Self-organizing Control of Urban Tra c Signal Based on Multiway Intersection … · 2012-06-30 · Self-organizing Control of Urban Tra c Signal Based on Multiway Intersection O set-setting

Self-organizing Control of Urban Traffic Signal

Based on Multiway Intersection Offset-setting Model

WISNU JATMIKO1, ADI WIBOWO2, ABDURRAHMAN S. K.1,HERRY1, A. A. KRISNADHI1, ADE AZURAT1

T. FUKUDA3, K. SEKIYAMA3

1Faculty of Computer Science, 2Dept. of Informatics,3Dept. of Micro-Nano Systems Engineering1Universitas Indonesia, 2Diponegoro University,3Nagoya University1Depok, Jawa Barat, 2Semarang, Jawa Tengah,3Chikusa-ku, Nagoya

1,2INDONESIA, [email protected]

Abstract: This paper proposes a model of distributed self-organizing traffic control with self-organizingmap in real situation. This model can be used as a general setting for controlling almost any type ofintersection. It uses nonlinear coupled oscillator with multiway intersection and automatically adjuststhe cycle time, split, and offset parameter of the controller. Results show increased speed and reduceddelay under all traffic conditions.

Keywords: Urban Traffic Control, Distributed Self-organizing Control, Multiway Intersection

1 Introduction

Traffic control system is an important componentof an intelligent transportation system which isaimed to manage flow of vehicles optimally suchthat congestions and accidents are avoided asmuch as possible. One of its principal applica-tion is implemented as a traffic signaling mech-anism that minimizes delay when vehicles travelthrough several consecutive intersections. Such asystem now has an increasingly significant role inthe light of urbanization, population growth andincreased motorization.

In an urban area where traffic density can eas-ily lead to congestions and jams, a traffic signalnetwork of relatively closely spaced intersectionsneed to operate in a coordinated fashion. Themain objective of such coordination is to regulategreen times, i.e., the duration of the green sig-nals, so that vehicles can travel through some ad-jacent signalized intersections without significantstops and delays. This is often difficult to achievewithin an uncoordinated traffic signal networksince the high traffic density frequently yields ve-hicle queues in front of an intersection that blockother vehicles coming in from neighboring inter-sections. On the other hand, a coordinated signalnetwork will provide a primary benefit of reducedvehicle stops and delays. Such benefits will allow

the traffic to proceed more efficiently, allowing forenergy conservation. Secondarily, a coordinatedtraffic signal network is able to regulate vehiclespeed because signals are set so that more stopsare incurred for vehicles that travel faster than theintended speed. Furthermore, such a coordinatednetwork leads to a more efficient use of intersec-tions by grouping vehicles into platoons [1].

There have been several approaches to solvethe coordinated traffic signal control prob-lem. Wei et al. presented a macroscopic two-dimensional cellular automata model of an urbantraffic signal control system in which each inter-section is regarded as a cell and the flow pressureis treated as the state [2]. Wang et al. used therules of adaptive control system based on geneticstudy classification algorithm to solve the traf-fic signal’s separated, complex, nonlinear featuresand prevent failure of the control rules in urbanregional coordination traffic signal control system[3]. Also, Srinivasan et al. proposed multiagentsystems based on online learning of fuzzy neuralnetworks and hybrid computational intelligencetechniques [4].

In this paper, we develop a coordinated traf-fic signal control system that is based on a dis-tributed self-organizing map. The proposed sys-tem employs an entraintment model from Ku-ramoto [5] to synchronize signals at intersections.

WSEAS TRANSACTIONS on SYSTEMS and CONTROLWisnu Jatmiko, Adi Wibowo, Abdurrahman S. K., Herry, A. A. Krisnadhi, Ade Azurat, T. Fukuda, K. Sekiyama

E-ISSN: 2224-2856 1 Issue 1, Volume 7, January 2012

Figure 1: A real-world urban traffic net with mul-tiway intersection

Our solution is a novel and nontrivial modificationof the model in [6] by explicitly taking into ac-count left and right turns and multiway intersec-tions. The originating model itself has also beenprototyped for real-world situations as describedin [7, 8, 9]. However, it was not equipped to dealexplicitly with left and right turns which are quitecommon in the real-world situations. The prob-lem of dealing with left right turns has also beenattacked by Sekiyama et al. They proposed a self-organizing route guidance system (SRGS) whichcooperates with traffic signal control to handleleft and right turns in an efficient manner [10].However, such a guidance system relies on the in-formation about the travel destinations of eachvehicle; a requirement that is not always easy tosatisfy in many situations. In addition, this ap-proach assumed an idealized model of grid-like in-tersections and hence, not deal with multiway in-tersections which are common in the real world asshown in Fig. 1. We also provide simulation re-sults in a complex map scenario which representscertain areas in Jakarta.

This paper is organized as follows. Section2 describes basic approach of coordinated trafficsignal control. Section 3 describes a developmentof signal network by nonlinear coupled oscillatorwith multiway intersection and adjustment of allthe three parameters (cycle time, spilt and offset)based on the completely decentralized approach.Section 4 describes the simulation of the proposedmodel using a simulator software that we devel-oped. The simulator also provides a visualizationof the simulation to demonstrate the effectivenessof the proposed model under unstructured con-dition like in Indonesia. Results of simulation ofthe proposed model are given at the end of thissection. The paper is concluded in Section 5 to-

gether with some remarks for future directions ofthis research.

