Research Article Development and Evaluation of Bus ...downloads.hindawi.com/journals/ddns/2015/928350.pdfDiscrete Dynamics in Nature and Society Generate the travel time ti j 1,j (j2,i2)

Research ArticleDevelopment and Evaluation of Bus Operation Control SystemBased on Cooperative Speed Guidance

Jing Teng and Weimin Jin

Key Laboratory of Road and Traffic Engineering Ministry of Education Tongji University Shanghai 201804 China

Correspondence should be addressed to Weimin Jin jwmemail01126com

Received 17 July 2014 Accepted 3 October 2014

Academic Editor Yongjun Shen

Copyright copy 2015 J Teng and W Jin 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

Buses often have strong bunching or large interval tendency when traveling further along the route To restrain this further deteri-oration of operation service this paper developed a bus operation control system to dynamically adjust bus speed bus dwell timeand traffic signal timings along the running path In addition a simulation platformwas developed to evaluate the proposed controlsystemwith the actual data collected from bus route number 210 in ShanghaiThe simulation results show that the proposed controlsystem canmitigate the amplification trend of the headway deviation along the route to produce headways within a given tolerance

1 Introduction

The uncertainty of bus operation environments such asthe dynamic and stochastic traffic congestion and passengerdemand often causes the unreliability of bus operationservice On busy lines with short headways buses usuallyarrive at stops irregularly easily in bunches which leads tothe increase of passenger waiting time and the decrease ofbus arrival punctuality rate In China bus transit systemin the urban area is featured by the short frequency andno time-check points available on the bus route There areseveral factors affecting the quality of bus operation serviceWith buses traveling further along the route the effect ofrandom factors will gradually be balanced while the effect ofdirectional factors (eg weather condition traffic congestionand driver behavior) may becomemore andmore significantwhich eventually leads to bunching phenomenon To alleviatethe effect of directional factors the recognition of a busbeing late or early should be proactively predicted In thatway the bus operators will have adequate time to restore thebuses headway regularity Besides bus operators build slackinto their schedules which also leave room for the controlThe development of advanced public transportation system(APTS) such as the automatic vehicle location (AVL) systemand the automatic passenger count (APC) system and thecommunication technologies makes the dynamic control ofbus operation possible

2 Literature Review

There aremainly two types of operation control strategies thecontrol strategy at stations and that on road sections Holdingcontrol (holding buses at control stops) is a common effectivemethod aiming at maintaining the planned bus schedule orheadway [1ndash4] controlling the departure time to improve thestability of bus system For non-frequently serviced bus routetarget schedule control is taken while for short frequentlyserviced bus route target headway control is used Holdingcontrol strategies can be generally divided into two categoriesone is the headway threshold-based control model in whichbuses are determined to hold at stops based on the deviationof their headway from the planned headway and the other isholding times optimization model in which the holding timeof each control stop is obtained through mathematical mod-els aiming at minimizing the passengers waiting time [2 5]

Single control point of holding control strategy is usuallyset in the high passenger demand stop or the middle sectionof the line [6] Unfortunately single-point control cannotsucceed for long routes with frequent service and a strongbunching tendency [7] Other point control includes theintersection signal control which is one of the effective waysto reduce bus headway fluctuation [8] The speed controlis continuous control method Salek [9] used the Kalmanfilter forecasting models and proposed the idea of link speedcontrol in different level The fluctuation coefficient of the

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2015 Article ID 928350 8 pageshttpdxdoiorg1011552015928350

2 Discrete Dynamics in Nature and Society

travel speed and smoothing coefficient of the driving wereproposed [10 11] Chen et al proposed an adaptive cruisecontrol system coordinated with the signal control strategyfor BRT system [12]

Daganzo and Pilachowski [13] designed a control systemwith integration of cruise speed control and holding controlunder bus-bus cooperation condition based on dynamicallypredicting adjacent headway and proposed three combina-tion control strategies to prevent buses from bunching Maet al [14] proposed the economic-driving assistance systemThe system can provide drivers with real-time bus speed andholding times which makes the bus running state adapt todownstream intersection signal control and avoid bus stopsat the intersections thereby reducing fuel consumption andair pollution emissions

