Scientia IranicaTransactions D: Computer Science & Engineering and Electrical Engineering
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Formalized learning automata with adaptive fuzzy coloured Petri net;an application specific to managing traffic signalsS. Barzegar a,∗, M. Davoudpour b, M.R. Meybodi c, A. Sadeghian b, M. Tirandazian b
aDepartment of Electronic and Computer Engineering, Qazvin Islamic Azad University, Qazvin, P.O. Box 34197-1416, IranbDepartment of Computer Science, Ryerson University, Toronto, ON M5B 2K3, CanadacDepartment of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, P.O. Box 15875-4413, Iran
Received 5 July 2010; revised 26 October 2010; accepted 14 February 2011
This work is dedicated to Professor Lotfi Zadeh on the occasion of his 90th Birthday.
KEYWORDSAdaptive coloured Petri nets;Fuzzy logic;Learning automata;Traffic signal control.
Abstract Investigation of the chaotic behavior of traffic streams at urban intersections due to signals hasinvolved researchers in endeavoring to predict a smooth traffic flowmodel for stabilizing traffic congestionand avoid unnecessary delays. In this paper, we study a hybrid adaptive model, based on a combination ofcoloured Petri nets, fuzzy logic and learning automata, to efficiently control traffic signals. We show thatin comparison with results found in the literature, vehicle delay time is significantly reduced using theproposed method.
Coloured Petri Nets (CPN) are a tool by which thevalidation of discrete-event systems is studied and modeled.CPNs are used to analyze and obtain significant and usefulinformation from the structure and dynamic performance ofthe modeled system. Coloured Petri nets mainly focus onsynchronization, concurrency and asynchronous events [1].The graphic features of CPNs specify the applicability andvisualization of themodeled system. Furthermore, synchronousand asynchronous events present their prioritized relationsand structural adaptive effects. The main difference betweenCPNs and Petri nets (PN) is that in CPNs, the elements areseparable, but in PNs, they are not. ‘Coloured’ indicates theelements specific feature. The relation between CPNs and
∗ Corresponding author.E-mail address: [email protected] (S. Barzegar).
ordinary PNs is analogous, in high level programming language,to an assembly code (low level programming language).Theoretically, CPNs have precise computational power, butpractically, since high level programming languages have betterstructural specifications, they have greater modelling power.
The drawback of CPN is their non-adaptivity [2] andtherefore it is not possible to access previous informationavailable in CPNs. If there is more than one transition activated,then each transition can be considered as the next shot. This‘Coloured’ Petri net characteristic indicates that since severalevents occur concurrently and event incidences are not similar,when events do occur, they do not change by time, andthis phenomenon is in contrast to the real, dynamic world.Simulation would be similar to execution of the main program.Our purpose is to use the simulated model for analyzing theperformance of the systems, and as a result, system problemsandweakpointswould be identified. However, classic CPN toolscan do nothing to improve and solve the problems, and also itis not possible to predict the next optimized situation.
In this paper, we present an Adaptive Fuzzy Coloured Petrinet based on learning automata. Using the information fromprevious states of the system and reactions of the dynamicenvironment, an Adaptive Fuzzy Coloured Petri net will predictthe next optimized situation. This will update the current stateof the system and will change and activate the probability ofoccurrence in time. The performance of the reaction on systemsin the dynamic environment will significantly help the FuzzyColoured Petri nets to learn and get trained. In this paper, wehave used CPN tools for Fuzzy CPN simulation.
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Figure 1: Eight-phase transition model.
Furthermore, we have studied application of the adaptivemodel mentioned in the previous paragraph to control trafficsignals. The adaptive model is represented to optimize thescheduling of traffic signals across intersections. Optimizing themethods used to control the traffic signals is significant, sinceit reduces air pollution, fuel consumption and improves timeefficiency. The proposed algorithm uses the learning automatato adjust fuzzy functions defined in the input parameters of theproblem.
Fuzzy logic was first used in traffic control systemsby Pappis and Mamdani [3]. They simulated an isolatedintersection composed of two one-way streets with no turns.Later, Niittymaki and Pursula [4] also simulated an isolatedintersection where the proposed fuzzy logic controller ledto a shorter vehicle delay and fewer stops. Niittymaki andKikuchi [5] developed a fuzzy logic algorithm to control signalsfor pedestrians. Through simulation, it was shown that theiralgorithm performed better than the conventional one. Chiu [6]used fuzzy reasoning to control multiple intersections withno turns. Fuzzy rules were used to adjust cycle time, phasesplit and offset parameters. Later, Niittymaki [7] introduced asimple, two-phase, fuzzy signal controller. It was shown thatthe fuzzy logic controller performed better than the vehicle-actuated controller.
In our test model, we study an intersection with two maindirections, namely North–South and East–West [8], with atraffic signal having 8 transitional phases, as shown in Figure 1.
Controlling traffic signals could be considered event discretesystems, which represent the level of synchronization andconcurrency. Since the main advantage of PNs is observingsynchronization and concurrency, existing PNs are the bestchoice for simulation, analysis and evaluation of an urban trafficnetwork. Therefore, we have used CPNs as a tool [1,9].
The rest of the paper is structured as follows. In Section 2,we present learning automata as the basic learning strategyused in our proposed method. In Sections 3 and 4, Fuzzy CPNsand the Adaptive Coloured Petri net are briefly introduced.The proposed algorithm is introduced in Section 5. Section 6explains the analysis of the proposed algorithm, and itscomparison with the results of fuzzy algorithms used forscheduling traffic signals. Finally, we have the concludingremarks.
2. Learning automata
Learning automata is an abstract model that randomlyselects one action out of its finite set of actions and evaluates iton a randomenvironment, then again evaluates the same action
Figure 2: Relationship between learning automata and its environment.
and responds to the automata with a reinforcement signal.Based on this action and the received signal, the automatonupdates its internal state and selects its next action. Figure 2illustrates the relationship between an automaton and itsenvironment.