2 Coordinated Traffic SignalControl

The common traffic signal parameters for control-ling traffic flow are cycle time, split adjustment,and offset. We assume that a traffic signal com-pletes one round of signaling that consists of aperiod of red signal and a period of green signal.Between the red and green signals, there may bea small, fixed period of clearance time, typicallyrepresented in real situations as a yellow signal.Cycle time denotes the time required for a signalbetween the start of a particular signaling roundto the start of the signaling round that follows.Split is the fraction of the cycle time that is al-located to each phase for a set of traffic move-ments. Offset is the time difference between thebeginning of green phases for a continuous traf-fic movement at successive intersections that maygive rise to a green wave along an arterial [11].

Figure 2: Coordination between nearest intersec-tions for achieving the optimal flow of traffic.

In Fig. 2(a), a vehicle travels from intersec-tion 1 to intersection 4. If the traffic light at in-tersection 1 is green, then intersection 1 will co-ordinate with intersection 2 to control the offsetvalue. This will enable the vehicle to pass throughwithout stopping at intersection 2, as seen in Fig.



Figure 3: Traffic light control optimization resultbetween nearest intersections

Figure 4: Bi-directed graph model for n-way in-tersection.

2(b). Likewise in Fig. 2(c) and Fig. 2(d), thevehicle can go without stopping at intersection 5and 6, allowing it to attain an optimal velocity ofthe vehicles during its travel. The result of trafficlight control optimization can be seen in Fig. 3.

3 Swarm Self-organizing Map

In the following, we describe the traffic signalnetwork model based on swarm self-organizingmap which generalizes for multiway intersections.Sekiyama et al. have presented the original, un-derlying model in [6] in which all intersections arealways assumed 4-way with two main directions oftraffic and arranged in a grid-like network. Here,we extend the model to n-way intersections andalso taking into account left and right turns. Forthe sake of completeness, we will start first withthe original derivation.

3.1 Traffic Signal Network Model

Consider a model of an urban traffic signal Sifor a multiway intersection by bidirected graphas shown in Figure 4. The signal Si is ith signal

in the coordinated signal network containing N(possibly different types of) intersections. EachSi has a cycle time Ti and ni neighboring signalsSij , j = 1, . . . , ni. Note that each Sij which isdefined as a neighbor of a particular Si is also asignal on its own with different value of i in thenetwork.

Let εij be the normalized (incoming) trafficflow from Sij to Si, i = 1, . . . , N , j = 1, . . . , ni,which is defined as follows:

εij =1

ρim · Ti

∫ t+Ti

tρij(t) · dt

ρij(t) =1

Rij

Vij(t)∑k=1

Lijk (t)

where:

• ρim is the road capacity constant from Sij toSi; note that the subscript m is not an indexvalue to signify a constant, unlike the j’s;

• ρij(t) is the (traffic) density from Sij to Si ata particular time t;

• Rij is the road length from Sij to Si;

• Vij(t) is the number of vehicles in the roadfrom Sij to Si at time t;

• Lijk (t) is the length of the kth vehicle in theroad between signal Sij and Si at time t; thisvalue varies in time since the queue of ve-hicles in the road between Sij and Si alsochanges over time; .

3.2 Modelling Signal Network UsingNonlinear Coupled Oscillators

Let φi be the phase description of the signal Sigiven in its modulo-2π value. Each signal Si isviewed as an oscillator whose dynamics is basedon Kuramoto’s model of nonlinear coupled oscilla-tors and has the following generalized formulationbased on phase description:

φi(t) =dφidt

= ωi +K

ni

ni∑j=1

εijΓi(φi, φij) (1)

where Γi is a periodic function such that

Γi(φi, φij) = Γi(φi + 2π, φij) = Γi(φi, φij + 2π)



and ωi =2π

Tiis the natural frequency of Si.

From now on, we use a simple sinusoidal func-tion in place of Γi for the model in (1) as follows,

φi = ωi +K

ni

ni∑j=1

εij sin(φij − φi) (2)

Euler’s formula (eiθ = cos θ + i sin θ) implies that

sin(φij − φi) =ei(φij−φi) − e−i(φij−φi)

2i

which can be used to rearrange (2) as follows:

φi(t) = ωi +K

ni

ni∑j=1

εijei(φij−φi) − e−i(φij−φi)

2i

= ωi +K

2i

(e−iφi

ni∑j=1

εijnieiφij

− eiφini∑j=1

εijnie−iφij

)(3)

If Ai and Bi are defined as follows,

Ai =

ni∑j=1

εijnieiφij Bi =

ni∑j=1

εijnie−iφij (4)

Then (3) can be written as follows,

φi(t) = ωi +K

2i

(e−iφiAi − eiφiBi

)(5)

Again, the Euler’s formula can be used to re-arrange (5) as follows:

φi(t) = ωi +K

2i

((cosφi − i sinφi)Ai

− (cosφi + i sinφi)Bi

)= ωi +

K

2i

((Ai −Bi) cosφi

− (Ai +Bi)i sinφi

)(6)