The spatial variations of bus headway deviation canreflect the effect of directional factors Based on analyzingthe spatial variations of bus headway deviation this paperproposed a proportional headway threshold In addition thispaper proposed the bus operation control system based oncooperative speed guidance for the whole route It relies onthe cooperative speed control with other control strategies

The remainder of this paper is organized as followsFirst the methodology (including the control principlecontrol threshold control system architecture and controlalgorithm) will be introduced Then the performance of theproposed control will be evaluated by a case study using asimulation method Finally conclusion and future researchwill be addressed

3 Methodology

31 Control Principle Theheadway deviation from the depar-ture terminal stop to the stop buses depart from (ie thedifference between the departure headway of the stop and thescheduled headway) is defined as the path headway deviationFrom the historical bus trajectories in the whole day (asshown in Figure 1) it is found that with buses traveling fur-ther on the bus route the variance of headway deviation tendsto increase [15 16] The headway deviation is so large (egstop number 21008) that it is difficult to restore the down-stream headway regularity with buses traveling further alongthe route The single point control or small-scope control ofthe route seems not to restrain this strong bunching tendencysuccessfully From the perspective of the control target itshould reduce the headway deviation at the terminal stop(ensuring bus departure punctuality in the reverse direction)as well as some key midway stops (high passenger demand)

32 Proportional Control Threshold The headway deviationat the terminal stop some key midway stops and some keyintersection should fall within the tolerated scope The redline marks the boundaries of bus deviation that would beslightly late or early from the scheduled headway deviation asshown in Figure 1 The control threshold at each check nodeis given by

Δℎ119894= 119905119894

Δℎ119889

119905119889

(1)

21001 21003 21005 21007 21009 21011 21013Stop number

Hea

dway

bia

s (s)

minus100minus200minus300minus400minus500minus600

6005004003002001000

Figure 1 Headway deviation with buses traveling on the route(control unavailable)

where Δℎ119894is the absolute value of control threshold at node 119894

119905119894is the path travel time at node 119894 Δℎ

119889is the absolute value of

allowedmaximum headway deviation at the terminal stop 119905119889

is the path travel time at the terminal stop

33 Control System Architecture Figure 2 illustrates the basicarchitecture of the proposed bus operation control systemThis control system is regarded as the subsystem of busoperation dispatch system to maintain the established sched-ule The signal control only is unreliable because driversrsquobehavior is unpredictable without speed adaption On thecontrary speed adaption only also lacks stable effect dueto the interaction from the other vehicles which can besolved by signal control Holding control cannot succeedfor long routes with frequent service and a strong bunchingtendency Therefore these three control strategies are simul-taneously implemented to dynamically revise the fluctuationof driver behaviors in the control system The system candynamically adjust bus speed bus dwell time and trafficsignal timings with buses traveling further along the routefrom the departure stop to destination stop With the helpof real-time communication between buses and operationcenter the departure headway between adjacent buses can becollected and sent to the control center when buses departfrom the stop and the center can send the message to busesSimultaneously with the real-time communication betweenbuses and the signal controllers the buses can send requestmessage to the signal controllers and the signal controllerscan adjust signal timings

34 Control Algorithm As shown in Figure 3 the processof bus control system consists of four steps (1) no action(2) speed adjustment (3) signal adjustment and (4) delaynotification It takes no action if the detected headwaydeviation is less than the threshold at some key nodes (suchas key intersection and key stop) If the detected headwaydeviation is beyond the threshold the speed adjustmentprocedure is launched and the bus driver is notified It isstill possible that speed adjustment alone fails to bring theheadway deviation back within the given tolerated scopeThen the signal timing adjustment procedure is triggered and

