a novel signal-scheduling algorithm with quality-of-service provisioning for an isolated...

536 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 9, NO. 3, SEPTEMBER 2008

A Novel Signal-Scheduling AlgorithmWith Quality-of-Service Provisioning

for an Isolated IntersectionRichard Wunderlich, Cuibi Liu, Itamar Elhanany, and Tom Urbanik, II

Abstract—There have been countless efforts directed towardefficiently controlling the flow of vehicular traffic through anintersection. This paper describes an algorithm designed for thesignal control problem that employs concepts drawn from thefield of packet switching in computer networks. The novel methodproposed utilizes a maximal weight matching algorithm to min-imize the queue sizes at each approach, yielding significantlylower average vehicle delay through the intersection. Of particularinterest are scenarios in which differentiated services are offered tovehicle classes with differing priorities. Lyapunov function-basedanalysis is provided, deriving the conditions under which thesystem is guaranteed to be stable. The algorithm is compared to anoptimized fixed-time controller and a vehicle-actuated controllerusing the VISSIM traffic simulation environment. Simulation re-sults demonstrate the performance gain obtained when using theproposed scheme, particularly in the scenario in which vehicleroutes are unequally distributed, and multiple classes of serviceare desired.

Index Terms—Lyapunov stability analysis, signal control algo-rithms, traffic management.

I. INTRODUCTION

THE FIRST traffic signals were manually operated me-chanical signs erected in the late 19th century [1]. The

first coordinated lights appeared in the early 20th century;the system consisted of three consecutive lights that could betraversed without stopping while driving at only 20 mi/h [1].These signals were usually operated by police officers andwere prone to mechanical failure. With the advent of moderncomputerized traffic signaling systems and due to the immenseamount of traffic that now pulses through the streets that theycontrol, new and more complex control methods are beingproposed. All of these methods share a common goal: to max-imize the traffic throughput at controlled intersections whilemaintaining driver safety.

Manuscript received October 11, 2007; revised January 23, 2008, April 25,2008, and May 7, 2008. The Associate Editor for this paper was D. Dailey.

R. Wunderlich was with the Department of Electrical Engineering andComputer Science, The University of Tennessee, Knoxville, TN 37996 USA(e-mail: [email protected]).

C. Liu and I. Elhanany are with the Department of Electrical Engineering andComputer Science, The University of Tennessee, Knoxville, TN 37996 USA(e-mail: [email protected]; [email protected]).

T. Urbanik, II is with the Department of Civil and Environmental Engi-neering, The University of Tennessee, Knoxville, TN 37996 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITS.2008.928266

Since an intersection is the basic component of a trafficnetwork, optimizing the performance of an isolated intersectioncontributes to improving the overall performance of a trafficnetwork. Concentrating on developing an effective arbitrationpolicy without the large overhead of intersection coordinationprovides a base upon which to build future work concerningmultiple-intersection traffic networks.

The signal timing and control algorithms concerning isolatedintersections have extensively been studied. In 1958, Websterintroduced a formula for determining signal settings at anisolated intersection on the basis of average vehicle delay [2].The Microprocessor Optimized Vehicle Actuation system is aself-optimizing system designed to reduce delays and stops andto maximize capacity during peak periods [3]. An intelligentisolated intersection control system was proposed earlier, inwhich a two-step process was applied that develops the rulesof fuzzy control [4].

In an earlier work, a queuing theory was implemented intraffic control, and the problem of scheduling traffic at an inter-section was addressed by structuring the problem as a Markovdecision process [5]. Newell first proposed an adaptive trafficcontrol strategy based on queuing model, and Mirchandani andZou developed an approach to evaluate this adaptive system foran isolated intersection based on queuing theory [6], [7]. It hasbeen shown that by using dynamic programming techniques,which aim to solve the Bellman equation given a stochasticmodel of the system, an optimal control strategy can be ob-tained [8]. However, in real life, a model of the system isnot provided. Approximating a model yields limited resultsdue to the nonstationarity and non-Markovian characteristics ofvehicular traffic flows at intersections.

Without the ability to test the new and increasingly complexcontrol techniques on live traffic flows (due to obvious safetyconcerns), it becomes necessary to use computers to simulatetraffic flows to facilitate the cycle length testing and verificationprocess. The standard method of signal timing has been theoptimization of traffic cycles in offline computations accordingto statistical measures of traffic flows under certain conditionssuch as morning traffic, rush hour, etc. Controllers programmedwith several different cycles can then choose the cycle that ismost appropriate for the current traffic conditions. Moreover,many controllers have the ability to modify the cycle length,depending on the detection of vehicles, the time of day, the dayof the year, and other factors.

In this paper, we present Longest Queue First MaximalWeight Matching (LQF-MWM)—an algorithm for scheduling

1524-9050/$25.00 © 2008 IEEE

WUNDERLICH et al.: SIGNAL SCHEDULING ALGORITHM WITH QUALITY-OF-SERVICE PROVISIONING 537

Fig. 1. Intersection model with standard phase numbering.

signals at an isolated intersection to maximize the trafficthroughput while minimizing the average latency experiencedby the traversing vehicles. In particular, we employ a queue-size-based maximum weight matching (MWM) framework thathas been drawn from the field of data packet switching. Wederive the stability properties of the algorithm and demonstrateits performance under different vehicular traffic patterns.