Then from (4), we obtain

Ai −Bi =

ni∑j=1

εijnieiφij −

ni∑j=1

εijnie−iφij

=

ni∑j=1

εijni

2i

(eiφij − e−iφij

2i

)

= 2

ni∑j=1

εijnii sinφij (7)

Ai +Bi =

ni∑j=1

εijnieiφij +

ni∑j=1

εijnie−iφij

=

ni∑j=1

εijni

2

(eiφij + e−iφij

2

)

= 2

ni∑j=1

εijni

cosφij (8)

If,

ai =

ni∑j=1

εijni

cosφij bi =

ni∑j=1

εijni

sinφij

then (7) and (8) can be written as,

Ai −Bi = 2ibi Ai +Bi = 2ai

Thus, (6) is equivalent to

φi(t) = ωi +K (bi cosφi − ai sinφi) (9)

With the Kuramoto’s model, we aim for anentrainment condition of (2) which is modeled as

φi(t) = ωi +Kσi sin(φi − φi) (10)

where φi is the weighted phase average of theneighboring signals.

Equating (9) and (10) using substraction for-mula of sines yields

bi cosφi − ai sinφi = σi sin(φi − φi)= σi(sin φi cosφi − sinφi cos φi)

= σi sin φi cosφi − σi sinφi cos φi

We thus have for the coefficients of cosφi andsinφi:

bi = σi sin φi ai = σi cos φi (11)

It follows from (11) that

sin φi =biσi

cos φi =aiσi

tan φi =biai

φi = arctan

(biai

)σi =

√a2i + b2i (12)



3.3 Self-organization of Offset Settings

Our aim now is to apply the solution of theentrainment condition described in the previoussubsection to derive the offset settings. The solu-tion we will describe here is applicable for generaln-way intersections, n > 2. For such n-way in-tersections, we first assume that each of n incom-ing directions is provided with its own split time,i.e., each is considered to have an exclusive mainphase. Within one main phase those, the corre-sponding incoming traffic flow may cross the in-tersection in all directions (go straight, turn right,turn left, etc.). Later on, we will provide the pro-posed solution with a feature that allows some ofthe phases combined for efficiency without nec-essarily ignoring some of the other phases. Forexample, this will allow the intersection to havegreen signal for two opposite directions so thatboth traffic flows may go in the straight directionat the same time. In particular, we will arguethat this generalizes the model from [6] which onlydeals with 4-way intersections that have two mainphases without explicitly taking into account ve-hicles that turn right or left.

Let ψi be the relative phase between φi andφi, where

ψi = φi − φi

Then the dynamics of the relative phase is ex-pressed by

ψi = Ωi − ωi −Kσi sinψi (13)

where Ωi is the natural frequency of ψiThe entrainment is reached whenever the

phase value φi no longer changes with respect tothe weighted phase average of all neighboring sig-nals. Thus, this phase-locking condition of (13)occurs whenever ψi = 0 which implies that

sinψi =Ωi − ωiKσi

ψi = arcsin

(Ωi − ωiKσi

)∣∣∣∣Ωi − ωiKσi

∣∣∣∣ ≤ 1

where σi will be a constant σi when oscillator Siis phase-locked with the neighboring signals. The

Figure 5: Possible values of p in Si−1 on a four-way intersection.

value of σi, according to (12), is given by

σi =

√a2i + b2i

ai =

ni∑j=1

εijni

cos ∆φij

2

bi =

ni∑j=1

εijni

sin ∆φij

2

where ∆φij is the phase difference between φijand φi which is defined by

∆φij = φij − φi (14)

To achieve the green-wave effect between twoneighboring signals Si and Si−1, the offset differ-ence in (14) has to reach a value, say ∆φ∗ij . In ann-way intersection, sources of an incoming traf-fic to Si from Si−1 is assumed to be originatedfrom the neighboring signals of Si− 1, except Si.Hence, let ∆φ∗ij

p→qbe the desired offset between φij

and φi where in Si, it corresponds to the qth splittime Ti,q and in the signal Si−1, it corresponds tothe pth split time. We derive ∆φ∗ij

p→qbelow.

In Fig. 5 which describes the situation in a4-way intersection, the source of incoming traf-fic from the direction indicated by q = 4 actuallyoriginate from the incoming traffic to Si−1 labeledby p ∈ 1, 3, 4. The problem is which value of pis to choose. It is impossible to pick all possiblevalue of p because this will make the synchroniza-tion of all three directions into a single direction



Figure 6: Offset-setting between successive sig-nals for p→ q direction before adjustment

Figure 7: Offset-setting between successive sig-nals for p→ q direction, adjusted to green

Figure 8: Offset-setting between successive sig-nals for p → q direction, adjusted to green andtravel time

q impossible due to the fact that each of thosedirections begin at different phase. Hence, we areforced to choose one of the possible directions forp. In this model, the value p is deliberately chosento achieve appropriate offset settings of consecu-tive intersections along the path in the directionof heavy traffic to reduce delay at red lights.

Consider Fig. 6, 7, and 8. In order to derivethe desired offset settings, we initially assume thatboth phases of Si−1 and Si begin at the same time(Fig. 6) when entrained. We present the situationwith respect to the whole cycle length of 2π. Note

that each signal has its own split settings, givenby the values of T ’s which will be derived later.