Discrete Dynamics in Nature and Society 3

Bus operation procedure

ControllerCheck thedeparture headway

Bus operationcontrol system

Control strategies Implementers

Bus operator

Traffic manager

Speed controlDwell time

Interval traveltime

Departure timeat terminal stop

Road trafficcontrol system

Intersectioncontrol

Departure headway

Holding control

Figure 2 Control system architecture

Start

Determine the headway threshold

Estimate the headway at thedownstream intersection

Current speed is instable scope

Too slow

Speed adjustmentldquospeed up to pass the

intersectionrdquo End

Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

Speed adjustmentldquospeed down to wait

next cyclerdquo

Fail

Fail

Generate thesignal timing

plan

Estimate the headway at thedownstream stop

Adjustment becomesimpossible

Delaynotification

Wait to pass theinteraction

Bus holding

Adjustment isallowed

Figure 3 Flow chart of the control algorithm


Space

Stop

Time

Headway at intersection

Max

imum

allo

wed

spee

d

Curre

nt sp

eed

Min

imum

allow

ed sp

eed

Dwell time Holding time

Headway at stop

Figure 4 Speed adjustment procedure

the busrsquo headway irregularity is reduced If any appropriateadjustment becomes impossible delay information would benotified to passengers waiting at the corresponding bus stopsthrough electronic stop sign or mobile phone

The speed adjustment procedure is the main componentof control system as shown in Figure 4 If the detectedheadway deviation at stop is less than the threshold buseskeep the current speed Otherwise buses will be instructedto change their current speeds If the estimated headwaydeviation at intersection is less than the threshold the signaltiming plan will be maintained and the holding control willnot be launched Otherwise the holding control andor thesignal control will be triggered The speed adjustment is alsoappropriate to the control of early buses (Figure 4)

The speed is calculated in the two following scenarios

(1) Speed Down to Wait Next Cycle The time that the bus trip119894 departs from the intersection 119868 is given by

Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878+ 119905119867= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867

(2)

The control threshold is determined by the following equa-tion

(Dep119894119868minus Dep119894minus1

119868) minus Δ119875

0= Δℎ119894

119895 (3)

Substituting (2) into (3) leads to

(Dep119894119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867minus Dep119894minus1

119878) minus Δ119875

0= Δℎ119894

119878 (4)

Thedeparture time at intersection falls within the green phaseof the current cycle 119905sg le Dep

119894

119878+ (1198711198781198681198811015840) + 119889119894

119878+ 119905119867le 119905eg

1198811015840= 119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)

The adjusted speed of the link is given by

119881119895119895+1=

119881min119895119895+1 119881

1015840lt 119881

min119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868

119871119878119868

119905eg minus Dep119894119878 minus 119889119894119878 minus 119905119867

le 1198811015840le max119881max

119878119868

119871119878119868

119905sg minus Dep119894119878 minus 119889119894119878 minus 119905119867

(5)

(2) SpeedUp to Pass the IntersectionThe time that the bus trip119894 departs from the intersection 119868 is given by

Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878 (6)



119868) minus Δ119875

0= Δℎ119894

119895 (7)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894

119878minus Dep119894minus1

119878) minus Δ119875

0= Δℎ119894

119878 (8)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878le 119905eg 119881

1015840=

119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)


Stop 1

Stop 2Stop 3 Stop 4

Stop 5

Stop 6

Stop 7

Stop 8

Stop 9

Stop10

Stop 11

Stop 12

Stop 13

Stop 14

N

Stop name(1) Yonghe Village(2) GaopinWenshui(3) YongheYuanping(4) YongheWanrong District(5) WanrongYonghe(6) WanrongLingshi

(7) Guangzhong WestGonghexinlu(8) GonghexinluYanchang(9) Zhabei Park(10) GonghexinluZhongshan North(11) GonghexinluZhonghuaxinlu(12) ZhongxingXizang North

(13) Xizang NorthQufu(14) XinzhaWenzhou

Regular stopTransfer stop with line 1Transfer stop with line 8

Figure 5 Bus route number 210 located in Shanghai


119881119895119895+1=

119881max119895119895+1 119881

1015840gt 119881

max119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868119871119878119868

119905eg minus Dep119894119878 minus 119889119894119878

le 1198811015840le max119881max

119878119868119871119878119868

119905sg minus Dep119894119878 minus 119889119894119878

(9)

where 119881119878119868

is the recommended speed of the link betweenstop 119878 and intersection 119868 119881max