The environment can be defined by E = {a, b, c}, wherea = {a1, a2, . . . , ar} represents a finite input set, b = {b1,b2, . . . , br} represents the output set, and c = {c1, c2, . . . , cr} isa set of penalty probabilities; each element, ci of c , correspondsto one input of action ai. An environment, in which b can takeonly binary values, 0 or 1, is called the P-model environment.Also, by further generalization of the environment, it is possibleto have finite output sets with more than two elements thattake values in the interval [0, 1]. Such an environment is calledthe Q-model environment. Finally, when the output of theenvironment has continuous random variables, and assumesvalues in the interval [0, 1], this environment is then known asan S-model environment. Learning automata are classified intoa stochastic fixed-structure, and a stochastic variable-structure.In the following, we only consider variable-structure automata.
A variable-structure automaton is defined by the quadrupleE = {a, b, p, T } in which a = {a1, a2, . . . , ar} is a set ofactions (or outputs of the automaton). The output or actionof an automaton is an instant of n denoted by a(n), whichis an element of the finite set, a = {a1, a2, . . . , ar}. b =
{b1, b2, . . . , br} represents the input set or response set, p =
{p1, p2, . . . , pr} represents the action probability set and finallyp(n + 1) = T (a(n), b(n), p(n)) represents the learningalgorithm. The following shows the action of the automatonbased on the action probability set, p. The automaton randomlyselects an action, ai, and performs it on the environment.After receiving the environment’s reinforcement signal, theautomaton updates its action probability set based on (i) forfavorable responses, and (ii) for unfavorable ones.
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pj(n + 1) =b
r − 1+ (1 − b)pj(n), ∀j, j = i, (2)
where a and b are reward and penalty parameters, respectively.If a = b, the automaton is called LRP . If b = 0, the automaton iscalled LRI and, if 0 < b < a < 1, the automaton is called LRεP .
For the S − LRP model learning automata, a linear algorithmis given below:
More information about learning automata can be found in [10].
3. Fuzzy coloured Petri nets
Coloured Petri nets were introduced by Kurt Jensen in 1987,as a developed model of Petri nets. Coloured Petri nets areappropriate tools for mathematical and graphical modeling.Coloured Petri nets have numerous applications, and much re-searchhas takenplace,with respect tomodeling, describing andanalyzing systems, which have synchronized, asynchronized,distributed, parallel, non-deterministic or random natures. Infact, Petri nets aremodels that could represent the performanceand state of the system at the same time. There has been enor-mous research done in the following areas,
(i) Controlling and learning systems using coloured Petri nets,(ii) Optimizing Petri net structures using genetic program-
ming,(iii) Learning and reasoning the ambiguous problems using
fuzzy coloured Petri nets.
However, there is no record of adapting coloured Petri nets andusing learning automata in Petri nets.
A formal definition of CPN is as follows [1]:
Definition 1. A Coloured PN (CPN) is a 6-tuple CPN =
(P, T , C, I−, I+,M0) where:
1. P = {p1, p2, . . . , pn} denotes a finite and non-empty set ofplaces,
2. T = {t1, t2, . . . , tm} denotes a finite and non-empty set oftransitions, P ∩ T = ∅,
3. C is a colour function that assigns a finite and non-emptyset of colors to each place and a finite and non-empty set ofmodes to each transition
4. I− and I+ denote the backward and forward incidencefunctions defined by P × T , such that:
I−(p, t), I+(p, t) ∈ [C(t) → C(p)MS], ∀ (p, t) ∈ P × T .
5. M0 denotes a function defined on P , describing the initialmarking, such thatM0(p) ∈ C(p)MS .
A formal definition of a FCPN is as follows [11]:
Definition 2. A generalized non-hierarchical Fuzzy ColouredPetri net is defined as 12-tuple FCPN = (Σ, P, T ,D, A,N, C,G,E, β, f , I) where:
1. Σ = {σ1, σ2, . . . , σl} denotes a finite set of non-emptytypes, called colour sets where l ≥ 0.
2. P = {PC , PF } denotes a finite set of places;– PC = {pc1, pc2, . . . , pcm} denotes a finite set of places
that model the dynamic control behaviour of a system,and is called control places wherem ≥ 0;
– PF = {pf1, pf2, . . . , pfn} denotes a finite set of placesthat model the fuzzy production rules, and is called fuzzyplaces where n ≥ 0, and PC ∩ PF = ∅.
3. T = {TC , TF } denotes a finite set of transitions;– TC = {tc1, tc2, . . . , tci} denotes a finite set of transitions
that are connected to and from control places, and iscalled control transition where i ≥ 0;
– TF = {tf1, tf2, . . . , tfj} denotes a finite set of transitionsthat are connected to or from fuzzy places, and is calledfuzzy transition where j ≥ 0, and TC ∩ TF = ∅.
4. D = {d1, d2, . . . , dh} denotes a finite set of propositions,|PF | = |D|.
5. A = {a1, a2, . . . , ak} denotes a finite set of arcs, k ≥ 0, andP ∩ T = P ∩ A = T ∩ A = ∅.
6. N: A → P × T ∪ T × P denotes a node function, and it mapseach arc to a pair, where the first element is the source nodeand the second element is the destination node; the twonodes have to be of different kinds;– In: an input function that maps each node, x, to the set of
nodes that are connected by an input arc(x) → x;– Out: an output function thatmaps each node, x, to the set
of its nodes that are connected to x by output arc(x) → x.7. C : (P ∪ T ) → Σss is a colour function, which maps each
place and transition to a super-set of colour sets.8. G: T → expression which denotes a guard function:
∀t ∈ T : [Type(G(t)) = Boolean∧ Type(Var(G(t))) ⊆ Σ],
where Type(Vars) denotes the set of types, {Type(v)|v ∈
Vars}. Vars denotes the set of variables, and Var(G(t))denotes the set of variables used in G(t).