Suppose the green-wave is reached wheneverthe incoming traffic to Si in the qth direction islargely determined by the incoming traffic to Si−1in the pth direction. Thus, the green split thatcorresponds to Si in qth direction must start notearlier than the start of the green split that corre-sponds to Si−1 in the pth direction. Let Ti−1,p andTi,q be respectively the split time of Si−1 in thepth direction and Si in the qth direction. Also, letTcl be the fixed duration of time clearances dur-ing transition from red to green and green to red.Then, as seen in Fig. 7, the start of Si must beshifted at least as much as ∆T ∗ which is definedas:

∆T ∗ = (

p−1∑m=1

Ti−1,m−q−1∑m=1

Ti,m) + (p− q)Tcl (15)

However, the formulation above does not yettake into account that vehicles may take a consid-erable amount of time to travel from Si−1 to Si.Hence, let t∗ij the expected time for a vehicle toreach Si from Si−1 defined as

t∗ij =lijvmaxij

where lij is the distance between adjacent signalsand vmax

ij is the speed limit of the road betweenSi−1 = Sij and Si. The desired offset betweentwo successive signals is thus defined as

∆φ∗ijp→q

= 2πt∗ij + ∆T ∗

Ti(mod 2π) (16)

The desired offset above can then be used to ob-tain the desired relative phase, in accordance to(11), and (12), as follows

∆φ∗i = arctan

(∑nij=1 εij sin ∆φ∗ij∑nij=1 εij cos ∆φ∗ij

)

Following (13), the desired natural frequency forsignal Si can thus be expressed by the desiredrelative phase as

ω∗i = Ωi − σ∗iK sin ∆φ∗i

where Ωi can be approximated as ωi, the resultingcompromised frequency of the signals when theyare phase-locked [6].



3.4 Updating Natural Frequency

We assume initially the natural frequency of eachsignal Si is set with some initial value. For the de-sired natural frequency ω∗i , the natural frequencyωi of signal Si is updated according to,

ωi(τi+1) = ωi(τi)+α(ω∗i −ωi(τi))+β(ω∗i −ωi(τi))

where τi is the scaled time, α, β ∈ (0, 1) are posi-tive constants and ω∗i is some base frequency valuefor signal Si which is provided to prevent drift ofnatural frequency

3.5 Split Settings

Let Ti(τi) denote the cycle time of signal Si:

Ti(τi) = Ti1(τi)+Ti2(τi)+· · ·+Tin(τi)+nTcl (17)

Here, Tcl is the duration of clearance, andTik(τi), (k ∈ 1, 2, ..., n) are respectively split timesfrom Si on k direction. The split time Tik(τi) isupdated at the beginning of signal cycle in propor-tion to the sum of normalized amount of incomingtraffic of every direction in Si.

The normalized amount of incoming traffic fora direction is defined for k = 1, . . . , ni by

rik = εik (18)

We can thus find the desired split time for direc-tion k for k = 1, . . . , ni as

T ∗ik =rik(τi)∑n

m=1 rim(τi)(Ti(τi)− nTcl) (19)

and the updating function of split time Tik is de-fined for k = 1, . . . , ni by

Tik(τi + 1) = Tik(τi) + γ(T ∗ik − Tik(τi))

where γ is updating constant, i.e., learning rate,that will determine how fast the current split timeis moving to the desired split time.

3.6 Merging Directions into One SplitTime

The intersection model discussed in previous sec-tion is intended for an n-way intersection wherethere are n incoming traffic flow with its own dif-ferent direction, and each is allowed for its ownexclusive time to cross the intersection. This in-duces n time splits for each direction in one cycle

Figure 9: Direction of Sij1 and Sij2 is merged onsame split.

of signaling. In real situation, we often find ann-way intersection where some directions are al-lowed to cross the intersection together. For ex-ample, a 4-way intersection may be arranged suchthat incoming traffic from two opposite directionsare allowed to go straight during the same timesplit. This particular model was actually consid-ered in the original paper from Sekiyama et al.[6] where a 4-way intersection is divided into twotime split. Thus, our solution here generalizes themodel there.

Consider an n-way intersection where c direc-tions are merged, 1 ≤ c < n as illustrated in Fig.9. Since there is a reduced number of split time,our split setting calculation has to be adjusted.adjustments to split setting calculation. The cy-cle time previously defined in (17) is modified intothe following:

Ti(τi) = Ti(τi) + · · ·+ Ti (n−c)(τi) + (n− c)Tcl

The total incoming traffic flow of the merged di-rections is also taken into account. Thus, (18)must be modified appropriately. For example, inFig. 9, it holds that rik = εij1 + εij2 where thedirection k is formed as the combination of di-rections j1 and j2. In addition, the equation ofsplit time for direction k given in (19) has to bemodified as follows:

T ∗ik =rik(τi)∑n−c

m=1 rim(τi)(Ti − (n− c)Tcl)

There is a problem however with merging some di-rections specified in this section. Consider againa 4-way intersection with incoming traffic from



north, west, south, and east directions, and allvehicles travel on the left side of the road. Orig-inally, there should be 4 splits in one cycle time.If we combine traffic that come from north andsouth direction into one split, then the traffic willbe safe as long as all vehicles from north go to thesouth and all vehicles from south go to the north.This won’t be the case if some vehicles from thenorth wish to turn right to the west direction orsome vehicles from the south wish to turn right tothe east direction. Those vehicles are not safe be-cause there is no exclusive split which is allocatedfor them. In [10], this is solved by installing aroute guidance system that interacts directly withthe vehicles. We differ in this respect by avoidingsuch interactions with the vehicle. Our solutionemploys traffic signal phasing as described in thesubsequent section.