119878119868is the maximum allowed

speed of the link between stop 119878 and intersection 119868 119881min119878119868

isthe minimum allowed speed of the link between stop 119878 andintersection 119868 Δ119875

0is the headway of the departure terminal

stop Δℎ119894119868is the value of control threshold at intersection 119868 119905

119867

is the holding time at the stop 119905119867le 119905

max119867

119905sg is the start timeof green phase 119905eg is the end time of green phase 119871

119878119868is the

distance between stop 119878 and intersection 119868 119905119894119895119895+1

(119895 ge 2 119894 ge 2)is the link travel time 119889119894

119878is the dwell time at stop 119878 Dep119894

119878is

the time that bus trip 119894 departs from stop 119878 Dep119894119868is the time

that bus trip 119894 departs from intersection 119868


Generate the travel timetijminus1j (j ge 2 i ge 2)

Determine busarrival time

Arrij

Generate bus dwell timedij = 120572 + 120573b

Determine busdeparture time

Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop

Bus operating module

Generate the departuretime at the terminal stop

Depi1i = i + 1

i le 108

Dispatch module

Generate the travel timewijj+1

Control module

headway bias( (Depij minus Depiminus1j minus Depi1 minus Depiminus11 lt Δhij))

Figure 6 Flowchart of transit simulation procedure

4 Case Study

41 Experimental Data The experimental data of bus oper-ating was obtained from the AVL data of bus route number210 located in Shanghai AVL records from April 15 2013 toSeptember 15 2013 (500 amndash1000 pm) As shown in Figure5 the southbound corridor has 14 stops and is 975 kilometerslong fromYonghe Village stop to XinzhaWenzhou stopTheroute is frequently serviced with the scheduled headway of 3ndash5 minutes during peak periods and 7ndash10 minutes during off-peak periods Passenger data was obtained fromfield surveys

42 Simulation Process The simulation updates the locationsof all buses in sequence at regular simulation time stepsThe simulation model includes three subcomponents thedispatch module the bus operating module and the controlmodule Figure 6 presents the simulation process of the busesThe simulation procedure describes the bus operationalstatus departure from the start stop travelling on the road

arrival at the stop and departure from the stop serving pass-engers at the stop and adjusting speed on the road

The bus operating module simulates the operation pro-cess of each bus as well as its operating environment Bustravel time is usually simulated using normal and lognormaldistribution [5]Through statistical analysis of historical datait is found that bus travel time follows normal distributionBased on the generated travel time the bus arrival timeat immediate-downstream stop can be determined Besidesthrough statistical analysis of the field data passengers arriveat the bus station randomly following the Poisson distribu-tion For the frequently serviced bus lines (ie the scheduledheadway of less than 10 minutes) this assumption is reason-able The dwell time is assumed to be a linear function ofboarding count 119887 the equation is given by 119889119894

119895= 120572 + 120573119887 and

the parameters 120572 120573 can be specified from the experimentaldata After determining the dwell time the time that busdeparts from the stop Dep119894

119895 is derived The signal timing

plans of each intersection are generated one cycle by one cycle


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(a) Control unavailable

0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control

Figure 7 Distribution of headway deviation with buses traveling onthe route

when the simulation startsThe starting time and ending timeof green phase will be updated in simulation step

The control module simulates the adjustment bus speedprocess Before generating the next link travel time (speed)it will check whether headway deviation between adjacentbuses is within the given range If not it will change the busspeed and regenerate the next link travel time (speed)

When a complete simulation process of the bus trip isfinished the dispatch module will generate the departuretime of next trip at the start stop according to the scheduledtimetable

43 Measures of Effectiveness Three performance measuresare used to compare different control strategies the headwayvariance the passenger waiting time and the travel timeThetravel time can reflect the efficiency of the system while theheadway variance calculated for all trips and stops can reflectthe system stability

