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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1

A Traffic Signal Optimization Model forIntersections Experiencing Heavy

ScooterndashVehicle Mixed Traffic FlowsChien-Lun Lan and Gang-Len Chang Member IEEE

AbstractmdashIn response to the need for designing signal plansfor congested intersections caused by heavy scooterndashvehicle mixedflows this paper presents our formulated model for optimizingboth the cycle length and signal timings for isolated intersectionsThe proposed model accounts for the interactions between scooterand vehicle flows and reflects the maneuverability of scooters inthe queue formation and discharging process The robustness ofthe proposed formulations has been evaluated with field data andlaboratory experiments The signal optimization model groundedon such formulations for scooterndashvehicle mixed flows has alsobeen implemented at an intersection and assessed with a rigor-ous before-and-after field analysis Our research concludes thatincorporating the unique properties of scooter flows is essentialfor design and development of effective signal control strategiesto contend with recurrent congestion caused by heavy mixedscooterndashvehicle flows

Index TermsmdashMixed scooterndashvehicle flows optimization trafficsignals

I INTRODUCTION

CONSIDER a congested intersection experiencing heavyvolume of scooter flows as shown in Fig 1 where

scooters with their flexible maneuverability are often able tofilter through vehicle flows and advance to the intersection stopline Due to the need for less space during either the flowpropagation or the formation of standing queues scooters tendto take advantage of the remaining space between passengercar flows to exercise parallel movements within the same travellane and to form multiple queues

This type of urban congestion caused by heavy scooterndashvehicle mixed flows is commonly observable in manydeveloping countries particularly in major Asian cities [1]ndash[4]Inadequate public transport systems coupled with the costand difficulty in finding parking space has incentivized morecommuters to select the scooter as the primary transportationmode and consequently caused more chaos to their congested

Manuscript received March 22 2014 revised July 20 2014 and September15 2014 accepted November 12 2014 This work was supported in part bythe Ministry of Transportation and Communications and in part by the NationalScience Council of Taiwan under Grant 101-2917-I-564-070 The AssociateEditor for this paper was J E Naranjo

The authors are with the Department of Civil and Environmental Engineer-ing University of Maryland College Park MD 20742 USA (e-mail cllanumdedu gangumdedu)

Digital Object Identifier 101109TITS20142376292

Fig 1 Typical approach with scooterndashvehicle mixed traffic flows

urban traffic flows Hence how to effectively contend with suchurban mixed-flow congestion is the foremost concern of trafficcommunities in most developing countries Unfortunatelyneither operational guidelines nor design software for tacklingsuch a complex yet imperative issue is available in state-of-the-art literature or state-of-the-practice studies

Conceivably one of the essential tasks to address the ur-ban congestion by scooterndashvehicle mixed flows is to developeffective tools for design of intersection signal plans and forevaluation of various arterial progression strategies For theformer issue the core of research is to observe and formulatethe interactions between scooter and vehicle flows in the inter-section queue formation and discharging process so that one canoptimize the signal plan with existing control methodologiesAdditional efforts to investigating the interactions and conflictsbetween vehicle and scooter flows in the arterial propagationprocess including car-following and lane-changing behaviorswill be essential for understanding the latter issue and fordeveloping signal progression models

This paper intends to address the first vital issue of producinga reliable tool for signal design for intersections experiencingheavy scooterndashvehicle mixed traffic The focus of the tooldevelopment is to structure a set of convenient yet effectiveformulations to reflect the interdependent relations between thescooter and vehicle queue lines within a travel lane and accountfor the interactions within the mixed scooterndashvehicle flows inthe queue formation and discharging process

1524-9050 copy 2014 IEEE Personal use is permitted but republicationredistribution requires IEEE permissionSee httpwwwieeeorgpublications_standardspublicationsrightsindexhtml for more information


2 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS

II MODELING THE QUEUE FORMATION FOR

SCOOTERndashVEHICLE MIXED TRAFFIC FLOWS

In review of the related literature it is noticeable that mostexisting studies for traffic signal optimization are focusedon intersections with mainly passenger car traffic flows Forexample the class of simulation-based methods employedvarious macroscopic traffic simulation models to capture thevehicle delays and discharging times which in turn serve asthe basis for optimizing signal plan [5]ndash[16] In contrast theschool of mathematical programming models applied analyticalformulations to represent the delays and queues at differentstages of signal operations under various traffic demands andthen solved the optimal cycle length and timing for each phasewith optimization algorithms [17]ndash[28] Some other studiesconcerning network signal design also addressed the interre-lations between the signal plans and the traveler responses totheir route choices [29]ndash[33] The large body of such literaturedespite their significant contributions in arterial signal controlhas not yet addressed any scooter-related traffic issues

Rather than developing control models the very scant re-cent studies on urban scooter traffic issues have focused oninvestigating the scooterndashvehicle mixed flow properties witheither microscopic or mesoscopic simulation methods For ex-ample Arasan and Koshy [34] applied the coordinate-referencemethod to replicate vehiclendashscooter flow movements on a 2-Dplane at the microscopic level and Mathew et al [35] proposeda sublane concept within a travel lane to advance the movementof scooter flows in an arterial Instead of replicating individualscootersrsquo behavior some researchers intended to simulate theirspace needs in exercising longitude and lateral movementsusing the cellular automaton (CA) model [36] [37] Since thephysical space in a travel lane is conceptually viewed as manyequal-size cells in the CA modeling such simulation models aremesoscopic in nature and need extensive field data for param-eter calibration Some researchers also utilized heterogeneoustraffic simulations for describing the level of service in mixedurban traffic flows [38]

Recognizing that understanding the complex scooterndashvehicleflow properties remains at the infancy traffic researchers drivenby the design needs have explored the use of passenger carequivalence (PCE) methods where scooter flows are convertedto an equivalent number of passenger cars Along the same linesome researchers have focused on estimating the PCE valuesbased on the relationship between traffic stream speed and theresulting mixed-flow density in a link [39]ndash[41] For the samepurpose Branston and Zuylen [42] and Hadiuzzaman et al [43]focused on investigating the impact of scooters on the inter-section saturation flow rate and capacity Several researchersalso argued that scooters in the stop queue condition will eitherincrease the start-up lost time of passenger cars or reducetheir saturation flow rate [44]ndash[46] To circumvent the need toaddress scootersrsquo dynamic properties some researchers also ad-ventured the potential of converting passenger cars into scooterequivalent units [47] [48]

Overall among the limited studies for scooterndashvehicle mixedflows the PCE-based methods remain the most popular prac-tice in design of traffic signals in many developing countrieswhere scooters have emerged as one of the primary transport

Fig 2 Queue lengths with various scooter demands

modes However such a convenient conversion method suffersfrom the lack of rigorous algorithms to estimate the mostappropriate PCE that can reliably reflect the actual delays andcongestion caused by the target level of mixed scooterndashvehicleflows Moreover if the congested traffic volume consists ofa large share of scooter flows their conversion to PCEs mayresult in unrealistically long intersection traffic queues Thisis due to the fact that the PCE conversion may reflect tosome extent the equivalent volume impact from scooters butcannot capture the maneuverability of scooters that often formsa substantially short queue length from the intersection stop line(see Fig 2) Failing to account for the impact of scooters onthe intersection queue formation and discharging process maysignificantly overestimate the required green time for signalizedintersections and yield an unrealistic bandwidth on the designof arterial progression

