Investigation on Two-Stop-Line Signalized Roundabout ...downloads.hindawi.com/journals/jat/2019/5720290.pdf · Investigation on Two-Stop-Line Signalized Roundabout: Capacity and Optimal

Research ArticleInvestigation on Two-Stop-Line Signalized RoundaboutCapacity and Optimal Cycle Length

Ze-hao Jiang 12 Tao Wang 3 Chao-yang Li3 Fei Pan1 and Xiao-guang Yang 1

1Key Laboratory of Road and Traffic Engineering Ministry of Education Tongji University Shanghai 200092 China2Department of Civil and Earth Resources Engineering Kyoto University Kyoto 606-8501 China3School of Naval Architecture Ocean amp Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China

Correspondence should be addressed to Ze-hao Jiang 528jzhtongjieducn and Tao Wang wt127sinacom

Received 9 February 2019 Revised 24 April 2019 Accepted 8 May 2019 Published 29 May 2019

Academic Editor David F Llorca

Copyright copy 2019 Ze-hao Jiang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Two-stop-line signalized roundabouts (TSLSR) are widely utilized in China To calculate the capacity and optimal cycle lengthaccurately a model considering internal space constraint of the roundabout is developed in this paper Firstly the operationalprinciple of TSLSR is analyzed TSLSR is modeled as being equivalent to a four-phase intersection with left-turn protection phasesand the left-turn lane is further simplified as the ldquoshort-lane modelrdquo Secondly based on the above analysis the capacity of TSLSRis modeled and additionally the accuracy and sensitivity of the model are also analyzed Finally the optimal cycle length of TSLSRwhich maximizes the capacity is put forward Results show that the accuracy of the capacity model is low without considering theinternal space constraint of the roundabout However the model developed in this paper is shown to improve the accuracy (about20) and control the relative error to be within 10 The parameter sensitivity analysis demonstrates that the cycle length andradius of the central island have a significant influence on the capacity of the left-turn lane and results in an optimal value of signalcycle length maximizing the capacity

1 Introduction

The circular configuration of roundabouts requires vehiclesto circulate in a counterclockwise direction (in the China andother right-hand traffic countries) and has been employedsuccessfully to change conflict points from crossing conflictsto merging conflicts They also help reduce traffic speedsas a result of their deflection angle on entry and circularconfiguration The reduced vehicle speeds and motor vehicleconflicts are the reasons why roundabouts are considered atraffic safety enhancement method According to HighwaySafety Manual [1] the safety will be significantly improvedif a signalized intersectionstop-controlled intersection isconverted to a modern roundabout For example in urbanareas if a single-lane or two-lane signalized intersectionis converted to a modern roundabout the injury crashmodification factor (CMF) is 040 whichmeans the expectednumber of injuries would decrease by 60 [1] In additionroundabouts always have good landscape effects and are

often geographical symbols of the cities Because of theabove advantages roundabouts have been widely used inChina

With the continuous development of economy and rapidgrowth of vehicle ownership in China traffic congestion isgetting increasingly worse in Chinese cities However manyof Chinarsquos roundabouts were built decades ago and are locatedin the city center areas As a result roundabouts are oftencongestion points of road networks

Since the entering traffic must yield to the circulatingtraffic and then wait for a gap to enter the roundabout it isuncommon to have roundabouts carrying more than 3000vehicles per hour [2] To break through the capacity limitthere are two feasible optionsThe first approach is to converta roundabout to a signalized intersection or an interchangeThis option usually has high construction costs with seriousimpacts on the operation of the road network The secondchoice is to only repaint the traffic marks and equip trafficsignals at the roundabout to enhance the capacity This

HindawiJournal of Advanced TransportationVolume 2019 Article ID 5720290 9 pageshttpsdoiorg10115520195720290

2 Journal of Advanced Transportation

Before Aer

Figure 1 A before-and-after scenario by using the TSLSR

ASCR TSLR

1

4

YIELD

3

1

2 4

3

4 22

3

1

Modern roundabout

Figure 2 The schematic diagram of modern roundabout ASCR and TSLR

method has been proven by some engineering projects ledby us as a cost-effective way to handle high traffic demandsFigure 1 shows a case from Xiamen City China in which thelooking up and traffic congestion during the peak hour at theroundabout have been significantly alleviated