In the real world, some vehicles, such as an ambulances, firetrucks, or police cars, have particular demands for time andrequire an increased level of service. In this paper, we arbitrarilyassign a high priority to a vehicle class to demonstrate thedifferential service given to different vehicle types. The high-priority vehicle class and its value are selected by the inter-section designer based on operational characteristics, includingaverage queue lengths, flow rates, etc. In LQF-MWM, theheavy truck class is selected as the high-priority vehicle class.

The rest of this paper is structured as follows: In Section II,a description of the system model is provided, along with adiscussion of the signal cycle attributes, data constraints, andthe simulation environment. Section III describes the algorithm,and its stability properties are obtained. Section IV presentssimulation results, and in Section V, conclusions are drawn, andan outline for future work is proposed.

II. SYSTEM MODEL

A. Intersection Configuration

The intersection under consideration is illustrated in Fig. 1.This is a four-approach intersection with through lanes (thatalso serve as right-turn lanes) and exclusive left-turn lanes.Each phase in this intersection is labeled following the NationalElectrical Manufacturers Association convention. This intersec-tion is an adequate test case, not only because it appears oftenin real-world traffic networks but also because its symmetryallows for a fairly straightforward analysis. It should be noted,however, that this control technique may be applied to anyintersection layout.

In the intersection used, all approaches are 1000 m long.The long leads into the intersection help ensure that arrivingtraffic is properly distributed and that vehicles do not build upat the inputs of the network. This is particularly important forsimulation runs with traffic levels approaching the saturationlevel. The left-turn lanes provide 100 m of vehicle queuespace to help avoid blocking at the lane-branching point. Thedistribution of vehicle route selection (i.e., left, straight, orright) is identical for all approaches. These parameters havearbitrarily been chosen, but the goal is to simulate a somewhatrealistic case simply to demonstrate the operation of the controlmethod. It is important to remember that this method will workfor any intersection under any load conditions as long as certaincriteria are met (as will be discussed in Section III).

B. Performance Measures

Fundamental measures for evaluating the performance ofa traffic controller (particularly at an isolated intersection)include vehicle delay, traffic throughput, vehicle stops, andaverage queue size. Analyzing the overall delay experienced bya vehicle that has traversed the network is a direct indication ofhow long the vehicle has had to wait at the intersection priorto traversing it. Throughput measures the number of vehiclesper hour that pass through an intersection and is indicativeof the overall controller performance. Vehicle stops refers tothe number of times that a vehicle must come to a stopwhile attempting to traverse a traffic network. Naturally, theminimization of stops is a primary goal of traffic controllers.However, the queue sizes are the most important measure thatwe study in this paper. As expressed by Little’s theorem [9],the average delay experienced by the vehicles in the networkis directly proportional to the average queue size [10]. Thus,minimizing the average queue sizes can, in general, minimizethe average vehicle delays.

Although minimizing the queue sizes is a primary motivationof the LQF-MWM algorithm, the overall vehicle delay is themeasure that we use to compare the performance of the controlmethods used. Given the inherent symmetry of the networkunder consideration and the identical speed of the vehicles, ifthere are no queuing delays, then all of the vehicles will havean identical time delay traversing the intersection, regardless ofthe path taken. Therefore, the queuing time delay is obtained bysubtracting the best-case time consumed traversing the network(i.e., no intersection delay) from the overall time that eachindividual vehicle has spent in the network.

C. Traffic Cycle Attributes

For the intersection to properly operate, and in an effort toensure the safety of the vehicles, the traffic cycle length mustbe valid. Commonly, the cycle consists of phases placed in aparticular order, each interval of which is given some amount ofcycle time. The ring diagram for the test intersection is depictedin Fig. 2, in which time progresses from left to right, indicatingthat the left-turn phases become active before the correspondingstraight/right phases for each approach (referencing the phasenumbering of Fig. 1).


Fig. 2. Eight-phase ring diagram for the intersection considered.

Phases are said to be compatible if they can concurrently begreen without creating traffic flow conflicts. A vertical barrierseparates the East–West phases from the North–South phases.Each of the phases is compatible with the phases above orbelow itself and on the same side of the barrier. All otherphase combinations are incompatible. The rows of the diagramare referred to as rings, which can independently be timed aslong as all rings cross the barriers at the same time. Note thatthe separations of the phases between the barriers (e.g., theseparation between phases 1 and 2) are based on the intervaltimes assigned to each phase and have arbitrarily been drawnin this diagram. Careful observation reveals that there are onlyeight unique phase combinations that are compatible.

Normally, the cycle is executed in an end-to-end fashion,with every phase receiving some interval time. Perhaps theonly deviation would be if vehicle detectors are used to skipphases when no vehicles are present. In the proposed controlmethod, the phases have no particular order and are actuatedbased on the queue sizes alone. This is not in conflict with thesimulation environment since we have the benefit of perfectdata; however, modifications to the general scheme may berequired when applying it to real-world systems, where factorssuch as imperfect vehicle detection, hybrid traffic flows, andside friction must be considered.

D. Data Constraints

For our purposes, we assume that certain vehicle informationis always available, which is a futuristic concept underling thedevelopment of Vehicle Infrastructure Integration (VII). Work-ing off of the assumption that every vehicle in the network isrunning an in-vehicle information system (IVIS) that is capableof communicating with the signal controller in some fashion,we are able to obtain vital telemetry information from eachvehicle. At the most basic level, we assume knowledge of thevehicle’s position in the network. An IVIS-equipped vehiclewith a Global Positioning System (GPS) module could easilyprovide this information in near real time.