9. E: A → expression which denotes an arc expressionfunction,
∀a ∈ A : [Type(E(a)) = C(p(a))MS∧Type(Var(E(a))) ⊆ Σ],
where p(a) is a place in N(a), and MS stands for multi-set.10. β: PF → D denotes a bijective mapping from fuzzy places
to a proposition.11. f : T → [0, 1] denotes an association function, which
assigns a certainty value to each colour used in each fuzzytransition.
12. I: denotes an initialization of double (δ, α),– δ: P → expression which denotes an initialization
function:∀p ∈ P : [Type(δ(p)) = C(p)MS].
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Figure 3: The FCPN denotation of fuzzy coloured rule of Type 1.
Figure 4: The FCPN denotation of fuzzy coloured rule of Type 2.
– α: denotes an association function, which assigns acertainty value in the range [0, 1] to each token in thefuzzy places.
The structure of Fuzzy Coloured Petri nets depends on fuzzyproduction rules. The composite fuzzy production rules couldbe distinguished by following three rule-types, respectively[12,13]:
Type 1: Simple fuzzy production rule (Figure 3):IF dj THEN dk (CF = u).
Type 2: Compound joined fuzzy production rule (Figure 4):If d1 AND d2 AND · · ·, AND dn THEN dk(CF = u).
Type 3: Compound disjoined fuzzy production rule (Figure 5):If d1 OR d2 OR · · ·, OR dn THEN dk(CF = u).
4. Adaptive coloured Petri net
By looking at the Petri net structure, we realize that thePetri net is considered a limited presentation tool with lowextension for solving real world problemswhich are considerednon-linear and dynamic. This tool is not able to self-educatein order to adapt to environmental changes. On the otherhand, with a more precise look at intelligent techniques foranalyzing, tools such as DAG (Directed acyclic graph) andPetri nets are needed, which have the capability to adapteducation by intelligent techniques, such as neural networksand fuzzy logic. All these intelligent techniques assess oneor more viewpoints. As an example of these viewpoints, wecan mention human knowledge or data processing, knowledgepresentation and learning. Therefore, it is necessary to design amodel, bywhichwe can express intelligent techniques andPetrinets as a single hybrid model and their combination. In recentyears, emerging solutions use a combination of intelligent andother techniques, which include another dimension of real timesystems [14–16]. Differentmethods of combinedmethods havebeen designed and implemented for solving various problems.Values, such as membership values, weights, certainty factorsand learning rules, with emphasis on intelligent techniques, are
Figure 5: The FCPN denotation of fuzzy coloured rule of Type 3.
in the Adaptive Petri net design, and have been investigated fordifferent problems. In the continuation, we assess two groupsof articles that focus on these trends. Asar et al. [2] analyzedvarious systems that are modeled with Petri nets as adaptivefeatures. These systems are separated into two groups:
1. Fusion hybrid,2. Combination hybrid.
Fusion hybrid. A large group of searches are categorized into thisgroup. Generally, papers and research which are placed in thisgroup have used intelligent technology like fuzzy logic with thehelp of Petri nets in real world problems. Examples of thesearticles are as follows.
Tsuji et al. [17] proposed an extended PNmodel that mergesthe attributes of fuzzy inference and neural networks. In thismodel, each token is given a positive real number value (notmore than 1). This value is a threshold of firing for a transition.Here, the boundedness, aliveness and reachability features of amodel have been analyzed.
Hadjinicolaou [18] proposed a neural Petri net model thatutilizes the Petri net for analyzing the behavior of a neuralnetwork. The neural Petri net model presented in this paperuses the certainty factor (that is, a real number) of weight perunit time, which changes the number of tokens over some unitof time.
Venkatesh et al. [19] presented a basic and fundamentalapproach to model neuron behavior through a High LevelPetri Net (HLPN). In this paper, a new element was added toHPN to implement all neural network features in the model.This element has been applied to places, transitions, arcs andweights.
Ahson [20] proposed a Fuzzy Neural Petri net model thatincorporates neural network features with fuzzy inferencetogether. In this model, the Neural Petri Net (NPN) utilizesplaces involving three subsets including input, hidden andoutput. The transitions are of two types including ordinaryand thresholding. Weights of Transitions are ordinary andthresholding. In input-place, transition weights are fixed to 1,while theweights on the hidden and output layers are trainableand can only take values between 0, 1 and −1. Therefore, TheNPN model is modified using fuzzy inference features.
Hirasawa et al. [21,22] examine Petri net potential from theperspective of the function distribution that exists in the humanbrain in the biological neural network, and proposes a revisedmodel of the Petri net, having the ability to learn as a Neuralnetwork. In this paper, a model based on the Petri net, named
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Learning Petri Network (LPN), proposed that the learning abilityof LPN is gained through the setting and weight adjustment.
Zha et al. [23] presented a Neural Fuzzy Expert Petri NetModel (NFEPN) with similar structure as [8], and demonstratedits unified approach to two applications, one involving theevaluation problem of non-rational design and its redesign, andthe other on the intelligent robotic assembly control process.
Tsang et al. [24] studied the learning capability in fuzzy Petrinets by modeling fuzzy production rules and incorporating aneural network learning algorithm. The learning algorithm ap-plied in this proposed model involves initialization, presentingtraining examples, feed forward computation and the backwardarc adjustment method.
Li et al. [25,26] proposed an Adaptive Fuzzy Petri Net(AFPN) model that has not only the descriptive advantagesof fuzzy Petri nets, but also a learning ability like the neuralnetwork. The work emphasizes the design of a dynamicknowledge inference framework, which is adjustable accordingto knowledge variation as human cognition and thinking. Itintroduces the weighted fuzzy production rule concept, whichgives a relative degree of importance to each proposition inthe antecedent, contributing to the consequence of a rule. Inthis paper, separate learning algorithms have been developed,called fuzzy reasoning and back propagation, respectively,to ensure convergence of adjustable weights and knowledgelearning under generalized conditions.
Chen et al. [27] proposed the model of a fuzzy Petrinet and an algorithm to generate a classifier network. Inthis proposed model, fuzzy rules are applied to the domainknowledge in order to help the local weight and certainty factorto get adjusted by online learning. Here, each input place isconsidered a feature of the model and, at each transition, isconsidered fuzzy production rules. Here, a token in any placeis a membership function.