3.7 Split Setting based on Traffic Sig-nal Phasing

Recall that the intersection model described sofar is based on a phase description in Kuramoto’smodel. Hence, one cycle can be considered as asequence of signal phases. A traffic signal phaseis a part of a cycle that is allocated to a stream oftraffic or a combination of two or more traffic flowshaving the right-of-way simultaneously during oneor more splits. The National Electrical Manufac-turers Association (NEMA) has adopted and pub-lished precise nomenclature for defining the vari-ous signal phasing to eliminate misunderstandingbetween manufacturers and purchasers [12]. Fig.10 illustrates the assignment of right-of-way tophases right-turn lanes by adapting NEMA phasenumbering standards and the common graphictechniques for representing phase movements.

Our scheme based on traffic signal phasingis specified in the form of rules that determinesphasing sequence, i.e., which directions should goat certain phases. Note that the NEMA phasenumbering is only provided for 4-way intersec-tions. We thus illustrate this scheme using itsapplication on a 4-way intersection. Other typesof n-way intersections can employ this scheme byfirst providing an appropriate numbering.

Consider a 4-way intersection (with incomingtraffic from the north, south, west and east) whosesignal is divided into two main phases which cor-respond respectively to horizontal and vertical di-

Figure 10: The traffic signal phasing for right-turn lane by adapting NEMA.

rections of traffic flows. This means that in onecycle both north-to-south and south-to-north di-rections obtain the same green signal phase, andsimilarly, both east-to-west and west-to-east di-rections obtain the same green signal phase at thenext split. Assume that vehicles travel on the left-side of the road, and every vehicle may turn leftanytime at the intersection. Note that no greensignal phase is dedicated solely for vehicles thatturn right at the intersection. The formulationfor split setting will be as follows.

Let Ti(τi) denote the cycle time of signal Siwhich consists of two main phases. Then,

Ti(τi) = Ti1(τi) + Ti2(τi) + 2Tcl

where Ti1(τi) is the split time of the main phasefor the vertical direction, and Ti2(τi) is the splittime of the main phase for the horizontal direc-tion. Ti`(τi), ` = 1, 2, is updated at the beginningof each signal cycle in proportion to the sum rikof normalized amount of the incoming traffic foreach directions.

ri1 = εi1 + εi3 ri2 = εi2 + εi4



The desired split time for incoming traffic flowsfrom horizontal and vertical direction is:

T ∗i` =ri`(τi)

ri1(τi) + ri2(τi)(Ti(τi)− 2Tcl)

The scheme presented above would be accept-able if there is only negligible amount of trafficthat turns right at the intersection. In a real situ-ation, this scheme forces any vehicles that wish toturn right to wait until it is safe to do so, i.e., whenthere is no vehicle going straight from the oppo-site incoming direction. In fact, this is the originalscheme adopted in [6]. In Fig. 10, this two-phasesignal combination corresponds to phases 2 and 6and phases 4 and 8.

However, the above scheme is not sufficientwhen the amount of traffic turning right (phases1, 3, 5, and 7) is not negligible. There will bean increased risk of collision and a longer vehicledelay which may cause traffic congestion. Oursolution is thus to accomodate explicit allocationfor those phases for turning right.

Let εi,k,a be the traffic density of vehicles go-ing straight (and turning left) and εik,b be thetraffic density of vehicles turning right; both val-ues are computed w.r.t., direction k, k = 1, . . . , 4(directions are labeled clockwise starting from thewest). Then the split time of a main phase Ti` inthe previous scheme is divided into three smallerphases depending on which of the previous traf-fic densities dominates over the other. Define for` = 1, 2:

T ∗i,`,a =εi,`,b

εi,`+2,a + εi,`,b(Ti` − Tcl)

T ∗i,`,b =εi,`+2,b

εi,`,a + εi,`+2,2(Ti` − Tcl)

T ∗i,`,a and T ∗i,`,b are the measures reflecting howmuch traffic of vehicles turning right from boththe opposite directions. T ∗i,`,a’s proportion w.r.t.,T ∗i` is determined by the ratio between traffic flowthat turns right and the sum of traffic flow thatturns right and traffic flow going straight fromthe opposite direction. Note that this sum is ob-tained from two traffic flows that cannot cross theintersection at the same time. Similarly, this alsoholds for T ∗i,`,b.

Now, the phase sequence is specified, depend-ing on the time variable τi, into the following casesas follows (see Fig. 10 for the phase number-ing, and Fig. 11, 12 and 13 for description of

[`, tr]

[`, st]

[`+ 2, tr]

[`+ 2, st]

Ti`(τi)

T ∗i,`,a

T ∗i,`,b

Figure 11: when T ∗i,`,a + T ∗i,`,b < Ti`(τi), sequenceof phases is 2+5, 2+6, 1+6; or 4+7, 4+8, 3+8.Labels st and tr are resp. for going-straight signaland turn-right signal w.r.t direction `. See Fig. 10for phase numbering.