The position of the vehicles is the only piece of informa-tion that we use for this control algorithm. Other informationmay include the vehicle’s speed, its intended route, or othercharacteristics. Vehicle speed data are also used to monitorvehicle stops for control method comparisons. The informationcurrently gathered by this system is not complicated and can beprovided by detection systems and GPS tracking systems thatare currently available.

Instead of counting vehicles with a complicated set of de-tectors, we simply ask the vehicles for their position and buildthe queues based on this information. While this simplifies thephysical setup of the intersection, the simulation is slowed byhaving to request information from each vehicle in the networkat every step of the simulation. However, this is not an entirely

unrealistic situation since all of the vehicles near an intersectionwould be communicating their telemetry data to the signalcontroller via VII anyway, which would then have to processall of that information to run the control algorithm. It is, ofcourse, entirely possible to use detectors to perform the queuecounting function without loss of performance, saving the costof the increased intersection complexity (and the introductionof detection errors). Using the position information to build thequeues is thought to be a more generalized solution because themethod can be applied to any intersection without the need fora complicated detector setup.

E. Evaluation Environment

To test and compare control methods, we have used theVISSIM traffic simulation environment, which is a micro-scopic multimodal traffic simulator that gives the user controlover all aspects of the network, such as vehicle type, driverbehavior, intersection control, and statistical data collection.The VISSIM simulator allows many types of signal con-trollers to be used, and a built-in fixed-time controller, i.e., theVehicle Actuated Programming (VAP) controller, and theASC/3 Software-In-the-Loop (SIL) controller are implementedin the simulation.

To fully understand the performance of the proposed controltechnique, it would be helpful to compare it with a currentcontrol method. In the results section, we study performancecompared with a fixed-time controller, i.e., the default con-troller in VISSIM. Under fixed-time control, the active phaseschange in the predetermined sequence as in the ring diagramof Fig. 2, with each phase having fixed-interval lengths. Thisis hardly a fair comparison due to the static nature (and partialobservability) of the fixed-time controller versus the proposedcontroller, since the latter relies on gathering data pertaining toapproaching vehicles and making subsequent informed signalcontrol decisions. We therefore need to compare this methodagainst another controller that utilizes vehicle information. Wechoose to use the ASC/3 traffic controller from Econolite sincethis is an industry-standard controller that has many advancedfeatures, the least of which is a vehicle-detection capability.

The proposed control method relies on the algorithm thatwill be discussed in Section III, the calculations for whichare carried out in MATLAB. VISSIM provides a ComponentObject Model (COM) interface to give control of the simu-lator to external applications. Using this COM interface fromMATLAB, we are able to load the traffic network, set simu-lation parameters, execute simulations, and collect data. Thecontrol routine single-steps through the traffic simulation whilecontrolling the signal group with the custom-designed controllogic. A schematic representation of the control interface flowis shown in Fig. 3. It is important to note that we have no con-trol over the actual signal controllers, which are only directlyinterfacing with the simulator.

Due to a limitation (or perhaps a protective behavior) of thesimulator, the COM interface allows for the reading of a signal’sstate but does not allow for the changing of the traffic signalstates directly. To control the many phases of the intersection,a simple VAP code controller monitors vehicle detectors in


Fig. 3. Schematic representation of the control interface flow.

Fig. 4. Phase connection diagram for the intersection examined.

the network that are associated with each phase. The VAPcontroller changes the state of the associated phase wheneverthe detector is activated. In the simulator, the detectors aredisabled to prevent vehicles from triggering them. Instead,when the LQF-MWM controller determines that a phase shouldbe changed, a trigger is issued from the MATLAB environment,which, in turn, signals the VAP controller to change the state ofthe corresponding signal group.

While the ASC/3 makes control decisions every tenth ofa second (the resolution of the simulator), the LQF-MWMalgorithm only makes control decisions every second. Duringeach control step, the algorithm loops through a list of all ofthe vehicles in the network and requests information, includingposition and speed, to build the vehicle queues and to determineif any vehicles have stopped. There does not seem to be anappreciable performance difference between the operation ofthe ASC/3 and the MATLAB controllers with respect to thefrequency of control decisions.

III. SIGNAL SCHEDULING ALGORITHM

We first consider the phase connection diagram shown inFig. 4. This diagram indicates which phases are used to mo-bilize a vehicle through the intersection from any input to anyoutput. Note that a vehicle cannot leave on the same link fromwhich it arrived. These data are given to the signal-schedulingalgorithm, along with phase-compatibility information, so thatit can evaluate the size and weight of each queue. These weightsreflect the service urgency of each queue.

In the stability discussion that follows, for the purpose ofclarity, the intersection is referred to as a node at which the links(approaches) are connected. This is intended to generalize theproof and to not introduce confusion between physical lanes ofthe intersection and the overall input–output characteristics ofthe intersection as a whole. Other terms used in the algorithm’sdescription include traffic flow rate and link capacity. The flowrate is a value that describes how much traffic is flowing on

Fig. 5. Intersection configuration sets considered by the algorithm.

a particular link relative to the overall capacity of the link.The capacity of the link is defined as the maximum numberof vehicles that could possibly traverse a link within a certainamount of time. These quantities are usually described in termsof vehicles per hour.