Jones and Tracy [28] attempted to model a railroadlaboratory test bed based on a real time, shared resource,multiprocessing design, incorporating the attributes of neuralnetwork, timing, and colored tokens in a Petri net. Gao et al. [29]focused on a Fuzzy Reasoning Petri Net (FRPN) to represent aFuzzy Production Rule system.
The first group emphasizes the fact that we can model a realexecuted model by the help of Petri nets and can change thesimulated model. Here, many changes in the original structureof the Petri net and the intelligent algorithm are undertakenin order to get settled next to each other for simulating realsystem behaviors. For further details of this group, the readershould refer to [19]. In this paper, with the help of Petri nets,we can control brain cell activity. This idea is a comparisonbetween a Petri net and a neural network. Here, places caninclude both the body of brain cells and the synaptic clefts(cell cleft node). Each place has various functions. The corecleft acts like internal and external points, while the cell bodycollects signal points and possesses a threshold level in orderto fire. Arcs are representatives of dendrites (the long branchof a neural cell for connecting to another cell) in neural cells,and axons (small branches of a neural cell) are functions orrelational arcs. As mentioned in the definition of process in thispaper, some change has occurred in the original structure of thePetri net. Here, each place or arc is representative of some kindof task and behavior in the real world. Therefore, this model is abiological sample of a humanmind. In thismodel, any biologicaloperations done in the brain (such as an eye closing order) areshown in the Petri model as probable formulas and probabilitydistribution function changes that have been defined for each
part of the brain. So in the group of FusionHybrid Systems, thereis a really implemented system that we are going to artificiallymodel. We can easily analyze and assess this artificial model,which is a sample of the real world, and we can apply theresults to the real world. The reason for the adaptability ofthis group is related to basic changes in Petri net configurationand its similarity to the real system framework. Some changesin the basic structure of the Petri net in this group of papershave occurred, and the outcome is fuzzy logic, which can givethe ability of learning and teaching to the Petri net by use ofintelligent algorithms, such as neural networks. This group hasalso some disadvantages. Most often, learning in the Petri netof this group causes an increase in operation complexity andcalculation overhead, because it takes a long time to model allcharacteristics of a real system along with using an intelligentalgorithm in the Petri net.
Combination hybrid. In this group, a relatively small groupof researchers are active in applying adaptive intelligenttechniques, in conjunction with Petri net methodology, to realworld problems. Here, design complexity is less than the firstmethod. Models of this group are simpler than models of thegroup of Fusion Hybrid, accordingly. Some papers are:
Hanna et al. [30] demonstrated the approach of integratingthe fuzzy Petri net and ANN to do two separate jobs tomaintain the product quality characteristics of a CNC millingmachine center. Here, it utilizes a fuzzy Petri net with ANN forthe modeling and control of surface roughness in the millingmachine process. This paper is an example of work in termsof a hybrid approach, using a Petri net and ANN. In this hybridmodel, besides other transitions related to the milling machineprocess, one transition, when fired, triggers the ANN to activate,and gets the ANN based output. If the ANN output is the sameas the PN, then another transition fires to repeat the cycle,otherwise the error recovery transition fires to activate variousparts of the machine for readjustment.
Song et al. [31] proposed an optimization technique for aFlexible Manufacturing System (FMS). With the help of thistechnique, the scheduling problem of resource allocation isbased on the colored Petri net and Hopfield neural networkmodel. Here, timing delay confederates with places andtime propagation with tokens. Also time delay is associatedwith places, and time propagation with tokens. This modelinvolves mapping the constraint relations between tasks,machines and the objective function, onto an energy function.Here, real world problems are modeled by using intelligenttechniques along with Petri net methodology. In this method,different technologies are placed next to each other and, byrelative changes in each technique, the presented model, forexecution in the environment, will be implemented with moreeffectiveness and precision, in comparison with the normalmode. This group uses the initial characteristics of the Petrinet, along with intelligent techniques, which are applied to theinternal works and requests of each part of the real system.Also a real and clear combination of intelligent characteristicswith current conditions of the system has been also suggestedin order to improve the current system position. Completedjobs of this group are less than in the group of Fusion HybridSystems.
As an example of this group, we study the idea of Fukudaet al. [32], regarding optimized systems for controlling the
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Table 1: Features and their linguistic descriptions.
Variables Linguistic descriptions
QC ,QN Few Moderate Many Too manyARC , ERC , ARN Short Medium HighSNeC , SneN Worse No change BetterESC , ESN Worse No change Better
accuracy of electromyogram sets, using the intelligence ofneural networks and the task model by Petri nets. This idea hasbeen assessed in the Robot Laboratory of Hiroshima Universityin Japan, on an artificial hand. The goal of this method is tocreate an optimizedmethod for reducing extramovement in anartificial hand. This is an example of integrating two differenttechnologies as a single system. In this idea, myoelectriccontrol has been organized for improving the accuracy ofelectrocardiograph sets for making different statistic plans,by using a neural network, and has been suggested as anevent driven task model. Each model and pattern of theelectrocardiograph is as an input of the neural network inwhich the teaching process wants to be executed. Sensors ofelectrocardiograph signals are placed on the hand and joints,and send a model of hand movements and the environmentstatus to the model of the neural network, periodically. Theneural network makes a task model of jobs and tasks of amodel, with regard to the primary information of a model,and gives it to the Petri net. This net compares it with regardto optimized and ideal conditions. This trend is applied untilcreation of an optimized model, and finally it is implementedin the environment. Each request sent to the Petri net isconsidered a task. So the applicable Petri net in this project isresponsible for analyzing the given request to the artificial handas a task model. The task model of the Petri net is for describingindependent information that is used for describing the outputof the neural system. The task model approximates the taskagent by use of the records gained from neural network results.The neural network is connected to electrocardiographmodels,and themodel enters the neural network as an input. The outputof the neural network is a task model, which has been analyzedand designed by the Petri net. As seen in the example, here, thePetri net will consider better conditions for the environment,with regard to the input and output of the neural network, inan adaptable mode.