This approach is called ldquotwo-stop-line signalized round-about (TSLSR)rdquo in this article Its significant advantagesare low transformation costs short construction time andlimited impact on urban road networks In addition thesignal control scheme can be flexibly adjusted according tochanges in traffic volume

In view of the importance of TSLSR in certain engi-neering applications this research aims to investigate anengineering-oriented approach to calculate the capacity andoptimal cycle length of TSLSR The remainder of this paperis organized as follows We first provide a literature reviewin Section 2 Section 3 demonstrates the basic operatingprinciple of TSLSR An engineering-oriented capacity calcu-lation model of TSLSR is discussed in Section 4 followedby numerical sensitivity and precision analysis in Section 5The calculation method of optimal cycle length maximizingthe capacity is then presented in Section 6 Finally Section 7concludes this study

2 Background Literature

In this section we provide a description of modern round-abouts and then conduct a literature review of approach-signal-control roundabout (ASCR) and two-stop-line signal-ized roundabout (TSLSR)

A modern roundabout [3] is a form of intersection inwhich the entering traffic must yield to the circulating trafficIn 1966 the UK adopted a rule known as the ldquopriority-to-the-circle rulerdquo [4] that required entering traffic to giveway to circulating traffic at all circular intersections Thisrule prevented roundabouts from locking up by not allowingvehicles to enter the intersection until there were sufficientgaps in circulating traffic In this way the entrance lanes ofmodern roundabouts are regarded as the minor road andthe circulatory lanes as the major road The roundabout canthus be considered as a typical stop-controlled intersection[5] Hence the entrance capacity [6] delay [7] and queuelength [8] can be calculated using the gap acceptance theoryA number of articles [6 9 10] provide detailed literaturereviews on the capacity models of modern roundabouts

ASCRs are circular intersections where traffic signals areequipped to control vehicles stopping before the approachstop line shown as dark bold line alongside the trafficlight in Figure 2 ASCR This idea was proposed in 1970s

Journal of Advanced Transportation 3

2nd stop line forle-turn vehicles

1st stop line forthroughamp le-turnvehicles

Figure 3 The typical geometric layout of a TSLSR

[11] As a result ASCRs have distinctly different operationalcharacteristics from modern roundabouts Since then aseries of studies demonstrated that adding signals at theapproaches of roundabouts can enhance the capacity [12]eliminate the locking up and reduce CO2 emissions [13 14]In order to calculate the capacity of ASCR HCM (HighwayCapacity Manual) method is usually employed in which thebasic formulation is the saturation flow rate multiplied bythe effective green time [12] However traffic delays andformation of long queues at the approaches will still occurbecause the spaces of circulatory lane inside the ASCRs arenot fully utilized

To make full use of the internal space of ASCR TSLSRwas invented and widely used in China [15] but has not beenpromoted abroad TSLSR has been verified by engineeringprojects and proved as a cost-efficient solution to enhance theroundabout capacity The key characteristics and operatingprinciple of TSLSR will be introduced in Section 3 Maet al [16] did a summative study on the integrated opti-mization of lane making and timing for TSLSR and provedTSLSR outperforms the signalized intersections and modernroundabouts in most cases However in this research torepresent the roundabout phase diagram a precedence graphwas developed which is rather complicated and difficult forengineering applications

3 Operating Principle of TSLSR

In this section the operational logic of TSLSR is first intro-duced Then TSLSR is simplified into a classic four-phase

signalized intersection in which the left-turn lane can befurther simplified as the ldquoshort-lane modelrdquo The discussionin this section is limited to symmetric four-arm roundaboutsbut it could be easily extended to TSLSR of other formssymmetric or not symmetric with more or less than fourarms

31 Operational Logic The typical geometric layout of aTSLSRwith symmetric four arms is shown in Figure 3 TSLSRis featured with two stop lines and two sets of traffic signals