A. LQF-MWM Signal Arbitration

We next describe the proposed signal arbitration algorithm.First, define the traffic load matrix as a doubly substochasticmatrix Λ = ‖λij‖ with admissible arrival rates, such that

N∑l=1

λil < c

N∑l=1

λlj < c (1)

where λij denotes the average rate of vehicles moving throughthe intersection from input link i destined for output link j (i isnot equal to j), c is the physical capacity of the links, and N isthe number of links that are connected at the intersection node(N = 4 in our case). The first part of (1) states that no link hasmore than its capacity in traffic traversing it. The second partguarantees that overloading any of the destination links will notoccur.

Let Q(t) = [Q11(t), . . . , Q1N (t), . . . , QNN (t)]T be thequeue occupancy vector in which each component representsthe number of vehicles currently queued at time t. For lanesthat are associated with two destinations (e.g., lane 6), weassume an equal queue size distribution between the flowsdestined for each of the two output links to simplify the proof.However, any different distribution would support the proof.Queues are served in accordance with the policy dictated bythe signal control algorithm. Due to the nature of the trafficflow, all Qii(t) = 0 ∀i (it is assumed that there is no loopbacktraffic). The signal-control algorithm selects a set of compatiblematches between a set of input and output links. The set ofmatchings is represented by a matching matrix ‖Sij(t)‖, 1 ≤i ≤ N, 1 ≤ j ≤ N , whose binary elements Sij(t) = 1 if andonly if (iff) input link i is selected by the control algorithm toconnect to output link j; otherwise, Sij(t) = 0.

There are four intersection-matching matrices considered bythe algorithm, as shown in Fig. 5. By comparing Fig. 5 with


Fig. 4, and referencing back to the ring diagram of Fig. 2,one can see that all possible combinations of the dual-ringphase scheme shown in Fig. 2 are “covered” by these match-ing matrices. In addition, these matching matrices cover allvalid link permutation matrices; this is a necessary conditionfor the validity of the algorithm. Letting the weight of amatching be denoted by W (t) = 〈Q(t), Sij(t)〉, it is noted thatgiven the four configurations of the intersection (i.e., matchingmatrices) described in Fig. 5, there are four correspondingweights, which we label Wm(t)m = 1, 2, 3, 4. We further de-fine κn(n = 1, 2, 3, 4) as the sum of weights corresponding toevery combination of three weights (Wm(t)). The indices ofsuch combination of weights are {1, 2, 3}, {1, 2, 4}, {1, 3, 4},and {2, 3, 4}. The algorithm selects the matching matrix thathas the highest value within the set of weights corresponding tothe largest element in κn. It is noted that the algorithm requiresthe calculation of the weights and κn to take place prior to eachconfiguration of the intersection. However, the computationalcomplexity involved in such arithmetic is rather low.

It should be noted that, inherently, the algorithm tends toselect lanes with larger queues. However, it is not necessarilythe case that the lane corresponding to the largest queue will beselected. This largest queue will be served iff it is a member ofthe maximal combination of queues. By choosing the maximalcombination of queues, the control method is able to move thegreatest number of vehicles through the intersection over time.We further note that an increased measure of priority can beapplied to a particular vehicle in the queue by simply givingit an increased individual value. That is, when the queues arebeing considered by the algorithm, the value of each vehiclecan independently be chosen beforehand (for example, basedon vehicle type). By artificially inflating the values of thequeues in this manner, we force the algorithm to service queueswith high-priority vehicles. Choosing values for the differentvehicle classes then becomes a matter of balancing betweenthe maximum queue sizes and the importance of the vehiclesconsidered.

B. Stability of the Algorithm

In this section, we provide a comprehensive stability prooffor the proposed algorithm. At its core, stability implies thatthe expected values of the queue sizes are all bounded. Anotherway of expressing this notion is to say that given the proposedsignal control algorithm, the average queue sizes are alwaysstrictly bounded.

We define Pk ⊂ RN×N as the set of (N !) permutation ma-

trices of an N × N matrix, i.e., matrices with only a single 1 ineach row and in each column. According to Birkhoff’s theorem[11], the following inequality holds:

Λ <∑

j

αjPj (2)

where∑

j αj = c. Equation (2) states that any doublysubstochastic matrix can be decomposed into a con-vex sum of permutation matrices. Let D(t) = [D11(t), . . . ,D1N (t), . . . , DNN (t)]T be a vector denoting the departure

process, for which the element Dij(t) represents the num-ber of vehicles departed from link i for link j during timeslot t. Hence, the evolution of the queue occupancy can beexpressed as

Q(t + 1) = Q(t) + A(t) − D(t) (3)

where A(t) is the number of vehicles arriving at the queueat time t. The intersection under study will be modeled bydiscrete-time queues, which, in turn, will be analyzed usingdiscrete-time Markov chain (DTMC) models.Definition 1: The weight produced by the LQF-MWM algo-

rithm at time t is given by

W ′(t) =⟨Q(t), S′

ij(t)⟩

=∑i,j

Qij(t)S ′ij(t) (4)

where S ′ij(t) denotes the matching configurations established

by the algorithm at time t. We next provide stability-related de-finitions, which will aid in establishing the stability propertiesof the algorithm.Theorem 1 (Variation of Foster’s Criterion) [12]: Given a

system of queues whose evolution is described by a DTMC withstate vector Q(t)∈N

M , if there exist ε∈R+ and B∈R

+ suchthat given the function L(Q(t)) = Q(t)QT (t), ‖Q(t)‖>B, thefollowing holds:

E[Q(t+1)QT (t+1)−Q(t)QT (t)|Q(t)

]<−ε‖Q(t)‖ (5)

the system of queues is strongly stable.The LQF-MWM signal control algorithm determines the

configuration of the signals in the intersection once every ktime slot units, which defines the switching interval. The latterloosely refers to the number of vehicles that can arrive or departand would typically be on the order of a few seconds. We nextpresent the core theorem of this paper.Theorem 2: An intersection running the LQF-MWM signal

control algorithm with aggregate traffic load destined to anyoutput link that is less than C/3 is stable for any finite switchinginterval.