5. Proposed algorithms
In this section, we propose a combinative algorithm tocontrol traffic signals across intersections. In this algorithm,fuzzy logic and learning automata are used for intelligentcontrol of traffic signals. In the proposed algorithm, learningautomata are used to adjustmembership functions of input andoutput parameters.
Before a detailed description of the algorithm and theprocess of adjusting fuzzy membership functions used inlearning automata, we first explain the following topics: fuzzylogic, features for intelligent control of traffic signals, primitiveselection of fuzzy membership functions and fuzzy rules,details of the proposed algorithm and modelling the proposedalgorithm.
5.1. Fuzzy logic system
Rule base fuzzy logic systems contain four components:rules, fuzzifier, inference engine and output processor (defuzzi-fier). In the rule base, there are collections of ‘If-Then’ state-ments. After the information is gathered, the inputs should get
fuzzified to become usable. Defuzzification is used for concur-rency in the fuzzy system.Moreover, in the rule base, the outputvariable of the ‘Then’ part in each ‘If-Then’ statement is a fuzzyamount, and the output of different rules would not necessarilybe the same. Thus to drive to a result, a fuzzy inference engine isdesigned and, with defuzzification, the crisp value of a decidingvariable will be calculated.
5.2. Specifications to intelligently control traffic signals
The issue of controlling traffic signals could be divided intotwo parts:
1. To determine the priority of the phases,2. To schedule the traffic signals. In this paper, we concentrate
on the second part [33–35].
The following are specifications considered for intelligentscheduling of traffic signals at an intersection: The averagenumber of vehicles waiting to cross the intersection is denotedby (QC ) (when the light is green). The average number ofvehicles waiting to cross the intersection is denoted by (QN )(when the signal turns green in the next phase). The averagerate of vehicles crossing through the green signal is denotedby (ARC , ERC ). The average rate of vehicles crossing throughthe green light in the next phase is denoted by (ARN , ERN ).The state of traffic at the intersection against the traffic inthe neighbourhood cross section is denoted by (SNeC , SNeN ).Predicting the state of traffic at a particular given time isdenoted by ∆t (within the next 10 min) on the basis ofachieved information from the previous time (ESC , ESN ). Thesefeatures would be considered as inputs to control the trafficsystem. The final result expected from the overall system is toimprove traffic congestion by increasing the period betweensignal changes. Each feature is defined as a fuzzy variable andeach have a specific linguistic description. Table 1 shows thefeatures and their corresponding linguistic descriptions. Theoutput specifications that determine the increased duration ofthe green signal are value Zero, A Few, Few, Moderate, Manyand Too Many.
5.3. Primitive selection of fuzzy membership functions
For each linguistic description of a fuzzy variable, amembership function is considered. All membership functionsare equipped with learning automata and a variable structure,which have the responsibility of regulating the fuzzy functionparameters. Fuzzy membership functions are either triangularor trapezoidal in shape, shown in Figures 6 and 7. The beginningand end parts of the membership functions are constant andpre-determined. The learning automata would regulate thecenter of membership functions to achieve the best timing andcontrol of the traffic signals. In each automaton, a number ofactions (denoted by m) are defined. The probability to chooseeach action of the learning automata at the beginning of thelearning process is determined by 1
m .The ratio of traffic at the neighbourhood intersections to
traffic at the current intersection (SNeC , SNeN ), and predictionof traffic in a specific period of time, ∆t (next 10 min),in the selected phase, on the basis of gathered informationfrom previous times (ESC , ESN ) are calculated by the following
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ESC , ESN ⇒State of average old traffic in tC + ∆t
State of average current traffic, (6)
SNeC , SNeN
⇒State of traffic in neighbor intersections
State of average current traffic
+
Rest time of current greensignal in current intersectionRest time of current green
signal in neighbor intersection + a
∗ b. (7)
a is the required time for the vehicle to arrive from theneighbourhood intersection to the detecting intersection, andits value is determined to be 7 s. b is probability of exit ofvehicles from the neighbourhood intersection to arrive at thementioned intersection, with value 0.8.
5.4. Fuzzy rules
Some of the fuzzy production rules are as follows:
1. IF QC is Few AND QN is Too Many, THEN EX is Zero.2. IF QC is Moderate AND QN is Few AND ARC is Short AND ARN
is High AND ERC is Medium, THEN EX is Zero.3. IF QC is Few AND QN is Moderate AND ARC is Short AND ARN
is short AND ERC is Medium, THEN EX is A Few.4. IF QC is Moderate AND QN is Too Many AND ARC is Medium
AND ARN is Medium AND ERC is High, THEN EX is Few.5. IFQC isModerate ANDQN isModerate, THEN EX isModerate.6. IF QC is Many AND QN is Many AND ARC is Medium AND ARN
is short AND ERC is Short AND SNeC is Worse AND SNeN isWorse AND ESC is Better AND ESN is No Change, THEN EX isMany.
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Table 2: Average delay per vehicle due to uniform arrivals.
7. IF QC is Many AND QN is Many AND ARC is High AND ARN isshort AND ERC is Medium AND SNeC is Worse AND SNeN isNo Change AND ESC is No Change AND ESN is Worse, THENEX is Too Many.
8. IF QC is Too Many, THEN EX is Too Many.
5.5. Details of the proposed algorithm
To control a traffic signal in an eight phase intersection, wehave used an algorithm that is a combination of fuzzy logicmethods and learning automata. The algorithm has two mainparts:
(i) To determine the green signal priority of phases;(ii) To increase the time of the selected phase (extender).
The minimum determined time for the green light is 10 s,that the extender of the phase can increase that amount to 5times more, which each time would be 0 to 10 s. As a result,the maximum time of a green signal would be determined as60 s [36]. Each time the algorithm is performed one secondbefore, the time is increased.