(i) Two stop lines the first stop lines are painted at theapproaches (see 1st stop line for through and left-turnvehicles in Figure 3) and the second stop lines are atthe circulatory lanes (see 2nd stop line for left-turnvehicles in Figure 3)

(ii) Two sets of traffic signals the signals are named asthe main signal and presignal respectively The onein front of the 1st stop line is the main signal and thatin front of the 2nd stop line is presignal

Figure 4 illustrates the typical signal phase diagram of aTSLSR The basic operating logic is as follows

(i) At the approaches of TSLSR left-turn vehicles andthrough vehicles utilize different lanes and are con-trolled by different signal lights

(ii) Left-turn vehicles should stop twice The first time isat the 1st stop line for through and left-turn vehiclesand the second time is at the 2nd stop line for left-turnvehicles (see P-2 and P-3 in Figure 4)


P-2

P-3 P-4

4 4

4 4

1

1 1

1

2

P-1

2 2

2

3

3 3

3

Figure 4 The typical signal phase diagram of a TSLSR

1st stop line

BD

2nd part ofqueuing area

1st part ofqueuing area

C

2nd stop line

shortlane

A

k

k

Figure 5 Short-lane analysis of right-turn lane

32 Equivalent Simplification as a Short-Lane Model Theabove analysis indicates that from the viewpoint of traf-fic signal control the operational logic of TSLSR can beessentially regarded as equivalent to a classic four-phaseintersection with left-turn protection phases Moreover con-sidering the interval space constraint of circulatory lanesas shown in Figure 5 the TSLSR can be further simplifiedas ldquoa classic four-phase intersection with right-turn shortlanesrdquo

The current research on the capacity of the short lane isrelatively mature In a study of Tian et al [17] they found thatthe capacity of a signalized intersection with a short right-turn lane is significantly related to the length of the short lanethe proportion of through and right-turn vehicles and thecycle length Ma et al [18] built a probiotic model to calculatethe capacity of signalized intersections with short lane inwhich three block scenarios including no blockage probableblockage and after blockage were taken into consideration


Table 1 Variable notations in this research

Variable notations Description Unit119862119905 Capacity of one through lane at the 1st stop line pcuh1198621198971 Capacity of one left-turn lane at the 1st stop line pcuh1198621198972 Capacity of one left-turn lane at the 2nd stop line pcuh119862119897 Overall capacity of one left-turn lane pcuh119862 Overall capacity of one direction approach pcuh1199041199051 Saturation flow of one through lane at the 1st stop line pcuh1199041198971 Saturation flow of one left-turn lane at the 1st stop line pcuh1198921199051 Effective green time for through traffic flow s1198921198971 Effective green time for left-turn traffic flow at 1st stop line s119879 Cycle length of the traffic signal s119879119900119901119905 Optimal cycle length of the traffic signal s11986210158401198972 Vehicle-storage capacity of 1st and 2nd part of queueing area pcu119898 Number of circulatory lanes assigned to left-turn traffic flow during phase P-2119899 Total number of circulatory lanes excluding right-turn lane120572119896 Radian of the 1st part of queuing area rad120573119896 Radian of the 2nd part of queuing area rad119877 Radius of the central island m119877119896 Radius of circulatory lane 119896 m119897V Average parking space for a vehicle normally is 6 m119902119894 Traffic volume of lane 119894 pcuh119889119894 Average traffic delay of lane 119894 s

4 Capacity Model

In this section we aim to put forward a model to calculatethe capacity of TSLSR particularly the internal space isconsidered Left-turn lanes and through lanes are the twomain concerns in the following analysis as the right-turnvehicles are normally not controlled by signals and free topass

To facilitate the presentation key variable notations usedhereafter in the paper are summarized in Table 1

41 Capacity at the 1st Stop Line The through traffic flow isonly controlled by the signal lights equipped at the 1st stopline Hence the roundabout after passing the 1st stop linewithout ever stopping before the 2nd stop line exits As aresult the capacity of through traffic flow can be calculatedusing HCMmethod [19] as shown in (1)