431 Headway Variance As shown in Figure 7 when buscontrol is not available bus headway deviation at the begin-ning of several stops varies little However with buses travel-ing further on the bus route the variance of headway devia-tion tends to increase When the proposed control systemis implemented the upper and the lower boundaries of theheadway deviation are decreased in some extentThe possiblereasons for this may be that at the first several stops the pro-posed control systempromptly corrects the irregularity of bus

No controlProposed control

3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number

Figure 8 Impact of bus control on average wait time

2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy


Figure 9 Comparison of travel time in different control strategies

headway reducing the bus headway deviation amplificationtrend

432 PassengerWaiting Time As shown in Figure 8 the con-trol system can decrease the average wait time considerablyWith buses traveling further on the route the average waittime varies little

433 Bus Travel Time As shown in Figure 9 the bus traveltime decreases slightly when the control system is imple-mented The system improves the regularity of the headwayat the cost of travel time of some tripsThe faster trips and theslower trips are balanced after control to a certain extent

5 Conclusion and Future Work

This paper proposed a proportional headway thresholdmodel which is a metric of the dynamic speed guidanceThebus operation control system integrates cooperative controlstrategies to reduce the accumulation of the headway devia-tion and through the experiment case it could be found thatthe control system can improve the stability and the efficiencyof the bus fleet and save the travel cost of the passengers

It is noted that the purpose of the current research isto improve the bus headway regularity of the route and thesignal timing adjustment procedure does not consider thepotential delays of other vehicles traveling opposite to bus at


intersectionWe will refine our control strategy if such delaysare serious

Conflict of Interests

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

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no 61174185)

References

[1] J G Strathman T J Kimpel K J Dueker et al ldquoBus transitoperations control review and an experiment involving Tri-Mets automated bus dispatching systemrdquo Journal of PublicTransportation vol 4 2001

[2] E E Osuna andG FNewell ldquoControl strategies for an idealizedpublic transportation systemrdquoTransportation Science vol 6 no1 pp 52ndash72 1972

[3] J Argote Y Xuan and V Gayah ldquoComparative analysis ofvarious bus control strategies a case study of the UC BerkeleyBear Transit Systemrdquo in Proceedings of the 12th Conference onAdvanced Systems for Public Transport Santiago Chile July2012

[4] Y Ji and H M Zhang ldquoDynamic holding strategy to preventbuses from bunchingrdquo Transportation Research Record Journalof the Transportation Research Board vol 3 no 2352 pp 94ndash103 2013

[5] D Koffman ldquoA simulation study of alternative real-time busheadway control strategiesrdquoTransportation Research Record no663 pp 41ndash46 1978

[6] L Fu and X Yang ldquoDesign and implementation of bus holdingcontrol strategies under real-time informationrdquo TransportationResearch Record Journal of the Transportation Research Boardno 1791 pp 6ndash12 2002

[7] C F Daganzo ldquoA headway-based approach to eliminate busbunching Systematic analysis and comparisonsrdquo Transporta-tion Research B Methodological vol 43 no 10 pp 913ndash9212009

[8] A Adamski and A Turnau ldquoSimulation support tool for real-time dispatching control in public transportrdquo TransportationResearch Part A vol 32 no 2 pp 73ndash87 1998

[9] S Salek ldquoA method for predicting the mean and varianceof transit segment and route travel timesrdquo in TransportationResearch Record Journal of the Transportation Research BoardNo 2256 pp 30ndash37 Transportation Research Board of theNational Academies Washington DC USA 2011

[10] Y Ding and S Chien ldquoImproving transit service quality andheadway regularity with real-time controlrdquo Transportation Re-search Record no 1760 pp 161ndash170 2001

[11] Z R Peng E D Lynde and W Y Chen Improving Ser-vice Restoration Using Automatic Vehicle Location MidwestRegional University Transportation Center College of Engi-neering Department of Civil and Environmental EngineeringUniversity of Wisconsin Madison Wis USA 2008

[12] Q Chen E Adida and J Lin ldquoAn investigation in real-time busholding policyrdquo in Proceedings of the 15th Hong Kong Societyof Transportation Study International Conference (HKSTS rsquo10)