This paper presents our research results on developing atraffic signal optimization model for isolated intersections ex-periencing heavy scooterndashvehicle mixed flows Unlike existingstudies the proposed signal optimization model explicitly con-siders the interaction between cars and scooters By includingthe large volume of scooter traffic the model can produce thesignal plan that better responds to the needs of scooterndashvehiclemixed traffic behavior and yields less traffic delays The re-maining sections are organized as follows Sections IIIndashV detailthe formulations to capture the mixed-flow queue formationand discharging process at an intersection approach followedby presentation of the signal optimization objective functionand solution heuristics in Section VI Summary of the exten-sive field assessment and a before-and-after study with ourdeveloped model are presented in Section VII Concludingcomments along with future research needs constitute the coreof the last section

III MODELING THE QUEUE FORMATION OF

SCOOTERndashVEHICLE MIXED TRAFFIC FLOW

Consider a typical approach with scooterndashvehicle mixedtraffic flows as shown in Fig 1 where each lane can be con-ceptually divided into sublanes to illustrate scootersrsquo movingand queue behavior with other vehicles For convenience ofmodel formulations one can decompose the queue formationprocess of the scooterndashvehicle flows to the intersection stop line


LAN AND CHANG TRAFFIC SIGNAL OPTIMIZATION MODEL FOR INTERSECTIONS EXPERIENCING TRAFFIC FLOWS 3

Fig 3 Flowchart for developing the scooterndashvehicle mixed traffic flow model

into the following consecutive stages 1) upstream arrival andlane choice 2) merging into existing queues and 3) dischargeprocess from the queue line

Fig 3 presents the flowchart for scooterndashvehicle mixed trafficformulations grounded on the field-observed information ofqueue formation and dissipation shown in Fig 4 The proposedscooterndashvehicle model iterates from time index t = 0 to theuser-defined duration T The processes for each time step aredepicted as follows

1) The model will first calculate the upstream arrival ratethe estimated travel time and the lane choice of vehiclesand scooters to derive their respective arriving rates tojoin the existing queue

2) The merging process of scooters takes the scooter arrivingrates and the number of scooters in the spillover queue asinputs and estimate scooter queue formation as follows1) merging into the scooter waiting area 2) formingthe queue parallel to passenger car queue lines and3) calculating the maximum possible number of scootersmerging into the stop queue

Fig 4 Graphical illustration of the scooterndashvehicle queue formation processat an intersection approach

TABLE IGEOMETRY AND VEHICULAR PARAMETERS

3) The merging process for passenger cars and buses con-sists of two parts 1) calculate the potential merging vehi-cles from their arriving rates and the number of vehiclesin the spillover queue and 2) calculate the maximumpossible number of vehicles merging into the stop queue

4) The number of vehicles merging into the stop queuewill be affected by the mutual lane blockage which isestimated by the queue lengths on all lanes For thosevehicles that cannot merge into the stop queue due toblockage or capacity limitation they will form as thespillover queues on the neighboring lanes

5) The scooterndashvehicle mixed discharge process can be thencalculated with the scooterndashvehicle mixed queue and thecorresponding traffic signal at time t

6) The model iterates to the next time step and stops when itreaches the user-defined duration T

To facilitate the presentation of the proposed model somekey notations relating to the geometry design and vehicularparameters are listed in Table I the variables used throughoutthis paper are also summarized in Table II



TABLE IIVARIABLE DEFINITIONS

A Upstream Arrival and Lane Choice

Let Iv[t] denote the flow rate of type-v vehicles entering fromall upstream approaches to the target intersection approachThen those vehicles joining the queue ie Av[t] as shownin Fig 4 can be expressed as

Av

[t+

lceilςv[t]

Δt

rceil]= Iv[t] (1)

where Iv[t] is the flow rate of type-v vehicles entering thisapproach at time step t ςv[t] is their travel time and v = 1 2

and 3 represent the scooter passenger car and bus respectivelySince link travel time varies with the speed of each type ofvehicles one can approximate their travel times from entry tojoin the queue with

ςv[t] =(ϑminus L[t]

)times (uv)

minus1 (2)

where ϑ is the link length uv is the average traveling speed oftype-v vehicles and L[t] is the average queue length across alllanes at time step t

As reflected in most field observations vehicles merginginto a lane group (ie a set of lanes serving the same turningmovement) have a tendency to use the lane exhibiting a shorterqueue and their distributions between queue lanes are generallya function of the existing queue conditions Hence one canformulate the distribution of entering scooterndashvehicle flows tothe available lanes as

alv[t]=Av[t]timesγmv [t]

⎛⎝(

Ll[t])minus1times

⎛⎝ sum

lprimeisinΓ(m)

(Llprime [t]

)minus1

⎞⎠

minus1⎞⎠

l isin Γ(m) (3)

where alv[t] is the arriving flow rate of type-v vehicles at theend of queue on lane l during the tth time interval γm

v [t] is theturning ratio toward movement m for type-v vehicles duringthe tth time interval and Ll[t] is the queue length of lane lserving movement m at the time step t The first two termsof (3) represent the flow rate of vehicles (except for scooters)entering a certain lane group and the third term is the ratiobetween the queue length on lane l and the sum of the queuelength on all lanes serving the movement m

Note that since scooters have a tendency to use the rightmostlane in a lane group a lane preference factor ηml is thusintroduced for scootersrsquo preference ie

al1[t] = A1[t]times γm1 [t]times ηml (4)

Naturally the summation of all scooter lane preference factorsserving movement m shall equal one that is

suml η

ml = 1In an approach containing a scooter waiting area (4)

should be modified to accommodate the geometry featuresFor instance scooters for through movement will merge into ascooter waiting area if the space available for queuing existsNote that the number of scooters merging into the scooterwaiting area will not contribute to the queue formations on eachlanes Hence let Q[t] be a variable representing the numberof scooters merging into the scooter waiting area and one canrewrite (4) as

al1[t] =(A1[t]times γm

1 [t]minus Q[t])times ηml m = 1 (5)

where γm1 [t] stands for the turning ratio of scooters on move-

ment m at time t m = 1 2 and 3 represent the through left-turn and right-turn movements respectively



Fig 5 Graphical illustration of the sublane concept

B Merging Into Queues

It is noticeable that the lateral space needed to merge intothe queue varies among vehicle types Since the field datareveal that each typical travel lane is most likely to concurrentlyaccommodate three parallel lines of scooters this paper thus hasdivided each lane into three sublanes as illustrated in Fig 5to capture the queue pattern of scooters Based on the requiredwidth for moving and queuing a bus is assumed to occupy threesublanes whereas a passenger car and a scooter are assumed tooccupy two and one sublanes respectively

1) Merging Process for Scooters As scooters arriving at theend of queue on the target approach their merging behaviorsmay vary with the encountered queue conditions For exam-ple these merging behaviors include the following 1) if thearriving scooters face an empty lane they will spread equallyacross all sublanes on the target travel lane 2) if the arrivingscooters approach a lane with some vehicles already stoppedin the queue they will try to merge onto the available spacesbetween the queue lines formed by passenger cars and 3) ifthe number of arriving scooters exceed the available spacesbetween passenger car queue lines those overflowed scootersare observed to spread equally across all sublanes on the targetlane Due to the space need of only one sublane the behaviorof the scootersrsquo merging process on a typical passenger car lanecan be described with the following three consecutive steps1) merging into the scooter waiting area (if such a waitingarea exists) 2) forming a queue line in parallel with othervehicles and 3) joining the queue line behind other stoppedvehicles