[`, tr]

[`, st]

[`+ 2, tr]

[`+ 2, st]

Ti`(τi)

T ∗i,`,a

T ∗i,`,b

Figure 12: When T ∗i,`,a + T ∗i,`,b > Ti`(τi), the se-quence of phases is 2+5, 1+5, 1+6; or 4+7, 3+7,3+8.

[`, tr]

[`, st]

[`+ 2, tr]

[`+ 2, st]

Ti`(τi)

T ∗i,`,a

T ∗i,`,b

Figure 13: When T ∗i,`,a + T ∗i,`,b = Ti`(τi), the se-quence of phases is 2+5, 1+6; or 4+7, 3+8.

each case). We assume w.l.o.g. that the timeτi ∈ [0, Ti`]. Also, ` = 1 (resp. ` = 2) in-dicates the horizontal (resp. vertical) direction.Note that in between changes of phase there is an



interval for clearance.

1. Case T ∗i,`,a + T ∗i,`,b < Ti`(τi)− Tcl:

• τi ∈ [0, Ti,`,a]: phase 2 and 5 if ` = 1;phase 4 and 7 if ` = 2

• τi ∈ [Ti,`,a + Tcl, Ti` − Tcl − Ti,`,b]: phase2 and 6 if ` = 1; phase 4 and 8 if ` = 2

• τi ∈ [Ti` − Ti,`,b, Ti`]: phase 1 and 6 if` = 1; phase 3 and 8 if ` = 2.

2. Case T ∗i,`,a + T ∗i,`,b > Ti`(τi)− Tcl:

• τi ∈ [0, Ti` − Tcl − Ti,`,b]: phase 2 and 5if ` = 1; phase 4 and 7 if ` = 2

• τi ∈ [Ti` − Ti,`,b, Ti,`,a]: phase 1 and 5 if` = 1; phase 3 and 7 if ` = 2

• τi ∈ [Ti,`,a + Tcl, Ti`]: phase 1 and 6 if` = 1; phase 3 and 8 if ` = 2.

3. Case T ∗i,`,a + T ∗i,`,b = Ti`(τi)− Tcl:

• τi ∈ [0, Ti,`,a]: phase 2 and 5 if ` = 1;phase 4 and 7 if ` = 2

• τi ∈ [Ti,`,a + Tcl, Ti`]: phase 1 and 6 if` = 1; phase 3 and 8 if ` = 2.

Obviously, the above rules only apply for 4-wayintersections with two main phases. However, theidea can easily be extended to other types of n-way intersections with their own configuration ofmain phases.

4 Simulation

This section describes how a real-world traffic net-work was modeled using a microscopic simula-tion software and presents the results as comparedagainst those obtained from fixed-time traffic sig-nals. There are two main parts of the software,namely the traffic signal control system (TSCS)and the simulator. Fig. 14 depicts the relation-ship between TSCS and the simulator.

4.1 The Traffic Signal Control System

The traffic signal control system (TSCS) is writ-ten in C with multithreading. The system cal-culate the traffic parameters of the entire trafficnetwork once for every beginning of each signalcycle.

Figure 14: Relationship TSCS and Simulator.

There are two kinds of threads for com-munication between TSCS and simulator: paththreads and lamp threads. The path thread isresponsible for obtaining traffic volume, averagevelocity of vehicles, and vehicle queue length atevery intersection on simulator. On the otherhand, the lamp thread is in charge of sending thetraffic light signal data to the simulator. In thissetting, whenever the TSCS needs some data withregards to certain intersections, it will send a datarequest through the path thread. The simula-tor then replies this request with the appropriatedata. In the opposite direction, the lamp threadis employed by the TSCS to send the traffic lightsignal parameters to the simulator, so that it canupdate the cycle time of the traffic signals.

4.2 Traffic Simulator

The traffic simulator is part of the simulation soft-ware that also has a graphical user interface. Thesimulator is written in Java using Java compo-nent framework. It is developed in such a waythat the designed or modeled traffic signal net-work can be implemented in the real world. Thesimulator maintains intersection threads for eachintersection in the modeled signal network. Thesampling rate for intersection threads is updatedevery 100 milliseconds. This enables intersectionthreads to make timely responses to the dynam-ically changing traffic network. During a simula-tion, the intersection threads are tuned to sam-ple for traffic parameters from the traffic networkonce every one cycle time. Fig. 15 show the traf-fic simulator and TSCS running concurently. Theinset shows the map of roads in certain Jakartaarea with 9 intersections comprising 3-way, 4-way



Figure 15: Running TSCS and Simulator.

Table 1: Details of the Simulation Parameter

Symbol Description Value

vmaxij maximum speed 60 Km/h

K coupling constant 0.1α, β rate of update of w 0.5, 0.05ω∗i base natural fre-

quency0.1

ρim road capacity 36 cars/roadγ updating constant

(learning rate)0.8

and 5-way intersections.