119862119905 = 11990411990511198921199051119879 (1)

On the other hand left-turn vehicles need to pass throughboth the 1st and 2nd stop lines before leaving the roundaboutAs a result the overall capacity of left-turn traffic flow is theminimum capacity of the two stop lines as shown in (2)

119862119897 = min (1198621198971 1198621198972) (2)

Similar to the through traffic flow capacity at the 1st stop linethe capacity of the left-turn traffic flow at 1st stop line can begiven by (3)

1198621198971 = 11990411989711198921198971119879 (3)

42 Capacity at the 2nd Stop Line When the left-turn signalat the 2nd stop line turns green the signal upstream of itwhich is the left-turn signal at the 1st stop line will turnred as shown in phases P-2 and P-4 in Figure 4 In otherwords when the left-turn vehicles are passing the 2nd stopline the corresponding 1st stop line will be shut down fromreleasing traffic flow Therefore in any given signal cycle themaximum number of vehicles passing through the 2nd stopline equals to the vehicle-storage capacity of 1st and 2nd partof queuing areasThese two queuing areas aremainly affectedby the number of circulatory lanes assigned to left-turn trafficflowAccording to the basic geometry knowledge the vehicle-storage capacity of 1st and 2nd part of queuing areas (shownin Figure 4) can be easily calculated by (4)

11986210158401198972 =119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V (4)

Then the capacity of left-turn traffic flow at the 2nd stop linecan be calculated using (5)

1198621198972 = 3600119879 11986210158401198972 = 3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V ) (5)

It should be noted here that in Chinarsquosmunicipal design code(CJJ-37 2012) the length of a car is usually considered tobe 6m In fact this length is larger than the actual valuebut we consider that the vehicle needs to maintain a safedistance from the preceding vehicle when parkingThereforethis value is still taken as 6m


Table 2 The accuracy test results

Cyclelength

VISSIMsimulation(benchmark)

Model withoutconsideration ofinterval spaceconstraint

model consideringthe interval space

constraint(proposed in this

paper)

Improvement of model accuracyafter considering internal space

constraints

Result Relative error Result Relative error60 297 310 438 311 471 -03470 397 321 -1913 378 -479 143480 438 329 -2480 428 -228 225290 409 336 -1789 466 1394 395100 475 341 -2821 498 484 2337110 560 345 -3835 522 -679 3157120 517 349 -3254 541 464 2790130 525 352 -3300 499 -495 2805140 456 354 -2231 463 154 2077150 386 357 -764 431 1166 -402160 437 358 -1798 408 -664 1134

43 Overall Capacity of One Direction Approach The overallcapacity of the approach lanes in one direction includes thethrough lanes and left-turn lanes This can be calculated by(6)

119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)

5 Numerical Analysis

51Model Accuracy Test In this section the numericalmodelaccuracy test and the sensitive analysis will be conducted

Model accuracy verification is to investigate the degreeof the model accuracy improvement when the internal spaceconstraint of the TSLSR is taken into consideration Themodel proposed in this paper will be compared with a modelwithout the consideration of the internal space constraint Amodel without the consideration of internal space constraintconsiders the capacity only at the 1st stop line which equals tothe saturation flow rate multiplied by the effective green time

At the same time since it is difficult to obtain thecapacity value of TSLSR under different geometric layout andsignal timing parameters this paper employs the VISSIMsimulation as the benchmark The TSLSR was modeled byVISSIM [20] by using Figure 3 as the base image The imagewas imported and scaled and the links and connectorsrepresenting the roadway were then drawn The roundaboutpriority rules were set by placing the conflict markers afterwhich calibration was done by adjusting the priority ruleparameters andminimumheadwaysTheminimumheadwayof through lanes is 2182s which is equivalent to a saturationflow of 1650pcuh Similarly the minimum headway of left-turn and right-turn lanes is 2322s which is equivalent to

a saturation flow of 1550 pcuh It should be noted thatthe above two saturation flow values are taken according tothe recommended value of HCM 2010 [19] The maximumdeceleration is -35ms2 the minimum headway (frontreal)is 10m In this VISSIM simulation right-turn vehicles thattake exclusive lanes are not controlled by signals and allpedestrians and bicycles are assumed to cross the road viaelevated overpasses