Merging into the scooter waiting area The scooter wait-ing area (see Fig 4) is a storage space exclusively designedfor scooters queuing at the stop line to accommodate scootersrsquohigh mobility The scooter waiting areas are often set up acrossthrough lanes as shown in Figs 1 and 4 Based on field obser-vations arriving scooters indeed mostly merge into the scooterwaiting areas Once the waiting areas have been fully occupiedscooters will then start to queue on those available travel lanesHence given the storage space of a scooter waiting area thenumber of scooters acceptable to merge into the scooter waitingarea is set as

Q[t] = minA1[t]times γ1

1 [t] χminus X[t]times (1 minus g1[t]) (6)

where X[t] is the number of scooters queued at the scooterwaiting area at time t χ is the storage space of scooter waitingarea and g1[t] is a binary variable indicating a green phase forthe through movement

Forming the queue lines on a sublane parallel to passengercar queue line (see Fig 5) For scooters arriving at the end ofqueue and not able to maneuver to the scooter waiting area theywill form a queue on the shortest sublane within their selectedlanes To estimate the number of scooters forming a queueline parallel to the passenger car queue line it is necessary toknow the available storage space and the number of arrivingscooters

To calculate the space available for scooters to form a queueline parallel to passenger car queue in the same lane one needsto estimate the existing queue length on each sublane whichis the summation of vehicle lengths multiplied by the numberof vehicles in queue by vehicle type ie

sumv τv middot xlβ

v [t] whereτv is the average length of a type-v vehicle and xlβ

v [t] is thenumber of type-v vehicles in queue on sublane β of lane l attime t

The available space for scooters to queue on a sublane paral-lel to passenger car queue ie φl[t] can be approximated withthe difference between the maximum queue length among allsublanes and the summation of queue lengths on each sublaneThus the available storage space for scooters to form a queueparallel to the queue line for passenger cars on the same lanecan be expressed as

φl[t]=maxβ

(sumv

τv middot xlβv [t]

)timesW lminus

sumβ

sumv

τv middot xlβv [t] (7)

where W l is the number of sublanes on lane l which is set to 3in Fig 5

Notably (τ1)minus1 times φl[t] denotes the number of scooters thatcan form a queue with the space of φl[t] Since the number ofscooters allowed to merge into a sublane ie ϕl[t] depends onboth the number of scooters arriving from upstream ie al1[t]and scooters already in a queue preceding to spillover queuefrom neighboring turn bay ie X l

1[t] (which will be simplifiedas ldquopreceding queuerdquo hereafter) one can show such relations as

ϕl[t] = minal1[t] + X l

1[t] (τ1)minus1 times φl[t]

(8)

Joining sublane queues behind other vehicles (see Fig 5)If the sublane space neighboring to the stopped vehicles cannotaccommodate all arriving scooters the remaining scooters needto mix with other types of vehicles and join the vehicle queueThe number of such scooters can be shown as

P l1[t] = al1[t] + X l

1[t]minus ϕl[t] (9)

where al1[t] is the number of arriving scooters on lane l duringthe tth time interval X l

1[t] is the number of scooters in thepreceding queue waiting to merge into lane l at time t and ϕl[t]denotes the number of scooters that form a parallel queue onlane l at time t

2) Maximal Possible Number of Vehicles Merging Into aStop Queue Note that the number of vehicles that may join thequeue on lane l denoted by P l

v[t] includes not only vehiclesarriving at the end of queue but also those already in thepreceding queue from the last time interval due to either the



Fig 6 Graphical illustration of the lane spillover and mutual blockage

lane blockage (shown as X lv[t] in Fig 6 for travel lanes) or

spillover from a neighboring turning bay (shown as X lv[t] for

turn bays)Hence the maximal possible number of vehicles that may

merge into the queue on lane l at time t can be expressed as

P lv[t] = alv[t] + X l

v[t] for travel lanes (10)


v[t] for turning-bays (11)

Let the available storage capacity of a lane be the differencebetween the length of a lane and its standing queue (ie Λl minusLl[t]) then such capacity can be shared by all types of vehiclesbased on their share of arriving flow rate (P l

v[t]) in the totalarriving flows (

sumv P

lv[t]) Hence the maximum flow rate of

type-v vehicles which may merge into the stop queue on lanel ie M l

v[t] can be expressed as

M lv[t]=P l

v[t]times(sum

vprime

P lvprime [t]

)minus1

times[(τv)

minus1times(ΛlminusLl[t]

)](12)

where τv is the average length of a type-v vehicle Λl is thelength of lane l and Ll[t] is the queue length on lane l at time tThe first term shows the proportion of available space shared byeach vehicle type and the second term represents the availablequeue space on lane l

IV BLOCKING EFFECT DUE TO

INSUFFICIENT BAY LENGTH

Note that the queue storage space available in each turn-ing lane or bay may not be fully utilized by the arrivingscooterndashvehicle mixed flow due to the differences in theirrequired physical space and the potentially insufficient baylength

The mutual blockage may occur when 1) the queue lengthon a through lane exceeds the entrance of its adjacent turningbay and 2) the queue vehicles on a turning bay have spilled overtheir storage space and thus block vehicles on the neighboringlane Those that could not merge into their target turning baysupon arrival are called spillover queues ie X l

v[t] where somelater arriving through vehicles ie X l

v[t] are often blocked bysuch spillover queues during their designated discharging timethus forming a second batch of queue line behind the spilloverqueue

Fig 7 Blocking effects of passenger cars and scooters

Fig 6 illustrates the blockage to left-turn vehicles caused bythe through queue traffic The binary variable ie bl[t] is usedto denote if a lane is blocked at time t ie

bl[t]=

1 if Llprime [t]gtΛl and lane lprime is adjacent to lane l0 otherwise

(13)

In summary the queue length on a lane actually consists ofthree types of queue vehicles 1) stop queues 2) vehiclesstopped behind vehicles spilling over from adjacent lanes and3) spillover queues from the adjacent lanes Therefore theactual queue length on a target lane can be estimated with thefollowing expression

Ll[t] = maxβ

(sumv


)

+sumv

(πlv

)minus1 middot τv middot X lv[t] +

sumv

(πlv

)minus1 middot τv middot X lprime

v [t] (14)

The first term in (14) represents the length of the vehicles in thestop queues the second term estimates the length of vehiclesqueued behind vehicles spilling over from the adjacent laneswhereas the third term reflects the length of spillover queuesfrom the adjacent lanes

A Blocking Impacts by Different Types of Vehicles

Different from passenger cars scooters prior to join thevehicle queue line often intend to take advantage of availablesublane space parallel to the existing queue line as shown inFig 7 However under the typical lane width of 36 m (12 ft)a spillover bus is observed to completely block the arrivingvehicles from merging into the available downstream spaceIn contrast a queuing passenger car about 2 m wide maycompletely block the arriving cars and buses but can onlypartially block the arriving scooters To reflect such blockageimpacts let the lane width be denoted by W l and the width ofa type-v vehicle be assumed as wv Then the reduction in theflow rate for those overtaking scooters will be wvW

l where abus is assumed to block the scooters completely Equation (15)uses a simple binary indicator to define the blockage status of agiven lane ie

κlv[t] =

1 if X lprime

v [t] ge 00 otherwise

(15)

where κlv[t] denotes whether lane l is blocked by type-v vehi-

cles or not



Therefore the reduced flow rate for scooters due to a laneblockage can be then calculated as