Hong Kong Society for Transportation Studies Hong KongChina December 2010

[13] C FDaganzo and J Pilachowski ldquoReducing bunchingwith bus-to-bus cooperationrdquoTransportation Research BMethodologicalvol 45 no 1 pp 267ndash277 2011

[14] W Ma H Xie and B Han ldquoDevelopment and evaluation ofan economic-driving assistance program for transit vehiclesrdquoEnergies vol 5 no 2 pp 371ndash385 2012

[15] G Chen J Teng S Zhang and X Yang ldquoTendency-basedapproach for link travel time estimationrdquo Journal of Transporta-tion Engineering vol 139 no 4 pp 350ndash357 2013

[16] G Chen X Zhou D Zhang and X Yang ldquoProportion-basedand tendency-based bus trajectory prediction modelsrdquo Journalof Transportation Engineering vol 139 no 9 pp 896ndash902 2013

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Stochastic AnalysisInternational Journal of


travel speed and smoothing coefficient of the driving wereproposed [10 11] Chen et al proposed an adaptive cruisecontrol system coordinated with the signal control strategyfor BRT system [12]

Daganzo and Pilachowski [13] designed a control systemwith integration of cruise speed control and holding controlunder bus-bus cooperation condition based on dynamicallypredicting adjacent headway and proposed three combina-tion control strategies to prevent buses from bunching Maet al [14] proposed the economic-driving assistance systemThe system can provide drivers with real-time bus speed andholding times which makes the bus running state adapt todownstream intersection signal control and avoid bus stopsat the intersections thereby reducing fuel consumption andair pollution emissions

The spatial variations of bus headway deviation canreflect the effect of directional factors Based on analyzingthe spatial variations of bus headway deviation this paperproposed a proportional headway threshold In addition thispaper proposed the bus operation control system based oncooperative speed guidance for the whole route It relies onthe cooperative speed control with other control strategies

The remainder of this paper is organized as followsFirst the methodology (including the control principlecontrol threshold control system architecture and controlalgorithm) will be introduced Then the performance of theproposed control will be evaluated by a case study using asimulation method Finally conclusion and future researchwill be addressed

3 Methodology

31 Control Principle Theheadway deviation from the depar-ture terminal stop to the stop buses depart from (ie thedifference between the departure headway of the stop and thescheduled headway) is defined as the path headway deviationFrom the historical bus trajectories in the whole day (asshown in Figure 1) it is found that with buses traveling fur-ther on the bus route the variance of headway deviation tendsto increase [15 16] The headway deviation is so large (egstop number 21008) that it is difficult to restore the down-stream headway regularity with buses traveling further alongthe route The single point control or small-scope control ofthe route seems not to restrain this strong bunching tendencysuccessfully From the perspective of the control target itshould reduce the headway deviation at the terminal stop(ensuring bus departure punctuality in the reverse direction)as well as some key midway stops (high passenger demand)

32 Proportional Control Threshold The headway deviationat the terminal stop some key midway stops and some keyintersection should fall within the tolerated scope The redline marks the boundaries of bus deviation that would beslightly late or early from the scheduled headway deviation asshown in Figure 1 The control threshold at each check nodeis given by

Δℎ119894= 119905119894

Δℎ119889

119905119889

(1)

21001 21003 21005 21007 21009 21011 21013Stop number

Hea

dway

bia

s (s)

minus100minus200minus300minus400minus500minus600

6005004003002001000

Figure 1 Headway deviation with buses traveling on the route(control unavailable)