The model accuracy test follows the steps below

Step 1 Change the cycle length of the roundabout Themaximum and minimum cycle lengths are set to be 160s and60s that is T sim [60s 160s] and the step size of the change is10s The duration of each phase is 1198794 and the starting loss is3s

Step 2 With each cycle length obtain the capacity of left-turn lanes by the following 3 approaches VISSIM simulationmodel proposed in this paper and the model without theconsideration of the internal space constraint

Step 3 Compare the results of the above three approaches

The model accuracy test result is shown in Table 2Using the results of VISSIM simulation as the benchmarkand comparing the models withwithout the consideration ofinternal space constraints it is easy to observe that the modelaccuracy has been greatly improved when taking the internalspace constraint into consideration Results show that therelative error of the model proposed in this paper is basicallyno more than 10 of which the maximum is 1394 andminimum is 154

When calculating the capacity without the considerationof internal space constraint the results have a large relativeerror compared with the VISSIM simulation and the averageerror is 2159 Compared with the model proposed inthis paper the capacity results without consideration of the


250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)

Signal cycle length (s)

R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m

(a) Capacity of through lane

0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m

(b) Capacity of right-turn lane

0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m

(c) Capacity ratio of left-turn lane to through lane

3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m

(d) Total capacity of approach

Figure 6 The sensitivity analysis results

internal space constraint are relatively small This is becauseif traffic signals are only equipped before the approach stoplines the roundabout at this time is equivalent to a large-sizesignalized intersection which requires a longer inter-greentime to clean the intersection [21] and results in a longergreen-lost time in one single cycle

52 Sensitivity Analysis Sensitivity analysis is also conductedto demonstrate the effect of different signal cycle lengths and

central island radius on the capacity of a TSLSR In this partthe signal cycle length varies from 60s to 160s and the centralisland radius varies from 10m to 60m Figure 6 shows theresults of sensitivity analysis

As shown in Figure 6(a) the capacity of a through laneincreases as the signal cycle length and the central islandradius increase This is because of the fact that longer signalcycle length means fewer signal switching interval resultingin less lost time Moreover when the central island radius is


higher the through traffic flow has a higher running speed incirculatory lanes therefore more vehicles can go through theroundabout

Figure 6(b) illustrates the impacts of signal cycle lengthand central island diameters on the capacity of a left-turnlane Similar to the through lane the capacity of a left-turnlane increases with the central island radius getting largerHowever the cycle length has a relatively complicated effectin which the capacity increases initially but then decreasesafter a thresholdWhen the signal cycle length is exactly equalto the threshold mentioned above the left-turn traffic flow inone signal cycle length can just fulfill both the 1st and 2ndpart of queuing areas Moreover if signal cycle length is lessthan the threshold left-turn vehicles cannot fulfill the 1st and2nd part of queuing areas and the queuing areas cannot givefull play to their capacity If signal cycle length is longer thanthe threshold spillback queues will occur and conflict withthe entering vehicles in the following phase which then leadsto a locking up of the roundabout At the same time thisphenomenon also inspires us to infer that there is an optimalcycle length of TSLSR

Figure 6(c) demonstrates the variation of the capacityratio of left-turn to through lanes with respect to signal cyclelength and central island diameters This figure is obtainedfrom the data shown in Figures 6(a) and 6(b) At last one canalso observe in Figure 6(d) that when the signal cycle lengthis lower the overall capacity of one direction is sensitive tothe cycle length However under high signal cycle length theoverall capacity of one direction is almost unchanged

6 Optimal Cycle Length

Cycle length is themost important and fundamental parame-ter in signal timing Generally for a signalized intersection alonger signal cycle length means larger capacity and longertraffic delays Therefore according to the classic timingtheory of signalized intersection the optimal value of signalcycle length is mainly based on the overall minimum delayFor instance in Webster method [22] the optimal cyclelength is given by (7)