ωl1[t] = min

sumv=23

wv times(W l

)minus1 times κlv[t] 1

(16)

As for other vehicle types no overtaking is possible whenblockage occurs The reduced flow rate can be computed withthe following expression

ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)

B Queue Formation Considering the Storage SpaceLimitation and Blocking Effect

Conceivably the actual vehicle flows to form the queue on alane should depend on the following 1) the arriving distributionof different types of vehicles and 2) the presence of laneblockages Hence the total number of type-v vehicles joiningthe queue on lane l at time step t is given by

Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)

where the first term gives the maximum merging flow due tostorage limitation and the second term considers the reducedflow rate due to lane blockage

The arriving scooters to queue behind existing vehicle queueline are assumed to spread across all sublanes as shown in

qlβ1 [t] =(πl1

)minus1 timesQl1[t] (19)

Note that either passenger car or bus flows will form a singlequeue on each lane following a typical queue-flow patternMoreover those arriving vehicles which cannot merge intotheir target turn bay and spill over to a neighboring lane canbe shown as

X lv[t+1]=

(P lv[t]minusQl

v[t])middotΔt if l is a turning-bay (20)

where P lv[t] is the number of vehicles that may join the queue

on turn bay l at time t and Qlv[t] is the number of vehicles that

actually join the queueAs for vehicles forming a queue line behind those spillover

vehicles they can be approximated as

X lv[t+1]=

(P lv[t]minusQl

v[t])middotΔt if l is a turning-lane (21)

V DISCHARGE PROCESS

The discharge process in scooterndashvehicle mixed flows differssignificantly from vehicle-only scenarios First scooters oftendo not follow the lane discipline and often drive in parallel withother vehicles Second traffic queues on those lanes connectedto the scooter waiting area will discharge after those scootersin the scooter waiting areas Hence scooters depending on thelocation they choose to stop may discharge both concurrentlyor sequentially with other vehicles

Fig 8 Graphical illustration of the discharging process

A Discharge Process in the Scooter Waiting Area

Scooter waiting areas include only scooter flows whichallows several rows of scooters to concurrently discharge inparallel at the onset of the green phase One can thus show thedischarge flow rate of scooters in this area as

D[t]=minQ[t]middotΔt+X[t] (π)minus1times(h1)

minus1timesg1[t]times(Δt)minus1

(22)

where π is the number of parallel scooters discharging from thescooter waiting area h1 is the average discharge headway ofscooters and g1[t] is a binary variable indicating if the throughmovement is given the green phase or not at time step t

Therefore for scooter queues on a scooter waiting area theflow conservation can be formulated as

X[t+ 1] = X[t] +(Q[t]minus D[t]

)middotΔt (23)

B Discharge Process for a Lane of Mixed Flows

Note that due to the discrepancy in the occupied space andoperational features (eg discharge headways and parallel driv-ing rows) the discharge flow rate varies between different vehi-cle types where scooters certainly have the highest dischargerate To account for the green time needed to discharge thetraffic flows having multiple vehicle types this paper proposesthe use of a mixed discharge rate weighted with the numberof each type of vehicles in the queue Fig 8 illustrates thedischarging process of scooterndashvehicle mixed flows where Ov

represents the occupied space of a type-v vehicle hv denotesthe average discharge time lag following a type-v vehicleand πl

v is the number of parallel driving lines for type-vvehicles

More specifically considering the difference in dischargeheadways occupied space number of vehicles in queue andparallel driving behavior one can approximate the averagedischarge rate of the scooterndashvehicle flow ie Sl[t] with

Sl[t] =

⎛⎝sumvX l

v[t] middot πlv middot hv middotOvsum

vX l

v[t] middotOv

⎞⎠

minus1

(24)

where πlv is the number of parallel discharging type-v vehicles

on lane l hv is the average discharge headway of a type-vvehicle Ov is the occupied space of a type-v vehicle and X l

v[t]is the number of type-v vehicles in queue on lane l at timestep t

Giving the preceding mixed-flow discharge rate the actualdischarge rate during the green phase for each vehicle type is



assumed to be proportional to its ratio in the total scooterndashvehicle mixed flow and can be shown as

slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)

where slv[t] is the discharge rate for type-v vehicles on lane l attime step t

Since the total vehicle demand to the target intersectionapproach is the summation of vehicles joining the queue ieQl

v[t] and those already in the queue ie X lv[t] the actual

departing flow rate from lane l at time step t shall be ex-pressed as

Dlv[t]=min

Ql

v[t]middotΔt+X lv[t] s

lv[t]timesgm[t]

times(Δt)minus1 l isinEs (26)

where gm[t] is a binary variable indicating a green phase for themovement m served by lane l and lane l is not affected by thescooter waiting area

However for those lanes affected by the scooter waiting areadenoted by Es (26) needs to be further modified as shown in

Dlv[t] = min

Ql

v[t] middotΔt+X lv[t] s

lv[t]times gm[t]

times(Δt)minus1 times E[t] l isin Es (27)

where E[t] is a binary variable indicating whether the scooterwaiting area is empty or not at time step t ie

E[t] =

1 if X[t] = 00 otherwise

(28)

Note that the total number of scooters can be discharged froma lane equal the summation of scooters discharging from allsublanes It is assumed that the distribution of the discharge rateamong all sublanes is based on their respective scooters in thequeue which can be formulated as

dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)

By considering the merging and discharging flow rates thenumber of scooters in queue on a sublane can be updated as

xlβv [t+1]=xlβ

v [t]+(qlβv [t]minusdlβv [t]

)middotΔt for βisinB(l)Bs(l)

(30)

where B(l) is the set of all sublanes on lane l and Bs(l) is theset of sublanes serving scooters forming a queue parallel to carqueue line on lane l

However since scooters may form a queue on a sublaneparallel to the passenger car queue line one needs to add anadditional term to (30) as

xlβ1 [t+1]=xlβ

1 [t]+(qlβ1 [t]+ϕl[t]minusd lβ

1 [t])middotΔt

for βisinBs(l) (31)

where ϕl[t] is the number of scooters that merge into sublane βparallel to other stopped vehicles on lane l at time step t

VI SIGNAL OPTIMIZATION MODEL

AND SOLUTION HEURISTICS

A Objective Function

The primary objective of the signal optimization model asshown in (32) is to minimize the total queue delays in thecontrolled area within a given time period ie

minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)

where i denotes the index of intersection approaches Standardequations representing the signal operation constraints areshown in

C ge Cmin C le Cmax (33)

Gp ge Gpmin GP le C forall p (34)sum

p

Gp + Ip = C (35)

Equation (33) ensures the cycle length ie C to lie betweenthe given minimum ie Cmin and maximum ie Cmax cyclelengths Equation (34) indicates that the green time for phase pshould be more than the given minimum green time ie Gp

minbut less than the cycle length The condition that the summationof phase durations and interphase lost times ie Ip shouldequal the cycle length is guaranteed in (35) The phase statusutilized in formulating traffic evolution can be generated with

gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1

(Gj + Ij) lt mod(t C)

lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)

gm[t] = gp[t]timesΨpm (37)

where (36) determines the value for binary variable gp[t] whichis used to indicate whether it is phase p or not at time t gp[t]is multiplied by a given phase-movement incidence matrix ieΨp

m to show the green time for each movement gm[t]In summary the signal optimization model for an intersec-

tion with heavy scooter flows can be recapitulated as

minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

st Equations (1)ndash(31) and (33)ndash(37)