In the simulator, every intersection has infor-mation such as the path length between the streetintersection, the vehicle velocity, cycle time signalphase, the number of vehicles passing through theintersection, road capacity and other intersectionsignal phase that are connected with this intersec-tion. The value of simulation parameters is givenin Table 1.

There are various scenarios to compare the ef-fectiveness between the conventional method andthe proposed method. There are two kinds oftraffic network which represent real world con-dition of the traffic network system in Jakarta.The first kind of network, depicted in Fig. 16,represents of rather sparse networks of intersec-tions found in certain regions in Jakarta. Thesecond kind of network, as depicted in Fig 17,represents compact networks of intersections inJakarta. In the traffic simulation, the followingrestrictions/conditions are applied.

1. Vehicle arrival follows a Poisson distribution.

Figure 16: Simple Map Scenario.

Figure 17: Complex Map Scenario.

2. The road capacity is 36 vehicle whose averagelength is 5 m (5 pixel in simulation).

3. The traffic capacity of Simple Map is 1400vehicles per hour, and the complex Map is5000 vehicles per hour.

4. Updates for traffic density is done every 20seconds (short experiments) and 10 minute-scale (long experiments).

5. The minimum and maximum green times are15 and 60 seconds, respectively.

4.3 Design of Experiments

Evaluations of the proposed model require a goodand comparable benchmark against which thesimulation results can be fairly compared. How-ever, it turns out to be rather difficult, becauseunlike related works in [2, 3, 6, 8, 9], our solu-tion strongly focuses on generalization to n-wayintersections. This renders the results from thoserelated works not directly comparable to our ex-perimental results. In addition, the cycle time,



Figure 18: Density Distribution on 600 s in Sim-ulator.

split time, and offset of traffic signals in Jakarta(the basis for our experiments) in the current traf-fic management system is set manually and keptfixed throughout their usage. Hence, it would bemore realistic if the simulations are benchmarkedagainst signal network with static settings.

Experiments are also designed to investigateinfluences of some novel features in the proposedmodel. First, for traffic of a particular incomingdirection at an intersection, our model incorpo-rate some parameters for offset setting that rep-resents dominant source of that incoming traffic(the p and q parameters in Section 3.3). Secondly,the model is also extended with traffic signal phas-ing that allows split times merge. There will thusbe experiments in which these affecting parame-ters are varied.

Overall, the experiments are done with re-spect to the two performance measures: (1) re-duced vehicle delay on average; and (2) averagevelocity over all vehicles. Each experiment cov-ers all of the three typical situations, namely inhigh, medium and low traffic density. High trafficdensity scenario is represents peak periods or rushhour. This period is a part of day in which trafficcongestion and crowding on public transport areat their highest. Typically, this happens twice aday, once in the morning, and once in the evening,i.e., the times during which most people commute.Medium traffic density scenario represents normalcondition. Normal condition happens in betweenpeak times in the middle of the day. Low trafficdensity scenario represents traffic condition dur-ing the night.

There will be two kinds of simulations: short

Figure 19: Density Distribution on 24 Hours Sce-nario in Simulator.

simulations of 600 seconds duration and long sim-ulations of 24 hours duration, see Fig. 18 and 19.Both are given a similar number of vehicles. Shortsimulations are characterized with a single peakof traffic volume. Short simulations are also in-tended to verify that the computation of the sim-ulator works well. Long simulations are charac-terized with multiple peak of traffic volume whichrepresents multiple peak hours that may happenin the real situation.

Both simulations are tested for simple mapsand complex maps with static settings or non-static settings. The scenarios for which non-staticsettings are applied, we vary the simulations onwhether or not the offset is adjusted with dom-inant source of incoming traffic. For example,if the traffic from a neighboring signal is actu-ally dominated by vehicles going straight (i.e., notturning right) at the neighboring signal, then us-ing offset adjustment means that we set the vari-ables p and q for Eq. (16) to represent this kind oftraffic. Also, we vary on whether or not there aresome incoming directions are merged (and thusapplying traffic signal phasing). To mirror thereal situation, the merge is done on two incomingtraffic from opposite directions so that it is pos-sible for vehicles going straight from both trafficare able to cross the intersection during the samegreen phase.

The simulation of the occurrence of accidentson the map, we made occurring the stalled vehiclein several roads. In this case make the long queueof vehicles occurred on the road. Moreover caus-ing other vehicles from crossing the street can notget into this road. In this simulation is not traffic



detour of the vehicle, but by default the vehiclewill move into an empty lane from the jammedroads.

4.4 Simulation Results

Table 2 and 3 provide the results of simulation asan average over separate runs of experiment. Weargue that this a reasonable presentation of typi-cal results because the variances for all cases aresufficiently small. The tables list results from fourkinds of scenario: 600s Straight-Dominant, 600sRight-Dominant, 24h-Straight-Dominant, and24h-Right-Dominant. The Straight-Dominanttypes indicate that the traffic in simulation is ar-ranged so that at each intersection, the numberof vehicles going straight dominates the numberof vehicles that turn right or left. Meanwhile, theRight-Dominant types indicate the opposite con-dition.