Proof: Since at most k vehicles may arrive during k timeslots, the following inequality holds:

Qij(t + k − 1) − Qij(t) ≤ k (6)

from which we can write

Qij(t + k − 1) − Qij(t) ≤k−1∑m=0

Aij(t + m) − kSij(t) (7)

for Qij(t) ≥ ηk. The term kSij(t) expresses the k consecutivevehicle traversals that may occur during a switching interval.Next, we construct a discrete-time quadratic Lyapunov function[13] L(t), which is defined as L(t) = 〈Qt, Qt〉 =

∑i,j Q2

ij(t).To prove that the algorithm yields a stable queuing system, wewould like to show that beyond a given threshold of maximumweight, there is a negative drift in the state (queue occupancies)


of the system. As an expression of a k time slot lag, we canwrite

L(t + k − 1) − L(t) =∑ij

(Qij(t + k − 1) − Qij(t))

× (Qij(t + k − 1) + Qij(t)) . (8)

For the case of Qij(t) ≥ k, we deduct the following:

E [L(t + k − 1) − L(t)|Q(t)]

≤∑ij

(k−1∑m=0

Aij(t + m) − kSij(t)

)E [2Qij(t) + k]

≤∑ij

2E [Qij(t)] (kλij − kSij(t)) +∑ij

k2

≤ 2k [〈Λ, Qt〉 − 〈S,Qt〉] + k2N2. (9)

Using (2), we know that

〈Λ, Qt〉 =

⟨∑j

αjPj , Qt

⟩

=∑

j

αj〈Pj , Qt〉

<∑

j

αj maxk

〈Pk, Qt〉. (10)

Given that∑

j αj = 1 (after normalizing the load matrix), weobtain 〈Λ, Qt〉 < maxk〈Pk, Qt〉 = 〈S∗, Qt〉 = W ∗(t), whichwould conclude the proof if all permutation matrices wereapplicable to the intersection. To evaluate the impact of thepartial connectivity that may be applied to the intersection, wenote that any permutation matrix can be majorized (or covered)by at most three of the allowable intersection configurations. Inother words, there exist l, m, and n such that

maxk

〈Pk, Qt〉 < 〈Rl, Qt〉 + 〈Rm, Qt〉 + 〈Rn, Qt〉 (11)

for some l �= m �= n ⊂ Ψ, where Ψ is the set of allowableintersection configurations. Since

〈Rl, Qt〉 + 〈Rm, Qt〉 + 〈Rn, Qt〉 < 3 maxj

〈Rj , Qt〉 (12)

we conclude that 〈Λ/3, Qt〉maxj〈Rj , Qt〉. �This result states that if the average aggregate traffic heading

to any given output link from all associated input links doesnot exceed c/3 (i.e., a third of the maximal physical capacityof the link), the algorithm will always yield a stable system.Instantaneously exceeding the capacity is acceptable as longas the average rate is bounded by c/3. This is irrespective ofthe distribution of traffic across the different input links. Forthe case of quality-of-service provisioning, the situation doesnot change, as long as the incoming and outgoing traffic loadsremain admissible over time.

Fig. 6. LQF-MWM example.

C. Numeric Illustration of the Algorithm

To better illustrate the LQF-MWM control algorithm, asimple example is provided, reflecting on the traffic scenariodepicted in Fig. 6. The weights of the truck and cars are20 and 1, respectively, expressing the higher priority givento trucks. A list of pairs and their corresponding weights isshown in Fig. 6. These weights express the summation ofan on-detector vehicle’s weight. From the list, it can be seenthat the phase pair 1 and 6 has the highest weight; therefore,phases 6 and 1 will turn green. Compared with the controllogic in the ASC/3 controller, which sequentially serves thephase pair according to the dual-ring phase scheme, the LQF-MWM yields better service provisioning, and the vehicle delayis significantly lower than that achieved by the ASC/3 controllogic.

IV. SIMULATION RESULTS

Using the VISSIM simulation environment, the intersectiondescribed is investigated under various traffic conditions formultiple control schemes. The primary variable considered isthe average traffic load. A value of 1800 vehicles/h (or onevehicle every 2 s) is taken to be the maximum traffic load foreach of the four approaches to the intersection. The incomingtraffic load is varied from near zero up to half of the maximumload c/2. For each data point, an average is taken over threeseparate simulation runs to obtain sufficient statistics. Inaddition, each run simulates 40 min of traffic flow. All vehicleswithin 100 m of the signal are counted as being in the queuefor that signal (as if it were a detector). In addition, both theASC/3 and MATLAB controllers use the same minimum andmaximum green times. However, the maximum green time is(at most) doubled for the MATLAB controller when extensionsfor high-priority vehicles are used.