where Δℎ119894is the absolute value of control threshold at node 119894

119905119894is the path travel time at node 119894 Δℎ

119889is the absolute value of

allowedmaximum headway deviation at the terminal stop 119905119889

is the path travel time at the terminal stop

33 Control System Architecture Figure 2 illustrates the basicarchitecture of the proposed bus operation control systemThis control system is regarded as the subsystem of busoperation dispatch system to maintain the established sched-ule The signal control only is unreliable because driversrsquobehavior is unpredictable without speed adaption On thecontrary speed adaption only also lacks stable effect dueto the interaction from the other vehicles which can besolved by signal control Holding control cannot succeedfor long routes with frequent service and a strong bunchingtendency Therefore these three control strategies are simul-taneously implemented to dynamically revise the fluctuationof driver behaviors in the control system The system candynamically adjust bus speed bus dwell time and trafficsignal timings with buses traveling further along the routefrom the departure stop to destination stop With the helpof real-time communication between buses and operationcenter the departure headway between adjacent buses can becollected and sent to the control center when buses departfrom the stop and the center can send the message to busesSimultaneously with the real-time communication betweenbuses and the signal controllers the buses can send requestmessage to the signal controllers and the signal controllerscan adjust signal timings

34 Control Algorithm As shown in Figure 3 the processof bus control system consists of four steps (1) no action(2) speed adjustment (3) signal adjustment and (4) delaynotification It takes no action if the detected headwaydeviation is less than the threshold at some key nodes (suchas key intersection and key stop) If the detected headwaydeviation is beyond the threshold the speed adjustmentprocedure is launched and the bus driver is notified It isstill possible that speed adjustment alone fails to bring theheadway deviation back within the given tolerated scopeThen the signal timing adjustment procedure is triggered and






Bus operator

Traffic manager


Interval traveltime



Intersectioncontrol

Departure headway

Holding control


Start




Too slow



Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No


next cyclerdquo

Fail

Fail


plan



Delaynotification


Bus holding




Space

Stop

Time


Max

imum

allo

wed

spee

d

Curre

nt sp

eed

Min

imum

allow

ed sp

eed


Headway at stop






Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878+ 119905119867= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867

(2)



119868) minus Δ119875

0= Δℎ119894

119895 (3)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867minus Dep119894minus1

119878) minus Δ119875

0= Δℎ119894

119878 (4)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878+ 119905119867le 119905eg

1198811015840= 119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)


119881119895119895+1=

119881min119895119895+1 119881

1015840lt 119881

min119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868

119871119878119868


le 1198811015840le max119881max

119878119868

119871119878119868


(5)


Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878 (6)



119868) minus Δ119875

0= Δℎ119894

119895 (7)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894


119878) minus Δ119875

0= Δℎ119894

119878 (8)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878le 119905eg 119881

1015840=

119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)


Stop 1

Stop 2Stop 3 Stop 4

Stop 5

Stop 6

Stop 7

Stop 8

Stop 9

Stop10

Stop 11

Stop 12

Stop 13

Stop 14

N







119881119895119895+1=

119881max119895119895+1 119881

1015840gt 119881

max119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868119871119878119868


le 1198811015840le max119881max

119878119868119871119878119868


(9)

where 119881119878119868







119867


max119867


119878119868is the




119878is






Arrij



Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop



Depi1i = i + 1

i le 108

Dispatch module


Control module



4 Case Study





119895= 120572 + 120573119887 and





0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Bus operator

Traffic manager


Interval traveltime



Intersectioncontrol

Departure headway

Holding control


Start




Too slow



Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No


next cyclerdquo

Fail

Fail


plan



Delaynotification


Bus holding




Space

Stop

Time


Max

imum

allo

wed

spee

d

Curre

nt sp

eed

Min

imum

allow

ed sp

eed


Headway at stop






Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878+ 119905119867= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867

(2)



119868) minus Δ119875

0= Δℎ119894

119895 (3)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867minus Dep119894minus1

119878) minus Δ119875

0= Δℎ119894

119878 (4)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878+ 119905119867le 119905eg

1198811015840= 119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)


119881119895119895+1=

119881min119895119895+1 119881

1015840lt 119881

min119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868

119871119878119868


le 1198811015840le max119881max

119878119868

119871119878119868


(5)


Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878 (6)



119868) minus Δ119875

0= Δℎ119894

119895 (7)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894


119878) minus Δ119875

0= Δℎ119894

119878 (8)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878le 119905eg 119881

1015840=

119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)