The performance of the algorithm is prioritized as follows:
1. One phase out of eight phases is selected to make the trafficsignal green.
2. The phase prioritizing section considers the priorities of thevehicles that have an emergency. Then, the average numberof vehicles waiting to cross the intersection is calculatedand accordingly the signal switches to green. For example,in any phase, if a vehicle exists having an emergency state,then the traffic signal in which the vehicle is located, turnsgreen and the previous phase, having a green signal, turnsred. Accordingly, in this way, the phase prioritizing sectionperforms itself.
3. In a selected phase, if there is no request for any vehicleto cross the intersection, then this phase is neglected andcontrol goes to part 2.
4. If there is a vehiclewith an emergency state present, then theextender should increase the duration of the green signal toenable the vehicle to exit the phase.
5. Repeat for 10,000 times:I. The extender of the green signal, in each learning au-
tomaton, would select one event considering the deter-mined probability. Therefore, as a result, for all inputparameters, QN ,Qc , four membership functions, and forall input parameters, ESC , ESN , SNeC , SNeN , ARC , ERC , ARN ,three membership functions would be created.
II. The membership degree for each parameter, ARC , ERC ,ARN , ESC , ESN , SNeC , SNeN ,QC ,QN , would be calculated
considering the achieved information from thefollowing:(i) The sensors, located at the intersections;(ii) The traffic information related to prior periods;(iii) Created membership functions in the previous part
(I).III. Considering the amount of achieved membership for
input parameters, and by activation of fuzzy rules, theoutput function would be determined.
IV. Considering the new traffic conditions at the intersec-tions, due to the increase of time in the green signal,a bonus or penalty is allotted to learning automata, ac-cordingly. Probability vectors of the learning automataof input parameter membership functions are updatedaccording to the following step:• If the Qc Queue condition is worse than before, a
penalty is assigned to the selected action; otherwise,a bonus is assigned to the selected action.
6. If no extra time was allotted to the green signal by theextender, or the extender was repeated five times, then thephase has to be changed, therefore, go to part 2, otherwise,go to part 3.
5.6. Modelling the proposed algorithm
Amodel is created and shown in the following figure, whichillustrates Coloured Petri net tools for controlling the traffic[1,37,38].
LA’s actions selector module. To obtain the best result, modelS in learning automata with different parameters has beentested. Each leaning automata consists of 10 actions with initialprobability, 0.1. In the S model, if αi action is selected after(n) repetitions, with the environment responding to it, thenthe unfavourable response would be βi(n) = 1. If the queuegets worse, a penalty is allotted, otherwise the environmentfavourable response would be:
βi(n) =1
1 +previousnew
QcQc
,
whichmeans that if the queue gets better, a reward is given, andwe could get a better response from the environment, which isshown in the simulation section. For eachmembership functionin S − LReP , learning automata are used with parameters a =
0.1 and b = 0.01, which are the rate of reward and penalty,respectively.
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Figure 8a: Main model.
Figure 8b: Determining the phases’ priorities submodel.
Fuzzifier module. Here, according to selected actions, theamounts of input parameter are converted to a fuzzy module.Note that for producing input parameters, QC and QN , Poissondistribution and, for remaining inputs, uniform distributionhave been used. Figure 8 represents a sample coloured Petri netfuzzifier module of parameter QN .
Rules and defuzzificationmodule. Rules are applied, and achievedresults are converted to numerical values. This shows the
amount of increased time applied to the green signal (Fig-ure 8) [39–41].
6. Simulation results
A uniform delay formula is used to calculate the averagedelay of each vehicle [42,43]. A simulatedmodelwas performed600 times by the colored Petri net tool to achieve the required
S. Barzegar et al. / Scientia Iranica, Transactions D: Computer Science & Engineering and Electrical Engineering 18 (2011) 554–565 563
Figure 8c: Rule and defuzzification submodel.
Figure 8d: QC fuzzifier module submodel.
results. The average delay of the 8 transitional phases iscalculated and shown in Table 2.
In [4], when the traffic volume in all directions reaches 1600,the mean delay in 2 transitional phases is approximately 27 (s).The calculatedmean delay of vehicles in 4 transitional phases isreported in [36] (Table 3).
7. Conclusions
In this paper, an adaptive fuzzy coloured Petri net hasbeen presented, based on learning automata, to efficientlycontrol traffic signals across intersections. The basis of therecommended algorithm was to combine fuzzy logic andlearning automata. Learning automata were used to regulate
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Table 3: Average delay per vehicle with abnormalities.
Phases 1 2 3 4AV (s) 32 19 20 20
and adjust membership functions in the fuzzy system. Thecomparative model tries to predict the perfect status, andrepresents the current status of the system according to theinformation achieved from the prior states, combined withthe reactions of the dynamic environment. The achieved delayaverage of (r) vehicles in our algorithms was compared to theother known algorithms for evaluation. The results achievedshowed that the proposed algorithm has a significantly betterperformance in achieving the specified goal.
References
[1] Jensen, K., Kristensen, L.M. andWells, L. ‘‘Coloured Petri nets and CPN toolsfor modelling and validation of concurrent systems’’, International Journalof Software Tools Technology Transfer, pp. 213–254 (2007).
[2] Asar, A., Zhou, M. and Caudill, R.J. ‘‘Making Petri nets adaptive: A criticalreview’’, IEEE Networking, Sensing and Control Proceedings, pp. 644–649(2005).
[3] Pappis, C.P. and Mamdani, E.H. ‘‘A fuzzy logic controller for a trafficjunction’’, IEEE Transactions on Systems, Man and Cybernetics, 7(10),pp. 707–717 (1977).
[4] Niittymaki, J. and Pursula, J. ‘‘Signal control using fuzzy logic’’, Fuzzy Setsand Systems, 116(1), pp. 11–22 (2000).
[5] Niittymaki, J. and Kikuchi, S. ‘‘Application of fuzzy logic to the control of apedestrian crossing signal’’, Transportation Research Record: Journal of theTransportation Research Board, 1651, pp. 30–38 (1998).