When this work began, the control schemes were evaluatedusing only cars in the network. This provided for some uni-formity with respect to the behaviors of the vehicles in the


Fig. 7. Phase selection counts for cars only. Homogeneous and heterogeneous truck distributions. The heterogeneous truck distribution leads to a larger differencebetween phase pairs [2 + 6] and [4 + 8].

network. However, a goal of this effort was to provide someincreased measure of service to trucks. Therefore, truck trafficis added to the network to compare the per-class quality ofservice between cars and trucks in the network. The weightingscheme used is such that a queue with a single truck will alwaysoutweigh another queue completely filled with cars. This wasdone only to emphasize the differences in service between thevehicle classes. The exact values of the priorities depend on theproperties of the intersection and are chosen by the operator atdesign time.

Two types of traffic flows are studied: 1) equal route distri-bution, in which there is an equal probability for all vehiclesto turn left, turn right, or go straight through the intersection;and 2) unequal route distribution, in which there is a morerealistic distribution of vehicle destinations. For the latter, thedistribution used is 70% straight, 20% right, and 10% left.These values are arbitrary and are only used to demonstratethe operation of the method. Note that any other values maybe used, as long as they do not violate the maximal loadconditions set forth in Section III. Since the distribution usedis the same for all approaches, the average outbound load neverexceeds the maximum physical capacity. While this distributionis arbitrarily chosen, it represents, in general, a more pragmatictraffic pattern. As proven in the aforementioned discussion, anytraffic distribution that does not violate the admissibility criteriaresults in stable operation.

Considered next is the truck traffic load allocated to eachapproach. Initially, 5% of the traffic is selected as trucks, andthis load is uniformly appended to all approaches (and uses thesame destination distribution as the cars). This setup resultsin rather uninteresting behavior, because all approaches endup having the same long-term average priority. That is, the

resulting prioritized traffic flow experiences the same delaycharacteristics as the nonprioritized traffic flow.

To avoid this, and to more clearly identify the impact of pri-oritization, an imbalance is enforced such that the approachesreceive 0%, 5%, 10%, and 15% truck traffic, clockwise fromthe North approach. This means that the North–South directionshave 5% truck traffic, and the East–West directions have 10%truck traffic.

Fig. 7 summarizes the phase count percentages, enablingan effective comparison of the different traffic compositionscenarios. We observe medium and high traffic loads betweenthree variations of truck distribution: 1) no trucks present;2) equal truck distribution; and 3) unequal truck distribution.Note that the phase call percentages are fairly well matchedbetween the first two cases. A closer look at Fig. 7 revealsthat, indeed, the disparity between phases 2 and 6 (eastboundand westbound) and phases 4 and 8 (southbound and north-bound) has become more significant: phases 2 and 6 haveincreased, whereas phases 4 and 8 have decreased, as would beexpected.

In addition, differences between the average vehicle delayare also notable. Intuitively, the addition of trucks to the trafficflow should increase the average delay. Trucks are slower tochange speed and, therefore, slow the vehicles behind them.Delay characteristics for three cases are shown in Fig. 8, whichindicates that the addition of trucks does, in fact, increasethe average delay. In addition, when the approaches are un-equally loaded with trucks, the result is another increase indelay. Certainly, the most challenging aspect of any schedulingscheme would be to minimize the delay for the worst-casescenario (unequal truck distribution), which we will address inthe following discussion.


Fig. 8. Vehicle delay comparison between three different traffic compositions.

A. Equal Route Distribution

The first case under consideration is the intersection withequal traffic route decisions. This means that each vehicle tendsto make straight, left-turn, and right-turn decisions with equalprobability. Such a setup gives the most basic form of trafficcontroller, namely, the fixed-time controller, which is a best-case scenario for traffic routing. Therefore, we compare ourmethod, along with the ASC/3, to the fixed-time controller.Note that the fixed-time controller has been optimized forthe c/3 traffic load point (i.e., 0.33 relative traffic load). Twovariants of the LQF algorithm are compared with both thefixed-time controller and the ASC/3. One uses no priority, andthe weight matrices are based on the queue sizes alone. Theother utilizes priority, where the trucks are counted with ahigher weight than the cars. This controller also has extensionsenabled, whereby the phase interval is extended when there isa high-priority vehicle still in the queue when the interval firstcomes to an end. The number of extensions is limited to at mostdouble the overall maximum green time for that phase interval.

The results of the delay analysis for this intersection configu-ration are shown in Figs. 9 and 10. Fig. 9 depicts a comparisonof the mean car delays for the four control variants considered.All controllers exhibit similar behavior, and there is almostno difference between them through a wide range of trafficvolumes. An exception, of course, is the fixed-time controller,which stands out as a poor performer at low volumes due toits ignorance of the presence of vehicles to be served and itsstrictly cyclic behavior.

Turning now to Fig. 10, we observe a larger variation be-tween the different control methods. This figure only providesthe average delay of the trucks in the network. In general, theASC/3 performs marginally better than the other controllers atvery low traffic volumes. Again, the fixed-time controller isa poor performer at lower volumes; however, its performanceclosely follows that of the ASC/3 and the nonprioritized LQF-MWM at medium and high loads for both cars and trucks.

The difference between the algorithms becomes much moreapparent when examining the vehicle delay histogram. Thelatter for equal route distribution is shown in Fig. 11. Thisshows a comparison between the ASC/3 (top) and the LQF-

Fig. 9. Average vehicle delay for equal route distribution with traffic com-posed of cars only.

Fig. 10. Average vehicle delay for equal route distribution with traffic com-posed of trucks only.