B Solution Heuristics

Since the proposed signal optimization model consists ofnonlinear constraints and binary variables it is naturally moreefficient to develop proper heuristics to generate solutionsThe idea behind the heuristics is to provide a set of signaltimings which satisfies traffic demands from each approach



under undersaturated conditions To do so an iterative methodwhich aims to eliminate residual queues on all intersectionapproaches with the optimal green timing allocation for eachphase is proposed as follows

Step 1 Initialization

mdash Given the initial timing plan

Set Gp = Gpmin C =

sump

Gp + Ip (38)

Step 2 Estimate the traffic evolution with thescooterndashvehicle mixed traffic model

mdash Estimate the residual queues for each move-ment ie Rmv in each approach with theunderlying traffic evolution models that is(1)ndash(31) (36) and (37)

Step 3 Calculate the signal improvement direction

mdash Estimate the average discharge rate for type-vvehicles on a movement ie smv by

smv=sumt

suml

slv[t]timesgm[t]times(sum

t

gm[t]

)minus1

forall lisinΓ(m) (39)

mdash Estimate the additional green time ie gm forthe need of all vehicle types on a movement by

gm = maxv

Rmv times (smv)

minus1 (40)

mdash Set the length of an increment for green time fora phase by

Gp = maxm

gm forall movement m served by phase p (41)

Step 4 Stopping rule

mdash If 1) Gp = 0 or 2) C =sum

p(Gp + Gp) + Ip ge

Cmax stop and output the signal timings ieGp If not continue to step 5

Step 5 Update signal timings

mdash Update the signal timing by Gp = Gp + Gp andC =

sump G

p + Ip go to step 2

VII EVALUATION OF THE PROPOSED

FORMULATIONS WITH FIELD DATA

Since the effectiveness of the proposed optimization modelfor scooterndashvehicle mixed flows hinges on the reliability ofthe underlying formulations for queue formation and dischargethis paper has conducted several evaluations with field data Thefirst assessment compares the cumulative throughputs per laneand per vehicle type between the field-observed and model-produced results whereas the second comparison shows thediscrepancy of the queue evolution process reflected in theactual data and the modelrsquos output The results of those twocomparisons with field data offer the basis to assess the ap-plicability of the proposed model The proposed model has

Fig 9 Survey site

been also implemented at an intersection for a before-and-afterperformance comparison

A Evaluation of the Per-Lane Cumulative Throughputs

Fig 9 shows the field site where the target approach includesone right-turn lane (150M) two through lanes (150M) and oneleft-turn bay (35M) A scooter waiting area is present precedingthe two through lanes

The data were collected on November 7 2013 between0400 PM and 0500 PM with two camcorders mountedover the target approach The per-lane and per-vehicle-typetraffic counts are aggregated in intervals of 5 min as shown inTable III The total volume consists of 1325 vehicles of which414 are scooters 558 are passenger cars and 28 arebuses The signal phases for the target approach are shown inFig 10 where the cycle length is 140 s and the green times ofthose phases are set as 60 30 and 50 s respectively

Fig 11 shows the cumulative throughputs between the modeland the field data Table IV recapitulates the difference betweenthe model-produced and the field-observed cumulated through-puts The overall difference in percentage across all lanes issummarized in the last row

Notably the differences between the total scooter through-puts by the model and from the field data fall between 8 and minus5given the total scooter throughput of 549 The same comparisonresults lie within the range of 4 and minus12 out of the totalthroughput of 739 passenger cars It should be mentioned thatthe discrepancy falls between 6 and minus9 for the bus throughputis relatively high which is inevitable due to its very smallvolume Overall the results of throughput comparison showthat the proposed formulations for scooterndashvehicle mixed flowscan reasonably reflect the actual traffic conditions

B Queue Formation and Discharging Process

Queue lengths and clearance times are the most criticalparameters for design of a signal plan The evaluation comparesthe field collected queue lengths and queue clearance timeswith those from the proposed model The field data werecollected by a video camera over a four-lane arterial as shown



TABLE IIIDISTRIBUTION OF TRAFFIC COMPOSITION FROM THE FIELD DATA

Fig 10 Phasing design for the target intersection

Fig 11 Model-produced versus field-observed cumulated throughputs

in Fig 12 The lanes are numbered from the leftmost lanetoward the rightmost lane A scooter waiting area is presentpreceding two rightmost lanes The stop queue length and thenumber of arriving and departing vehicles are recorded in a per-second basis for comparison The vehicles initially in queue arereported in Table V

As shown in Fig 13 the general shape of the model outputand the field data are sufficiently close The queue length esti-mated with the proposed formulations for scooterndashvehicle flowsis compared with field data and reported in Table V whichconfirms the promising features of the proposed model for fieldapplications The queue lengths estimated by PCEs (ranging

from 015 to 035) are also listed in Table V It is noticeable thatusing a PCE-based conversion method may yield unrealisticlong queues for those scenarios with high volumes of scooters

C Field Applications With the ScooterndashVehicle MixedFlow Model

The proposed signal optimization model has been imple-mented at an intersection with the signal phasing shown inFig 10 Traffic volumes were collected on November 7 duringthe peak hours (0500 PM to 0600 PM) and the total trafficvolume was about 5876 vehicles of which 674 are scooters306 are passenger cars and 2 are buses (see Table VI)The resulting signal timings based on the field data are shownin Table VII

The total traffic demand on November 12 for the aftersurvey was around 5876 vehicles but with different flow ratiosAmong them 658 are scooters 324 are passenger carsand 18 are buses Delays at each approach were collectedwith two camcorders mounted over the approach and one cam-corder at the upstream entrance of the approach The before-and-after comparison per approach delay with respect to vehicletype is reported in Table VIII The results show a reduction of392 in the total delay except for buses due to its very smallvolume

VIII CONCLUSION

This paper has presented an optimization model for design ofintersection signal timings under heavy scooterndashvehicle mixedtraffic flows To capture the spatial interactions between scoot-ers and vehicles this paper has proposed a set of formula-tions to reflect the queue formation and discharging processat intersection approaches Our extensive investigation resultsconfirm that the proposed model can yield realistic estimates ofthroughputs queue lengths and queue clearance times for themixed traffic flows A field implementation at an intersection ofheavy scooter flows and the before-and-after comparison alsoconfirmed the effectiveness of the proposed model



TABLE IVDIFFERENCES BETWEEN THE MODEL-PRODUCED AND FIELD-OBSERVED CUMULATED THROUGHPUTS

Fig 12 Site for field observations of the queue formation and dischargingprocess

TABLE VNUMBER OF VEHICLES AND QUEUE LENGTH

PRIOR TO THE DISCHARGE PROCESS

Future extensions along the same line shall include formu-lations of the scooterndashvehicle flow propagation along a linkand development of arterial progression models for traffic flowswith a high percentage of scooters The impact of high bus flowson the propagation of the scooterndashvehicle mixed flows shouldbe also a vital research subject

Fig 13 Comparison of queue length between the model output and the fieldresults

TABLE VITRAFFIC DEMANDS AT THE TARGET INTERSECTION (NOVEMBER 7 2013)

TABLE VIIORIGINAL SIGNAL PLAN AND MODEL OUTPUT

ACKNOWLEDGMENT

The authors would like to thank Dr H-J Cho for his con-structive suggestions during the entire research They would



TABLE VIIIBEFORE-AND-AFTER COMPARISON OF

PER VEHICLE DELAY PER APPROACH

also like to thank the transportation team members of NationalChiao Tung University and National Taiwan University forcollection and preliminary documentation of field data