119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)

Asmentioned before Figure 6(b) gives us inference that thereis an optimal cycle length value which is significantly affectedby the interval space constraint Therefore the Webstermethod is not suitable for calculating the optimal signal cyclelength of TSLSR and an optimal cycle length value of aTSLSRcan be obtained under the objective of capacitymaximizationas shown in Figure 7

7 Conclusion

In this study we proposed an engineering-oriented approachto calculate the capacity and optimal signal cycle length ofthe TSLSR which is characterized by equipped signal lightson both the approaches and circulatory lanes and setting upof two stop lines for left-turn traffic flows

45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)

Central island radius (m)

Optimal cycle length

Figure 7 The optimal cycle length of TSLSR

The operational logic of TSLSR is given in this paperwhich for a better understanding we demonstrate that itcould be equivalent to a four-phase signalized intersectionwith left-turn protection phases Furthermore the left-turnlane capacity model could be simplified as the ldquoshort-lanemodelrdquo Based on the above analyses we gave the formulafor calculating the capacity with the consideration of intervalspace constraint

The accuracy test shows that the model proposed in thispaper has a relatively high accuracy The sensitivity analysisshows that there is a threshold point of left-turn capacity asthe signal cycle length increases Hence different from theclassic timing theory such as Webster method an optimalcycle length of TSLSR can be obtained under the objectiveof capacity maximization

In further research along the line the impacts of pedes-trians and bicycles on the capacity will be taken into con-sideration Additionally some fundamental parameters suchas the saturation flow and green-lost time can be properlycalibrated

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (61773293) and Chinese GovernmentScholarship (201806260148)The authors convey their sinceregratitude


References

[1] American Association of State Highway and TransportationOfficials Highway Safety Manual AASHTO Washington DCUSA 2010

[2] Peoplersquos Republic of China Ministry of Construction Code forTransport Planning on Urban Road Peoplersquos Republic of ChinaMinistry of Construction Beijing China 1995

[3] T Tollazzi R Mauro D Zilioniene I I Otkovic and N Stama-tiadis ldquoModern roundabouts a challenge of the futurerdquo Journalof Advanced Transportation vol 2019 Article ID 3950891 2pages 2019

[4] K Todd ldquoA history of roundabouts in britainrdquo TransportationQuarterly vol 45 no 1 pp 143ndash155 1991

[5] N Wu ldquoA universal procedure for capacity determination atunsignalized (priority-controlled) intersectionsrdquo Transporta-tion Research Part B Methodological vol 35 no 6 pp 593ndash6232001

[6] R Guo L Liu and W Wang ldquoReview of roundabout capacitybased on gap acceptancerdquo Journal of Advanced Transportationvol 2019 Article ID 4971479 11 pages 2019

[7] C F Daganzo ldquoTraffic delay at unsignalized intersectionsclarification of some issuesrdquo Transportation Science vol 11 no2 pp 180ndash189 1977

[8] D Heidemann and H Wegmann ldquoQueueing at unsignalizedintersectionsrdquo Transportation Research Part B Methodologicalvol 31 no 3 pp 239ndash263 1997

[9] A Pratelli S Casella A Farina et al ldquoConventional andunconventional roundabouts a review of geometric featuresand capacity modelsrdquo International Journal of Transport Devel-opment and Integration vol 2 no 3 pp 225ndash239 2018

[10] J Bie H K Lo and S C Wong ldquoCapacity evaluation of multi-lane traffic roundaboutrdquo Journal of Advanced Transportationvol 44 no 4 pp 245ndash255 2010

[11] P Davies B Jamieson and D A Reid ldquoTraffic signal control ofroundaboutsrdquo Traffic Engineering And Control vol 21 no 7 pp354ndash357 1980

[12] A K Patnaik L A Agarwal M Panda and P K BhuyanldquoEntry capacity modelling of signalized roundabouts underheterogeneous traffic conditionsrdquo Transportation Letters pp 1ndash13 2018