[6] Chiu, S. ‘‘Adaptive traffic signal control using fuzzy logic’’, Proc. of the IEEEIntelligent Vehicles Symposium, pp. 98–107 (1992).
[7] Niittymaki, J. ‘‘Installation and experiences of field testing a fuzzy signalcontroller’’, European Journal of Operational Research, 131, pp. 273–281(2001).
[8] Huang, Y.S., Chung, T.H. and Lin, T. ‘‘Design and analysis urban trafficlights using timed colour Petri nets’’, Proc. of IEEE International Conf. onNetworking, Sensing and Control, pp. 248–253 (2006).
[9] Davoudpour, M. and Rudakov, E.V. ‘‘Formal model of decompositionalgorithm for functional block in discrete devices’’, Vestnik InstrumentsJournal, 1, pp. 90–98 BaumanMoscow State Technical University,Moscow,Russia (2006).
[10] Narendra, K.S. and Thathachar, M.A.L., Learning Automata: An Introduction,Prentice Hall (1989).
[11] Yeung, D.S., Liu, J.N.K., Shiu, J.N.K. and Fung, G.S.K. ‘‘Fuzzy coloured Petrinets in modelling flexible manufacturing systems’’, ITESM, pp. 100–107(1996).
[12] Ouchi, Y. and Tazaki, E. ‘‘Learning and reasoning method using fuzzycoloured Petri nets under uncertainty’’, Proc. of the IEEE International Conf.on Computational Cybernetics and Simulation, 4, pp. 3867–3871 (1997).
[13] Zhou, C. and Jiang, Z. ‘‘Fault diagnosis of TV transmitters based on fuzzyPetri nets’’, Proc. of the IMACSMulticonference on Computational Engineeringin Systems Applications (CESA), pp. 2003–2009 (October 4–6, 2006).
[14] Khosla, R. and Dillon, T. ‘‘Intelligent hybrid multi-agent architecturefor engineering complex systems’’, International Conference on NeuralNetworks, 4, Houston, TX, ISBN: 0-7803-4122-8, pp. 2449–2454 (2002).
[16] Rutkowski, L. and Cpalka, K. ‘‘Flexible neuro-fuzzy systems’’, IEEETransactions on Neural Networks, (ISSN: 1045-9227) 14(3), pp. 554–574(2003).
[17] Tsuji, K. and Matsumoto, T. ‘‘Extended Petri net models for neuralnetworks and fuzzy inference engines — their net structural properties’’,IEEE International Symposium on Circuits and Systems, New Orleans, LA, 4,pp. 2670–2673 (2002).
[18] Hadjinicolaou, M.G., Abdelrazik, M.B.E. and Musgrave, G. ‘‘Structuredanalysis for neural networks using Petri nets’’, Proceedings by the 33rdIEEE Midwest Symposium on Circuit and Systems, Calgary, Canada, 2, pp.770–773, ISBN: 0-7803-0081-5, (2002).
[19] Venkatesh, K., Masory, O. and Pandya, A. ‘‘A high level Petri net model ofolfactory bulb’’, Proceedings of the IEEE International Conference on NeuralNetworks, 2, Sanfrancisco, CA, pp. 766–771 (2002).
[20] Ahson, S.I. ‘‘Petri net models of fuzzy neural networks’’, Proceedings in IEEETransactions on Systems, Man and Cybernetics, 35(6), pp. 926–932 (2002).
[21] Hirasawa, K., Oka, S., Sakai, S., Obayashi, M. and Murata, J. ‘‘LearningPetri network with route control’’, IEEE International Conference on Manand Cybernetics, Intelligent Systems for the 21st Century, 3, Vancouver, BC,pp. 2706–2711 (2002).
[22] Hirasawa, K., Ohbayashi, M., Sakai, S. and Hu, J. ‘‘Learning Petri networkand its application to nonlinear system control’’, Proceedings in IEEETransactions on Systems, Man, and Cybernetics, Part B: Cybernetics,(ISSN: 1083-4419) 28(6), pp. 781–789 (2002).
[23] Zha, X.F., Lim, S.Y.E. and Fok, S.C. ‘‘Integration of knowledge-based systemsand neural networks: neuro-expert Petri net models and applications’’,Proceedings in IEEE International Conference on Robotics and Automation, 2,pp. 1423–1428, ISBN: 0-7803-4300-X, (2002).
[24] Tsang, Eric C.C., Yeung, Daniel S. and Lee, JohnW.T. ‘‘Learning capability infuzzy Petri nets’’, Proceedings in IEEE International Conference on Systems,Man and Cybernetics, 3, pp. 355–360, ISBN: 0-7803-5731-0 (2002).
[25] Li, X. and Lara-Rosano, F. ‘‘A weighted fuzzy Petri netmodel for knowledgelearning and reasoning’’, Proceedings in IEEE International Joint Conferenceon Neural Networks, 4, pp. 2368–2372, ISBN: 0-7803-5529-6 (2002).
[26] Li, X., Yu, W. and Lara-Rosano, F. ‘‘Dynamic knowledge inference andlearning under adaptive fuzzy Petri net framework’’, Proceedings in IEEETransactions on Systems, Man, and Cybernetics, Part C: Applications andReviews, 30(4), pp. 442–450 (2002).
[27] Chen, X., Jin, D. and Li, Zh. ‘‘Fuzzy Petri nets for rule-based pattern clas-sification’’, Proceedings in IEEE International Conference on Communica-tions, Circuits and Systems and West Sino Expositions, 2, pp. 1218–1222,ISBN: 0-7803-7547-5 (2003).
[28] Jones, I.R. and Tracy, D.P. ‘‘A multi-threaded simulator for a distributedcontrol system’’, Proceedings in IEEE International Conference on Systems,Man and Cybernetics, 3, pp. 2272–2277, ISBN: 0-7803-7952-7 (2003).