REFERENCES

[1] P A Barter ldquoUrban transport in Asia Problems and prospects for high-density citiesrdquo Asia-Pac Develop Monit vol 2 no 1 pp 33ndash66 2000

[2] T P Hsu A F Mohd Sadullah and X D Nguyen ldquoA comparative studyon motorcycle traffic development of Taiwan Malaysia and VietnamrdquoJ East Asia Soc Transp Stud vol 5 pp 381ndash395 2003

[3] L V Leong and A F Mohd Sadullah ldquoA study on the motorcycle owner-ship A case study in Penang State Malaysiardquo in Proc Eastern Asia SocTransp Stud 2007 vol 7 pp 528ndash239

[4] A S Almselati R A Rahmat and O Jaafar ldquoAn overview of urbantransport in Malaysiardquo Soc Sci vol 6 no 1 pp 24ndash33 2011

[5] D I Robertson ldquoTRANSYT A traffic network study toolrdquo Road ResLab Berkshire UK LR-253 1969

[6] G C Drsquoans and D C Gazis ldquoOptimal control of oversaturated store- andforward transportation networksrdquo Transp Sci vol 10 no 1 pp 1ndash19Feb 1976

[7] N H Gartner ldquoOPAC A demand-responsive strategy for traffic signalcontrolrdquo Transp Res Rec vol 906 pp 75ndash81 1983

[8] D I Robertson and R D Bretherton ldquoOptimizing networks of trafficsignals in real timemdashThe SCOOT methodrdquo IEEE Trans Veh Technolvol 40 no 1 pp 11ndash15 Feb 1991

[9] TRANSYT-7F User Manual Federal Highway AdministrationWashington DC USA 1991

[10] M Papageorgiou ldquoAn integrated control approach for traffic corridorsrdquoTransp Res C Emerging Technol vol 3 no 1 pp 19ndash30 Feb 1995

[11] S C Wong ldquoGroup-based optimization of signal timings using theTRANSYT traffic modelrdquo Transp Res B Methodol vol 30 no 3pp 217ndash244 Jun 1996

[12] P Mirchandani and L Head ldquoA real-time traffic signal control systemArchitecture algorithms analysisrdquo Transp Res C Emerging Technolvol 9 no 6 pp 415ndash432 Dec 2001

[13] T H Chang and G Y Sun ldquoModeling and optimization of an oversat-urated signalized networkrdquo Transp Res B Methodol vol 38 no 8pp 687ndash707 Sep 2004

[14] TRANSYT 14 User Guide TRL Software Wokingham UK 2010[15] Y Liu and G L Chang ldquoAn arterial signal optimization model for inter-

sections experiencing queue spillback and lane blockagerdquo Transp Res CEmerging Technol vol 19 no 1 pp 130ndash144 Feb 2011

[16] Y Y Chen and G L Chang ldquoA macroscopic signal optimization modelfor arterials under heavy mixed traffic flowsrdquo IEEE Trans Intell TranspSyst vol 15 no 2 pp 805ndash817 Apr 2014

[17] R E Allsop ldquoEstimating the traffic capacity of a signalized road junc-tionrdquo Transp Res vol 6 no 3 pp 245ndash255 Sep 1972

[18] N H Gartner J D C Little and H Gabbay ldquoOptimization of trafficsignal setting by mixed-integer linear programming Part I The net-work coordination problemrdquo Transp Sci vol 9 no 4 pp 321ndash343Nov 1975

[19] N H Gartner J D C Little and H Gabbay ldquoOptimization of trafficsignal setting by mixed-integer linear programming Part II The net-work synchronization problemrdquo Transp Sci vol 9 no 4 pp 344ndash363Nov 1975

[20] N H Gartner S F Assmann F L Lasaga and D Hou ldquoA multi-band ap-proach to arterial traffic signal optimizationrdquo Transp Res B Methodolvol 25 no 1 pp 55ndash74 Feb 1991

[21] J D C Little M D Kelson and N H Gartner ldquoMAXBAND A programfor setting signals on arterials and triangular networksrdquo Transp Res Recvol 795 pp 40ndash46 1999

[22] B G Heydecker and I W Dudgeon ldquoCalculation of signal settings tominimise delay at a junctionrdquo in Proc 10th Int Symp Transp TrafficTheory 1987 pp 159ndash178

[23] C K Wong and S C Wong ldquoA lane-based optimization method forminimizing delay at isolated signal-controlled junctionsrdquo J Math ModelAlgorithm vol 2 no 4 pp 379ndash407 Dec 2003

[24] C K Wong and S C Wong ldquoLane-based optimization of signal timingsfor isolated junctionsrdquo Transp Res B Methodol vol 37 no 1 pp 63ndash84 Jan 2003

[25] C K Wong S C Wong and C O Tong ldquoA lane-based optimizationmethod for the multi-period analysis of isolated signal-controlled junc-tionsrdquo Transportmetrica vol 2 no 1 pp 53ndash85 Jan 2009

[26] R E Allsop ldquoSIGSET A computer program for calculating traffic ca-pacity of signal-controlled road junctionsrdquo Traffic Eng Control vol 12pp 58ndash60 1971

[27] R E Allsop ldquoSIGCAP A computer program for assessing the trafficcapacity of signal-controlled road junctionsrdquo Traffic Eng Control vol 17pp 338ndash341 1976

[28] G Improta and G E Cantarella ldquoControl systems design for an individualsignalized junctionrdquo Transp Res B Methodol vol 18 no 2 pp 147ndash167 Apr 1984

[29] R E Allsop ldquoSome possibilities for using traffic control to influencetrip destinations and route choicerdquo in Proc 6th Int Symp Transp TrafficTheory 1974 pp 345ndash374

[30] N H Gartner ldquoArea traffic control and network equilibriumrdquo in ProcLect Notes Econ Math 1976 vol 118 pp 274ndash297

[31] G E Cantarella G Improta and A Sforza ldquoA procedure for equilib-rium network traffic signal settingrdquo Transp Res A Gen vol 25 no 5pp 241ndash249 Sep 1991

[32] F A Marcianograve G Musolino and A Vitetta ldquoSignal setting optimizationwith route choice behavior and acyclic profiles of vehicular flows inroad networksrdquo Procedia Social Behav Sci vol 54 pp 1330ndash1338Oct 2012

[33] G E Cantarella P Velonagrave and A Vitetta ldquoSignal setting with demandassignment Global optimization with day-to-day dynamic stability con-straintsrdquo J Adv Transp vol 46 no 3 pp 254ndash268 Jul 2012

[34] V T Arasan and R Z Koshy ldquoMethodology for modeling highly het-erogeneous traffic flowrdquo J Transp Eng vol 131 no 7 pp 544ndash551Jul 2005

[35] T V Mathew C R Munigety A Cherian and A Ostawal ldquoA spacediscretization based simulation approach for non-lane based traffic con-ditionsrdquo presented at the Transportation Research Board 93rd AnnualMeeting Washington DC USA Jan 12ndash16 2014 Paper 14-3854

[36] L W Lan and C W Chang ldquoInhomogeneous cellular automata modelingfor mixed traffic with cars and motorcyclesrdquo J Adv Transp vol 39 no 3pp 323ndash349 2005

[37] L W Lan Y C Choiu Z S Lin and C C Hsu ldquoCellular automatonsimulations for mixed traffic with erratic motorcyclesrsquo behavioursrdquo PhysA Stat Mech Appl vol 389 no 10 pp 2077ndash2089 May 2010