[13] P Calıskanelli M Ozuysal S Tanyel et al ldquoComparison ofdifferent capacity models for traffic circlesrdquo Transport vol 24no 4 pp 257ndash264 2009

[14] F F Saccomanno F Cunto G Guido and A Vitale ldquoCom-paring safety at signalized intersections and roundabouts usingsimulated rear-end conflictsrdquo Transportation Research Recordvol 2078 no 1 pp 90ndash95 2008

[15] X Yang L Xiugang Z Guangwei et al ldquoThe traffic control andmanagement system for large roundaboutrdquo 2001

[16] W Ma Y Liu L Head and X Yang ldquoIntegrated optimizationof lane markings and timings for signalized roundaboutsrdquoTransportation Research Part C Emerging Technologies vol 36pp 307ndash323 2013

[17] Z Z Tian and N Wu ldquoProbabilistic model for signalizedintersection capacity with a short right-turn lanerdquo Journal ofTransportation Engineering vol 132 no 3 pp 205ndash212 2006

[18] W Ma Y Lu K An et al ldquoProbabilistic model for signalizedintersection capacity with short lanesrdquo Journal of Tongji Univer-sity (Natural Science) vol 40 no 11 pp 1641ndash1646 2012

[19] H C Manual HCM2010 Transportation Research BoardNational Research Council Washington DC USA 2010

[20] E Nyame-Baafi C A Adams and K K Osei ldquoVolumewarrants for major and minor roads left-turning traffic lanesat unsignalized T-intersections A case study using VISSIMmodellingrdquo Journal of Traffic and Transportation Engineeringvol 5 no 5 pp 417ndash428 2018 (English)

[21] Z Jiang and T Wang ldquoIntergreen time calculation methodof signalized intersections based on safety reliability theory amonte-carlo simulation approachrdquo Journal of Advanced Trans-portation vol 2019 Article ID 1941405 9 pages 2019

[22] Y Wang X Yang H Liang and Y Liu ldquoA review of the self-adaptive traffic signal control system based on future trafficenvironmentrdquo Journal of Advanced Transportation vol 2018Article ID 1096123 12 pages 2018

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Before Aer

Figure 1 A before-and-after scenario by using the TSLSR

ASCR TSLR

1

4

YIELD

3

1

2 4

3

4 22

3

1

Modern roundabout

Figure 2 The schematic diagram of modern roundabout ASCR and TSLR

method has been proven by some engineering projects ledby us as a cost-effective way to handle high traffic demandsFigure 1 shows a case from Xiamen City China in which thelooking up and traffic congestion during the peak hour at theroundabout have been significantly alleviated

This approach is called ldquotwo-stop-line signalized round-about (TSLSR)rdquo in this article Its significant advantagesare low transformation costs short construction time andlimited impact on urban road networks In addition thesignal control scheme can be flexibly adjusted according tochanges in traffic volume

In view of the importance of TSLSR in certain engi-neering applications this research aims to investigate anengineering-oriented approach to calculate the capacity andoptimal cycle length of TSLSR The remainder of this paperis organized as follows We first provide a literature reviewin Section 2 Section 3 demonstrates the basic operatingprinciple of TSLSR An engineering-oriented capacity calcu-lation model of TSLSR is discussed in Section 4 followedby numerical sensitivity and precision analysis in Section 5The calculation method of optimal cycle length maximizingthe capacity is then presented in Section 6 Finally Section 7concludes this study

2 Background Literature

In this section we provide a description of modern round-abouts and then conduct a literature review of approach-signal-control roundabout (ASCR) and two-stop-line signal-ized roundabout (TSLSR)

A modern roundabout [3] is a form of intersection inwhich the entering traffic must yield to the circulating trafficIn 1966 the UK adopted a rule known as the ldquopriority-to-the-circle rulerdquo [4] that required entering traffic to giveway to circulating traffic at all circular intersections Thisrule prevented roundabouts from locking up by not allowingvehicles to enter the intersection until there were sufficientgaps in circulating traffic In this way the entrance lanes ofmodern roundabouts are regarded as the minor road andthe circulatory lanes as the major road The roundabout canthus be considered as a typical stop-controlled intersection[5] Hence the entrance capacity [6] delay [7] and queuelength [8] can be calculated using the gap acceptance theoryA number of articles [6 9 10] provide detailed literaturereviews on the capacity models of modern roundabouts