MWM controller with priority and extensions (bottom). Thereare two different load points illustrated: The graphs on the leftare for c/4 (0.25 relative load), and the graphs on the right arefor c/2 (0.5 relative load). For the lighter loading condition, itcan be seen that the ASC/3 roughly equally delays both classesof vehicles. On the other hand, with the prioritized traffic flowof the LQF controller, we see that nearly all truck traffic isdelayed less than 1 min (the first bar group). The effect ofpriority on the truck delay is also clear from the histogramsfor c/2. At this load point, the ASC/3 again fairly evenly delaysthe traffic. If anything, the cars have a slight edge, given theirmore aggressive acceleration profile. With the LQF controller,however, the advantage is clearly given to the trucks, at theexpense of significantly delaying some cars.

The last performance study pertains to vehicle stops. Recallthat a vehicle is considered stopped if it ever comes to restduring its approach or passage through the intersection. Fig. 12shows the results of a comparison between the ASC/3 andthe LQF algorithm for equal route distribution. In general,the percentage of vehicles stopped grows as the traffic load


Fig. 11. Average vehicle delay histogram for equal route distribution at medium and high traffic loads for the ASC/3 and LQF controllers.

Fig. 12. Vehicle stops for equal route distribution comparing the ASC/3 controller with LQF-MWM (using priority scheduling and extensions).

increases. As expected, the ASC/3 almost equally stops bothclasses of vehicles. The LQF algorithm, using priority andinterval extensions, however, is able to maintain substantiallylower stops for the trucks across all traffic loads. In fact, stopsfor both cars and trucks are decreased when using the LQFalgorithm due to cars riding along with trucks through theintersection. At very low traffic volumes, however, the resultsmay not be entirely statistically sound, given the limited numberof trucks that actually enter the network.

B. Unequal Route Distribution

The case for which the traffic routing is unequally distributedis far more realistic and, therefore, more interesting to study.Certainly, the conditions of this isolated intersection are farfrom reality, but the potential of the control framework maystill be evaluated through these results. First, we examine theaverage vehicle delay for different control methods for thetwo classes of vehicles under consideration. We compare three


Fig. 13. Average vehicle delay for unequal route distribution with trafficcomposed of cars only.

variants of our approach to the ASC/3. The first uses no priority,and the weight matrices are based on the queue sizes alone. Thesecond uses priority but no interval extensions. The third usesboth priority and extensions, enabling the latter when a high-priority vehicle is in an active queue when the interval reachesits end. The extensions are made in 5-s increments, and thenumber of extensions is limited to at most double the overallmaximum green time for any phase interval. Thus, it retains thecondition needed for stability, which is a finite expectation onthe interval durations.

The car and truck delays are illustrated in Figs. 13 and 14,respectively. In Fig. 13, we see that the performances of theASC/3 and the LQF algorithm with no priority are quitecomparable. Moreover, it should be noted that car delays forthe two LQF variants with priority are appreciably higherthan the ASC/3 delay. This is due to the preference given toservicing the trucks. Referring to Fig. 14, we observe that truckdelays for the LQF algorithms are much lower for all mediumand high traffic loads when compared to the ASC/3 delay. Theaddition of interval extensions does not substantially affectthe results, but it does help both trucks—and the cars that arearound them—to more quickly traverse the intersection than inthe case with the ASC/3.

Turning now to the delay histogram in Fig. 15, oneobserves similar results as with those found in the equal routedistribution case. Again, at low volumes, nearly all truck trafficis ushered through the intersection with minimal delay for theLQF controller, whereas the ASC/3 delays more than 15% ofthe trucks for more than 1 min. At the higher volumes, we seethat the LQF controller is able to shift substantial numbers oftrucks toward the lower end of the delay spectrum. Referringback to Fig. 11, note that the performance is much better forthe unequal route distribution case than it is for the equal routedistribution case at the lower traffic load. This is explainedby the fact that more vehicles are headed straight and rightthan are turning left. This increases the throughput, allowingmore vehicles to traverse the intersection in a shorter amountof time.

Fig. 14. Average vehicle delay for unequal route distribution with trafficcomposed of trucks only.

Finally, we examine the stops comparison in Fig. 16. TheASC/3 appears to perform much better in this case than in thecase of equal route distribution. Again, this is due to its abilityto allow the majority of traffic (straight and right) to movethrough the intersection unimpeded, breaking only briefly toenable the left-turning traffic through.

The LQF controller has more stops at the lowest trafficloads, which could be due to a couple of factors. It is mostlikely due to the small delay that exists between the timethe algorithm detects the vehicle in the queue and when itcan activate the traffic light. In particular, the ASC/3 readsthe detector information ten times per second, whereas theLQF controller only reads the detectors once every second.This second of added delay decreases the responsiveness ofthe controller and affects the trucks more, because of theirmore moderate acceleration profile. In addition, as has beenpreviously mentioned, at the lower traffic loads, very fewtrucks actually pass through the intersection, which results insome statistical inaccuracies. However, the general trends canbe identified from the plotted data. Overall, and particularly athigh traffic loads, the LQF-MWM controller with quality-of-service provisioning outperforms the ASC/3 by a significantmargin.

V. CONCLUSION AND FUTURE WORK

This paper has presented a novel approach to controllingan intersection using notions adapted from the field of com-puter networking. A stable arbitration algorithm was developedand compared with an existing control technique. A rigorousstability proof was provided, suggesting that the algorithm isguaranteed to be stable for aggregate traffic flows that do notexceed a third of the physical capacity of the approaches. Thetechnique is extremely flexible, enabling dynamic quality-of-service provisioning for diverse heterogeneous traffic scenarios.Moreover, a MATLAB–VISSIM interface was presented as apowerful platform for research on traffic management. Theformal framework introduced in this paper is novel and generic,


Fig. 15. Average vehicle delay histogram for various control schemes.