[38] B R Marwah and B Singh ldquoLevel of service classification for urbanheterogeneous traffic A case study of Kanapur metropolisrdquo in Proc 4thInt Symp Highway Capacity 2000 pp 271ndash286

[39] G Tiwari J Fazio and S Pavitravas ldquoPassenger car units for heteroge-neous traffic using a modified density methodrdquo in Proc 4th Int SympHighway Capacity 2000 pp 246ndash257

[40] S Putra ldquoThe correction value of passenger-car equivalents for motorcy-cle and its impact to road performance in developing countriesrdquo ProcediaSocial Behav Sci vol 16 pp 400ndash408 2011

[41] A Dhamaniya and S Chandra ldquoConcept of stream equivalency factor forheterogeneous traffic on urban arterial roadsrdquo J Transp Eng vol 139no 11 pp 1117ndash1123 Nov 2013

[42] D Branston and H Zuylen ldquoThe estimation of saturation flow ef-fective green time and passenger car equivalents at traffic signals bymultiple linear regressionrdquo Transp Res vol 12 no 1 pp 47ndash53Feb 1978

[43] M Hadiuzzaman M M Rahman and M A Karim ldquoSaturation flowmodel at signalized intersection for non-lane based trafficrdquo Can JTransp vol 2 no 1 pp 77ndash90 2008

[44] T Nakatsuji G H Nguyen S Tweesilp and Y Tanaboriboon ldquoEffects ofmotorcycle on capacity of signalized intersectionsrdquo Infrastruct PlanningRev vol 18 no 5 pp 935ndash942 Sep 2001

[45] T Rongviriyapanich and C Suppattrakul ldquoEffects of motorcycles ontraffic operations on arterial streetsrdquo in Proc Eastern Asia Soc TranspStud 2005 vol 6 pp 137ndash146



[46] L V Leong W H Wan Ibrahim and A F Mohd ldquoEffect of motorcyclestravel behavior on saturation flow rates at signalized intersections inMalaysiardquo presented at the 23rd ARRB ConfmdashResearch Partnering WithPractitioners Adelaide SA Australia 2008 [Online] Available httpeprintsusmmy135241Effect_of_motorcycles_-_23rd_ARRB_Conferencepdf

[47] C C Minh K Sano and S Matsumoto ldquoThe speed flow and headwayanalyses of motorcycle trafficrdquo in Proc Eastern Asia Soc Transp Stud2005 vol 6 pp 1496ndash1508

[48] N Y Cao and K Sano ldquoEstimating capacity and motorcycle equivalentunits on urban roads in Hanoi Vietnamrdquo J Transp Eng vol 138 no 6pp 776ndash785 Jun 2012

Chien-Lun Lan received the BBA and PhDdegrees from National Chiao Tung UniversityHsinchu Taiwan in 2003 and 2008 respectively

He is a Graduate Research Assistant with theDepartment of Civil and Environmental EngineeringUniversity of Maryland College Park MD USAHis research interests include traffic operation andmanagement

Gang-Len Chang (Mrsquo13) received the BEng de-gree from National Cheng Kung University TainanTaiwan in 1975 the MS degree from NationalChiao Tung University Hsinchu Taiwan in 1979and the PhD degree in transportation engineeringfrom The University of Texas at Austin Austin TXUSA in 1985

He is a Professor with the Department of Civil andEnvironmental Engineering University of MarylandCollege Park MD USA His research interests in-clude network traffic control freeway traffic man-

agement and operations real-time traffic simulation and dynamic control ofurban systems

Dr Chang is a member of the American Society of Civil Engineers (ASCE)He has served as the Chief Editor of ASCE Journal of Urban Planning andDevelopment over the past 13 years



II MODELING THE QUEUE FORMATION FOR

SCOOTERndashVEHICLE MIXED TRAFFIC FLOWS

In review of the related literature it is noticeable that mostexisting studies for traffic signal optimization are focusedon intersections with mainly passenger car traffic flows Forexample the class of simulation-based methods employedvarious macroscopic traffic simulation models to capture thevehicle delays and discharging times which in turn serve asthe basis for optimizing signal plan [5]ndash[16] In contrast theschool of mathematical programming models applied analyticalformulations to represent the delays and queues at differentstages of signal operations under various traffic demands andthen solved the optimal cycle length and timing for each phasewith optimization algorithms [17]ndash[28] Some other studiesconcerning network signal design also addressed the interre-lations between the signal plans and the traveler responses totheir route choices [29]ndash[33] The large body of such literaturedespite their significant contributions in arterial signal controlhas not yet addressed any scooter-related traffic issues

Rather than developing control models the very scant re-cent studies on urban scooter traffic issues have focused oninvestigating the scooterndashvehicle mixed flow properties witheither microscopic or mesoscopic simulation methods For ex-ample Arasan and Koshy [34] applied the coordinate-referencemethod to replicate vehiclendashscooter flow movements on a 2-Dplane at the microscopic level and Mathew et al [35] proposeda sublane concept within a travel lane to advance the movementof scooter flows in an arterial Instead of replicating individualscootersrsquo behavior some researchers intended to simulate theirspace needs in exercising longitude and lateral movementsusing the cellular automaton (CA) model [36] [37] Since thephysical space in a travel lane is conceptually viewed as manyequal-size cells in the CA modeling such simulation models aremesoscopic in nature and need extensive field data for param-eter calibration Some researchers also utilized heterogeneoustraffic simulations for describing the level of service in mixedurban traffic flows [38]

Recognizing that understanding the complex scooterndashvehicleflow properties remains at the infancy traffic researchers drivenby the design needs have explored the use of passenger carequivalence (PCE) methods where scooter flows are convertedto an equivalent number of passenger cars Along the same linesome researchers have focused on estimating the PCE valuesbased on the relationship between traffic stream speed and theresulting mixed-flow density in a link [39]ndash[41] For the samepurpose Branston and Zuylen [42] and Hadiuzzaman et al [43]focused on investigating the impact of scooters on the inter-section saturation flow rate and capacity Several researchersalso argued that scooters in the stop queue condition will eitherincrease the start-up lost time of passenger cars or reducetheir saturation flow rate [44]ndash[46] To circumvent the need toaddress scootersrsquo dynamic properties some researchers also ad-ventured the potential of converting passenger cars into scooterequivalent units [47] [48]

Overall among the limited studies for scooterndashvehicle mixedflows the PCE-based methods remain the most popular prac-tice in design of traffic signals in many developing countrieswhere scooters have emerged as one of the primary transport

Fig 2 Queue lengths with various scooter demands

modes However such a convenient conversion method suffersfrom the lack of rigorous algorithms to estimate the mostappropriate PCE that can reliably reflect the actual delays andcongestion caused by the target level of mixed scooterndashvehicleflows Moreover if the congested traffic volume consists ofa large share of scooter flows their conversion to PCEs mayresult in unrealistically long intersection traffic queues Thisis due to the fact that the PCE conversion may reflect tosome extent the equivalent volume impact from scooters butcannot capture the maneuverability of scooters that often formsa substantially short queue length from the intersection stop line(see Fig 2) Failing to account for the impact of scooters onthe intersection queue formation and discharging process maysignificantly overestimate the required green time for signalizedintersections and yield an unrealistic bandwidth on the designof arterial progression