Both tables are arranged into columns thatdescribe experiments with traffic signal in staticsettings, and traffic signaling with our self-organizing scheme, either without or with adjust-ing offset with respect to dominant source of in-coming traffic. The simulations done using self-organizing scheme are further categorized intowhether or not the signaling phases of some in-coming traffic are merged using the scheme de-scribed in Section 3.6 and 3.7. Finally, in all cases,we do simulations in both simple and complexmaps as described by Fig. 16 and 17 (indicatedby S for simple maps and C for complex maps).

For the 600s-scenarios which simulates typicalsituation of morning rush hour with one peak, wedo 30 separate runs with different Poisson seedsfor each category. The results given by the firsttwo rows of each table are positive. In particu-lar, our model that also employs offset adjustmentand merge of signal phases yields higher averageof vehicles’ velocity and lower delay for each maptype. In our model, the results mean that on aver-age, a vehicle travels up to ca. 4 minutes faster fora 10km trip. For vehicle’s delay at intersections,the results also provide reduced delay i.e., the de-lay between 13% upto 56% shorter than that ofthe static settings. The results are also consis-tent in the sense that in both cases of Straight-Dominant and Right-Dominant, our model alwaysscores better performance for each map type. Inaddition, using offset adjustment is always better

than without using it, and merging some of signalphases typically improves the result.

Next, the 24h-scenarios are presented as thelast two rows of each table. These scenarios simu-late real traffic situation over 24 hours where therecan be several peaks (heavy traffic) interleavedwith normal or light traffic conditions. The sce-narios are realized with 6 separate runs for eachcategory. In comparison to the 600s-scenarios, the24 hours duration provides a more difficult chal-lenge because many more possibilities for complextraffic situations to occur. Despite that, the re-sults are still positive and of similar tendency tothose of the 600s-scenarios, albeit with a slightlysmaller gain. In these scenarios, our model alsoscores better performance for each map type. Wecan also see that using offset adjustment andmerging some signal phases improve the results.The gain for velocity is slightly smaller especiallyfor the Right-Dominant type, whereas the reduc-tion in delay is in between 13% and 42% shorterthan that of static settings.

The comparison of the results of the traffic ar-rangements during an accident can be seen in ta-ble 4. The results show that the proposed methodincreases the vehicle velocity when the accidentoccurs. This happens due to long queues of ve-hicles at particular street led to the reduction ofgreen time which direction into this street. There-fore, by default the vehicle will move to the lanewhich gives a longer green time at the adjacentintersections.

5 Conclusion

We have presented a model of self-organizing con-trol for urban traffic signal which is suitable forgeneral n-way intersections. The model has beensuccesfully prototyped and tested in both simpleand complex traffic network. The simulation re-sults has proved that the proposed model yieldsbetter performance than static and fixed signal-ing systems which are commonly implemented. Inparticular, the simulations demonstrated that theproposed model is able to improve the average ve-locity of vehicles, and at the same time, reduce ve-hicles’ delay at intersections. The proposed modelis also sufficiently robust and efficient in peak pe-riods or rush hour. However, further study andexperimental data is needed in order to provide a



Table 2: Average vehicles’ velocity (in km/h)

Self-organizing traffic signal network

Static Offset unadjusted Offset adjusted

Scenarios method withoutmerge dir.

with mergedir.

withoutmerge dir.

with mergedir.

S C S C S C S C S C

600s: Straight-Dominant 18.43 18.462 18.676 18.809 18.865 19.408 20.31 20.536 20.735 21.064

600s: Right-Dominant 18.775 18.778 19.218 19.741 19.041 19.39 20.59 20.788 20.405 20.415

24h: Straight-Dominant 22.87 21.757 22.966 22.872 23.194 22.921 25.245 24.318 25.56 24.859

24h: Right-Dominant 23.865 22.720 24.427 24.116 24.203 23.042 25.61 24.721 25.15 23.124

Table 3: Average vehicles’ delay at intersections (in s)

Self-organizing traffic signal network

Static Offset unadjusted Offset adjusted

Scenarios method withoutmerge dir.

with mergedir.

withoutmerge dir.

with mergedir.

S C S C S C S C S C

600s: Straight-Dominant 90.18 167.06 85.931 149.934 76.074 131.523 72.31 85.96 70.21 73.5

600s: Right-Dominant 97.15 197.26 92.569 192.049 88.208 172.368 75.13 110.12 81.43 142.4

24h: Straight-Dominant 263.82 504.04 248.0194 457.898 232.295 429.389 236.49 316.79 229.92 296.43

24h: Right-Dominant 312.69 598.41 297.952 559.843 286.705 541.939 248.07 397.05 262.89 510.51

real-scale implementation of the model on trafficsignaling devices. It is also noted that any work-ing implementation of the proposed model neces-sitates an accompanying traffic monitoring systemthat is able to provide traffic data required by theproposed model.

Acknowledgements: This work was sup-ported in part by the Incentive Research by theMinistry of Research and Technology Republic ofIndonesia 2010 and Riset Unggulan UniversitasIndonesia 2011.

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Table 4: Average vehicles’ velocity when Accicent (in km/h)

Simple Map Complex Map

Traffic Flow Static Method Self-organizing Static Method Self-organizing

Low 21.13 22.77 23.05 22.92

Medium 20.57 22.09 19.67 22.15

Heavy 18.24 19.03 18.87 19.98

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