Fig. 16. Comparison of percentages of trucks that reach a stop for ASC/3 and LQF-MWM.

such that it has the potential to be applied to much moreintricate traffic networks and flow-management tasks.

In the future, the design will move from the ASC/3 SILcontroller to a real ASC/3 control box. This involves updatingthe ASC/3 control database to allow the MATLAB controllerto make decisions about phase changes and have the ASC/3carry them out. The transition will be aided by the ability tohave a real ASC/3 in the control loop of the simulator. This willallow testing of the method before using a physical intersectionsetup. By the time a functional VII system is realized, thiscontrol method will be capable of operating in a real-worldtraffic control situation.

REFERENCES

[1] E. A. Mueller, “Aspects of the history of traffic signals,” IEEE Trans. Veh.Technol., vol. VT-19, no. 1, pp. 6–17, Feb. 1970.

[2] F. Webster, “Traffic signal settings,” Road Res. Lab., Her Majesty’sStationery Office, London, U.K., Road Res. Tech. Paper No. 39,1958.

[3] J. R. Peirce and P. J. Webb, “MOVA control of isolated traffic signals-recent experience,” in Proc. 3rd Int. Conf. Road Traffic Control, London,U.K., May 1990, pp. 110–113.

[4] D. Teodorovic, P. Lucic, J. Popovic, S. Kikuchi, and B. Stanic, “Intel-ligent isolated intersection,” in Proc. 10th IEEE Int. Conf. Fuzzy Syst.,Melbourne, Australia, 2001, vol. 1, pp. 276–279.

[5] X.-H. Yu and A. R. Stubberud, “Markovian decision control for trafficsignal systems,” in Proc. 36th IEEE Conf. Decision Control, San Diego,CA, Dec. 1997, vol. 5, pp. 4782–4787.


[6] G. F. Newell, “The rolling horizon scheme of traffic signal control,”Transp. Res., Part A Policy Pract., vol. 32, no. 1, pp. 39–44, 1998.

[7] P. B. Mirchandani and N. Zou, “Queuing models for analysis of trafficadaptive signal control,” IEEE Trans. Intell. Transp. Syst., vol. 8, no. 1,pp. 50–59, Mar. 2007.

[8] R. Sutton and A. Barto, Reinforcement Learning: An Introduction.Cambridge, MA: MIT Press, 1998.

[9] J. D. Little, “A proof for the queuing formula: L = λW ,” Oper. Res.,vol. 9, no. 3, pp. 383–387, May/Jun. 1961.

[10] W. A. Rosenkrantz, “Little’s theorem: A stochastic integral approach,”Queueing Syst. Theory Appl., vol. 12, no. 3/4, pp. 319–324, 1992.

[11] G. Birkhoff, “Three observations on linear algebra,” Univ. Nac. Tucumán.Rev. Ser. A, vol. 5, pp. 147–151, 1946.

[12] F. G. Foster, “On the stochastic matrices associated with certain queuingprocesses,” Ann. Math. Statist., vol. 24, pp. 355–360, 1953.

[13] L. R. A. Bacciotti, Lyapunov Functions and Stability in Control Theory,2nd ed. Berlin, Germany: Springer-Verlag, 2005.

Richard Wunderlich received the M.S. degreein computer engineering from The University ofTennessee, Knoxville, in 2007.

He was with the Department of Electrical Engi-neering and Computer Science, The University ofTennessee. His main research interest is intelligenttransportation systems. In particular, he designs con-trol algorithms and corresponding communicationprotocols for supporting prioritized traffic flow innext-generation traffic infrastructures.

Cuibi Liu received the B.S. degree in electronic in-formation science from Dalian Maritime University,Dalian, China, in 2007. She is currently workingtoward the Ph.D. degree in computer engineeringwith The University of Tennessee, Knoxville.

Her main research interests are intelligent trans-portation systems, high-speed optimal control tech-niques, and performance analysis.

Itamar Elhanany received the B.Sc., M.Sc., andPh.D. degrees in electrical and computer engineeringand the M.B.A. degree from the Ben-Gurion Uni-versity, Beersheba, Israel, in 1995, 1998, 2003, and2002, respectively.

He is currently an Assistant Professor with theDepartment of Electrical Engineering and ComputerScience, The University of Tennessee, Knoxville.During 2000–2003, he was with TeraCross, Inc.: afables semiconductor company developing terabit-per-second switch fabric integrated circuits, where

he held several key positions, including Chief Scientist. His research interestsinclude high-performance networking, machine intelligence, and reconfig-urable computing.

Tom Urbanik, II received the B.S. degree in forestengineering from the State University of New York,Syracuse; the B.S. degree in civil engineering fromSyracuse University; the M.S. degree in civil engi-neering from Purdue University, West Lafayette, IN;and the Ph.D. degree from Texas A&M University,College Station.

He is currently a Professor with the Department ofCivil and Environment Engineering, The Universityof Tennessee, Knoxville, where he is the GoodrichChair of Excellence in Transportation. He is an inter-

national expert in transportation system operation and management, includingadvanced traffic control systems, system performance measurement and opti-mization, highway–railroad grade crossings, transit priority, geometric design,and transportation management during natural and technological emergencies.His teaching and research interests are in traffic operations.

a novel signal-scheduling algorithm with quality-of-service provisioning for an isolated...

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