This paper presents our research results on developing atraffic signal optimization model for isolated intersections ex-periencing heavy scooterndashvehicle mixed flows Unlike existingstudies the proposed signal optimization model explicitly con-siders the interaction between cars and scooters By includingthe large volume of scooter traffic the model can produce thesignal plan that better responds to the needs of scooterndashvehiclemixed traffic behavior and yields less traffic delays The re-maining sections are organized as follows Sections IIIndashV detailthe formulations to capture the mixed-flow queue formationand discharging process at an intersection approach followedby presentation of the signal optimization objective functionand solution heuristics in Section VI Summary of the exten-sive field assessment and a before-and-after study with ourdeveloped model are presented in Section VII Concludingcomments along with future research needs constitute the coreof the last section

III MODELING THE QUEUE FORMATION OF

SCOOTERndashVEHICLE MIXED TRAFFIC FLOW

Consider a typical approach with scooterndashvehicle mixedtraffic flows as shown in Fig 1 where each lane can be con-ceptually divided into sublanes to illustrate scootersrsquo movingand queue behavior with other vehicles For convenience ofmodel formulations one can decompose the queue formationprocess of the scooterndashvehicle flows to the intersection stop line




















Av

[t+

lceilςv[t]

Δt

rceil]= Iv[t] (1)




)times (uv)

minus1 (2)




⎛⎝(

Ll[t])minus1times

⎛⎝ sum

lprimeisinΓ(m)

(Llprime [t]

)minus1

⎞⎠

minus1⎞⎠

l isin Γ(m) (3)






suml η























φl[t]=maxβ

(sumv


)timesW lminus

sumβ

sumv







(8)


P l1[t] = al1[t] + X l



















sumv P




M lv[t]=P l

v[t]times(sum

vprime

P lvprime [t]

)minus1

times[(τv)


)](12)










bl[t]=


(13)


Ll[t] = maxβ

(sumv


)

+sumv

(πlv


sumv

(πlv


v [t] (14)





κlv[t] =

1 if X lprime


(15)


cles or not




ωl1[t] = min

sumv=23

wv times(W l


(16)


ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)



Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)



qlβ1 [t] =(πl1



X lv[t+1]=

(P lv[t]minusQl






X lv[t+1]=

(P lv[t]minusQl


V DISCHARGE PROCESS







(22)




)middotΔt (23)






Sl[t] =

⎛⎝sumvX l


vX l

v[t] middotOv

⎞⎠

minus1

(24)








slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES












































































Av

[t+

lceilςv[t]

Δt

rceil]= Iv[t] (1)




)times (uv)

minus1 (2)




⎛⎝(

Ll[t])minus1times

⎛⎝ sum

lprimeisinΓ(m)

(Llprime [t]

)minus1

⎞⎠

minus1⎞⎠

l isin Γ(m) (3)






suml η























φl[t]=maxβ

(sumv


)timesW lminus

sumβ

sumv







(8)


P l1[t] = al1[t] + X l



















sumv P




M lv[t]=P l

v[t]times(sum

vprime

P lvprime [t]

)minus1

times[(τv)


)](12)










bl[t]=


(13)


Ll[t] = maxβ

(sumv


)

+sumv

(πlv


sumv

(πlv


v [t] (14)





κlv[t] =

1 if X lprime


(15)


cles or not




ωl1[t] = min

sumv=23

wv times(W l


(16)


ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)



Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)



qlβ1 [t] =(πl1



X lv[t+1]=

(P lv[t]minusQl






X lv[t+1]=

(P lv[t]minusQl


V DISCHARGE PROCESS







(22)




)middotΔt (23)






Sl[t] =

⎛⎝sumvX l


vX l

v[t] middotOv

⎞⎠

minus1

(24)








slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES









































































φl[t]=maxβ

(sumv


)timesW lminus

sumβ

sumv







(8)


P l1[t] = al1[t] + X l



















sumv P




M lv[t]=P l

v[t]times(sum

vprime

P lvprime [t]

)minus1

times[(τv)


)](12)










bl[t]=


(13)


Ll[t] = maxβ

(sumv


)

+sumv

(πlv


sumv

(πlv


v [t] (14)





κlv[t] =

1 if X lprime


(15)


cles or not




ωl1[t] = min

sumv=23

wv times(W l


(16)


ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)



Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)



qlβ1 [t] =(πl1



X lv[t+1]=

(P lv[t]minusQl






X lv[t+1]=

(P lv[t]minusQl


V DISCHARGE PROCESS







(22)




)middotΔt (23)






Sl[t] =

⎛⎝sumvX l


vX l

v[t] middotOv

⎞⎠

minus1

(24)








slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES






































































sumv P




M lv[t]=P l

v[t]times(sum

vprime

P lvprime [t]

)minus1

times[(τv)


)](12)










bl[t]=


(13)


Ll[t] = maxβ

(sumv


)

+sumv

(πlv


sumv

(πlv


v [t] (14)





κlv[t] =

1 if X lprime


(15)


cles or not




ωl1[t] = min

sumv=23

wv times(W l


(16)


ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)



Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)



qlβ1 [t] =(πl1



X lv[t+1]=

(P lv[t]minusQl






X lv[t+1]=

(P lv[t]minusQl


V DISCHARGE PROCESS







(22)




)middotΔt (23)






Sl[t] =

⎛⎝sumvX l


vX l

v[t] middotOv

⎞⎠

minus1

(24)








slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES




























































ωl1[t] = min

sumv=23

wv times(W l


(16)


ωlv[t] = min

κl2[t] + κl

3[t] 1 v = 2 and 3 (17)



Qlv[t] = min

P lv[t]M

lv[t]

times(1 minus ωl

v[t]times bl[t])

(18)



qlβ1 [t] =(πl1



X lv[t+1]=

(P lv[t]minusQl






X lv[t+1]=

(P lv[t]minusQl


V DISCHARGE PROCESS







(22)




)middotΔt (23)






Sl[t] =

⎛⎝sumvX l


vX l

v[t] middotOv

⎞⎠

minus1

(24)








slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES




























































slv[t] = Sl[t]times

⎛⎝X l

v[t]times(sum

vprime

X lvprime [t]

)minus1⎞⎠ (25)





Dlv[t]=min

Ql


lv[t]timesgm[t]




Dlv[t] = min

Ql


lv[t]times gm[t]



E[t] =


(28)


dlβ1 [t] =

⎛⎝xlβ

1 [t]times

⎛⎝sum

βprime

xlβprime

1 [t]

⎞⎠

minus1⎞⎠timesDl

1[t] (29)


xlβv [t+1]=xlβ



(30)



xlβ1 [t+1]=xlβ


1 [t])middotΔt







minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt

(32)




p

Gp + Ip = C (35)



gp[t] =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

1 ifpminus1sumj=1


lepminus1sumj=1

(Gj + Ij) +Gp

0 otherwise

(36)





minsumi

sumt

(sumv

suml

(Xil

v [t]+Xilv [t]+Xil

v [t])+Xi[t]

)middotΔt









Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES






























































Set Gp = Gpmin C =

sump

Gp + Ip (38)





smv=sumt

suml


t

gm[t]

)minus1



gm = maxv

Rmv times (smv)

minus1 (40)


Gp = maxm




p(Gp + Gp) + Ip ge




sump G

p + Ip go to step 2




Fig 9 Survey site




















VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES




































































VIII CONCLUSION












ACKNOWLEDGMENT







REFERENCES



































































ACKNOWLEDGMENT







REFERENCES






























































REFERENCES

























































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