Stop 1

Stop 2Stop 3 Stop 4

Stop 5

Stop 6

Stop 7

Stop 8

Stop 9

Stop10

Stop 11

Stop 12

Stop 13

Stop 14

N







119881119895119895+1=

119881max119895119895+1 119881

1015840gt 119881

max119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868119871119878119868


le 1198811015840le max119881max

119878119868119871119878119868


(9)

where 119881119878119868







119867


max119867


119878119868is the




119878is






Arrij



Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop



Depi1i = i + 1

i le 108

Dispatch module


Control module



4 Case Study





119895= 120572 + 120573119887 and





0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Space

Stop

Time


Max

imum

allo

wed

spee

d

Curre

nt sp

eed

Min

imum

allow

ed sp

eed


Headway at stop






Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878+ 119905119867= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867

(2)



119868) minus Δ119875

0= Δℎ119894

119895 (3)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894

119878+ 119905119867minus Dep119894minus1

119878) minus Δ119875

0= Δℎ119894

119878 (4)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878+ 119905119867le 119905eg

1198811015840= 119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)


119881119895119895+1=

119881min119895119895+1 119881

1015840lt 119881

min119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878minus 119905119867+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868

119871119878119868


le 1198811015840le max119881max

119878119868

119871119878119868


(5)


Dep119894119868= Dep119894

119878+ 119905119894

119895119895+1+ 119889119894

119878= Dep119894

119878+119871119878119868

1198811015840+ 119889119894

119878 (6)



119868) minus Δ119875

0= Δℎ119894

119895 (7)


(Dep119894119878+119871119878119868

1198811015840+ 119889119894


119878) minus Δ119875

0= Δℎ119894

119878 (8)


119894

119878+ (1198711198781198681198811015840) + 119889119894

119878le 119905eg 119881

1015840=

119871119878119868(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)


Stop 1

Stop 2Stop 3 Stop 4

Stop 5

Stop 6

Stop 7

Stop 8

Stop 9

Stop10

Stop 11

Stop 12

Stop 13

Stop 14

N







119881119895119895+1=

119881max119895119895+1 119881

1015840gt 119881

max119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868119871119878119868


le 1198811015840le max119881max

119878119868119871119878119868


(9)

where 119881119878119868







119867


max119867


119878119868is the




119878is






Arrij



Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop



Depi1i = i + 1

i le 108

Dispatch module


Control module



4 Case Study





119895= 120572 + 120573119887 and





0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Stop 1

Stop 2Stop 3 Stop 4

Stop 5

Stop 6

Stop 7

Stop 8

Stop 9

Stop10

Stop 11

Stop 12

Stop 13

Stop 14

N







119881119895119895+1=

119881max119895119895+1 119881

1015840gt 119881

max119895119895+1

119871119878119868

(Δℎ119894

119878minus Dep119894

119878minus 119889119894

119878+ Dep119894minus1

119878+ Δ1198750)

min119881min119878119868119871119878119868


le 1198811015840le max119881max

119878119868119871119878119868


(9)

where 119881119878119868







119867


max119867


119878119868is the




119878is






Arrij



Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop



Depi1i = i + 1

i le 108

Dispatch module


Control module



4 Case Study





119895= 120572 + 120573119887 and





0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Arrij



Depij

Check the departure

Yes

Yes

Yes

Yes

j = j + 1

j = j + 1

j le S + I

j le S + I

No

No

No

No

Stop

Stop

Stop



Depi1i = i + 1

i le 108

Dispatch module


Control module



4 Case Study





119895= 120572 + 120573119887 and





0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600


0

200

400

600

21001 21003 21005 21007 21009 21011 21013

Hea

dway

dev

iatio

n (s

)

Stop number

minus200

minus400

minus600

(b) After control








3500036000370003800039000400004100042000

21000 21005 21010 21015

Aver

age w

ait t

ime (

s)

Stop number


2022

2010

2000

2005

2010

2015

2020

2025

Trav

el ti

me o

f the

who

le ro

ute (

s)

Control strategy













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Development and Evaluation of Bus ...downloads.hindawi.com/journals/ddns/2015/928350.pdfDiscrete Dynamics in Nature and Society Generate the travel time ti j 1,j (j2,i2)