ASCRs are circular intersections where traffic signals areequipped to control vehicles stopping before the approachstop line shown as dark bold line alongside the trafficlight in Figure 2 ASCR This idea was proposed in 1970s

















P-2

P-3 P-4

4 4

4 4

1

1 1

1

2

P-1

2 2

2

3

3 3

3


1st stop line

BD



C

2nd stop line

shortlane

A

k

k







4 Capacity Model




119862119905 = 11990411990511198921199051119879 (1)


119862119897 = min (1198621198971 1198621198972) (2)


1198621198971 = 11990411989711198921198971119879 (3)


11986210158401198972 =119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V (4)


1198621198972 = 3600119879 11986210158401198972 = 3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V ) (5)




Cyclelength





paper)


constraints



119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)













250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















P-2

P-3 P-4

4 4

4 4

1

1 1

1

2

P-1

2 2

2

3

3 3

3


1st stop line

BD



C

2nd stop line

shortlane

A

k

k







4 Capacity Model




119862119905 = 11990411990511198921199051119879 (1)


119862119897 = min (1198621198971 1198621198972) (2)


1198621198971 = 11990411989711198921198971119879 (3)


11986210158401198972 =119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V (4)


1198621198972 = 3600119879 11986210158401198972 = 3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V ) (5)




Cyclelength





paper)


constraints



119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)













250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



P-2

P-3 P-4

4 4

4 4

1

1 1

1

2

P-1

2 2

2

3

3 3

3


1st stop line

BD



C

2nd stop line

shortlane

A

k

k







4 Capacity Model




119862119905 = 11990411990511198921199051119879 (1)


119862119897 = min (1198621198971 1198621198972) (2)


1198621198971 = 11990411989711198921198971119879 (3)


11986210158401198972 =119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V (4)


1198621198972 = 3600119879 11986210158401198972 = 3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V ) (5)




Cyclelength





paper)


constraints



119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)













250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





4 Capacity Model




119862119905 = 11990411990511198921199051119879 (1)


119862119897 = min (1198621198971 1198621198972) (2)


1198621198971 = 11990411989711198921198971119879 (3)


11986210158401198972 =119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V (4)


1198621198972 = 3600119879 11986210158401198972 = 3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V ) (5)




Cyclelength





paper)


constraints



119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)













250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Cyclelength





paper)


constraints



119862 = 119862119905 + 119862119897 = 11990411990511198921199051119879 +min1199041198971

sdot 1198921198971119879 [3600119879 (119898sum119896=1

120572119896 sdot 119877119896119897V +119899sum119896=119898+1

120573119896 sdot 119877119896119897V )](6)













250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



250

350

450

550

650

750

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=60 mR=50 mR=40 m

R=30 mR=20 mR=10 m


0

100

200

300

400

500

600

60 80 100 120 140 160

Capa

city

of l

e-tu

rn la

ne (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


0

02

04

06

08

1

60 80 100 120 140 160

Capa

city

ratio

of l

e-tu

rn to

thro

ugh

lane


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m


3 000

4 000

5 000

6 000

7 000

60 80 100 120 140 160

Ove

rall

capa

city

of o

ne ap

proa

ch (p

cuh

)


R=10 mR=20 mR=30 m

R=40 mR=50 mR=60 m













119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119879119900119901119905 = argmin119894sum1

119902119894 sdot 119889119894 = 15119871 + 51 minus 119884 (7)


7 Conclusion


45

60

85

120

140

160

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Opt

imal

cycle

leng

th (s

)







Data Availability




Acknowledgments



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Investigation on Two-Stop-Line Signalized Roundabout ...downloads.hindawi.com/journals/jat/2019/5720290.pdf · Investigation on Two-Stop-Line Signalized Roundabout: Capacity and Optimal