 17 no. 4 2013

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

00:

04 1

0 Fe

brua

ry 2

014