[29] Gao, M., Zhou, M.C., Huang, X. and Wu, Z. ‘‘Fuzzy reasoning Petri nets’’,Proceedings in IEEE Transactions on Systems, Man and Cybernetics, Part A:Systems and Humans, (ISSN: 1083-4427) 33(3), pp. 314–324 (2003).
[30] Hanna,M., Buck, A. and Smith, R. ‘‘Fuzzy Petri netswith neural networks tomodel products quality fromaCNC-millingmachining centre’’, Proceedingsin IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems andHumans, (ISSN: 1083-4427) 26(5), pp. 638–645 (2002).
[31] Song, A.H., Ootsuki, J.T., Yoo, W.K., Fujii, Y. and Aekigchu, T. ‘‘FMS’sscheduling by colored Petri net model and hopefield neural networkalgorithm’’, Proceedings in International Session Papers of the 34th SICEAnnual Conference, pp. 1285-1290, ISBN: 0-7803-2781-0 (2002).
[32] Fukuda, O., Tsuji, T., Takahashi, K. and Kaneko, M. ‘‘Skill assistance formyoelectric control using an event-driven task model’’, Proceedings inIEEE/RSJ International Conference on Intelligent Robots and Systems, 2,Lausanne, Switzerland, pp. 1445–1450, ISBN: 0-7803-7398-7 (2002).
[33] Sadeghian, A. ‘‘Nonlinear neuro-fuzzy prediction: Methodology, design &application’’, Proc. of the 10th IEEE International Conference on Fuzzy Systems(FUZZ-IEEE’2001), 2, pp. 1022–1026 (Dec. 2001).
[34] List, G.F. and Cetin, M. ‘‘Modeling traffic signal control using Petri nets’’,IEEE Transactions on Intelligent Transportation Systems, 5(3), pp. 177–187(2004).
[35] Zarandi, M.H.F. and Rezapour, S. ‘‘A fuzzy signal controller for isolatedintersections’’, Journal of Uncertain Systems, 3(3), pp. 174–182 (2009).
[36] Nair, B.M. and Cai, J. ‘‘A fuzzy logic controller for isolated signalizedintersection with traffic abnormality considered’’, Proc. of IEEE IntelligentVehicles Symposium, pp. 1229–1233 (2007).
[37] Li, L., Lin, W.H. and Liu, H. ‘‘Traffic signal priority/preemption controlwith colored Petri nets’’, Proc. of the 8th International IEEE Conference onIntelligent Transportation Systems, pp. 694–699 (2005).
[38] Zhang, L.G., Li, Z.L. and Chen, Y.Z. ‘‘Hybrid Petri net modeling of traffic flowand signal control’’, Proc. of the Seventh International Conference onMachineLearning and Cybernetics, pp. 2304–2308 (2008).
[39] Lee, J., Liu, K.F.R. and Chiang, W. ‘‘A fuzzy Petri net-based expert systemand its application to damage assessment of bridges’’, IEEE Transactionson Systems, Man, and Cybernetics, Part B: Cybernetics, 29(3), pp. 238–247(1999).
[40] Pedrycza, W. and Camargo, H. ‘‘Fuzzy timed Petri nets’’, Fuzzy Sets andSystems, 140(2), pp. 301–330 (2003).
[41] Ting, Y., Lu, W.B., Chen, C.H. and Wang, G.K. ‘‘A fuzzy reasoning designfor fault detection and diagnosis of a computer-controlled system’’,Engineering Applications of Artificial Intelligence, 21, pp. 157–170 (2007).
[42] Barzegar, S., Davoudpour, M., Meybodi, M.R., Sadeghian, A. and Tiran-dazian, M. ‘‘Traffic signal control with adaptive fuzzy coloured Petri netbased on learning automata’’, North American Fuzzy Information Process-ing Society (NAFIPS) (2010).
[43] Fambro, D.B. and Rouphail, N.M. ‘‘Generalized delay model for signal-ized intersections and arterial streets’’, Transportation Research Record,pp. 112–121 (1997).
S. Barzegar was born in Mashhad, Iran, in March 1984. He received his B.S.degree from Iran University of Science and Technology in September 2006,and his M.S. degree from Qazvin Islamic Azad University in August 2010, both
S. Barzegar et al. / Scientia Iranica, Transactions D: Computer Science & Engineering and Electrical Engineering 18 (2011) 554–565 565
in Computer Engineering. His research interests include Modeling, LearningAutomata, and Fuzzy Logic.
M. Davoudpour received a B.S. degree in Electrical Engineering from TehranAzad University, and M.S. and Ph.D. degrees in Information Technology andComputer Science from the Moscow State Technical University of Bauman in2006.
Currently, she is with the Computer Science Department at RyersonUniversity, Toronto, Canada. Her research interests include Non-LinearModeling, Petri Nets, Learning Automata, Fuzzy Logic and its Applications.
M.R. Meybodi received B.S. and M.S. degrees in Economics from ShahidBeheshti University in Iran in 1973 and 1977, respectively. He also receivedM.S. and Ph.D. degrees in Computer Science from Oklahoma University, USA,in 1980 and 1983, respectively. Currently, he is Full Professor in the ComputerEngineering Department of Amirkabir University of Technology, in Tehran, Iran.Prior to his current position, heworked from1983 to 1985 as Assistant Professorat Western Michigan University, and from 1985 to 1991 as Associate Professorat Ohio University, USA. His research interests include Channel Management in
A. Sadeghian received a B.S. degree from Tehran Polytechnic University, andM.S. and Ph.D. degrees from the University of Toronto, all in Electrical andComputer Engineering. He is now with the Department of Computer Science atRyerson University, and his research interests include Knowledge-Based ExpertSystems, Neural Networks, Adaptive Neuro-Fuzzy Networks and Non-LinearModeling.
M. Tirandazian received his B.S. degree in 1992, and M.S. and Ph.D. degreesin 1994 and 2006, respectively, from Pune University, India, all in ComputerScience. He has worked on and undertaken research into many areas ofcomputer science, namely, Computer Graphics and Artificial Intelligence, andhas designed algorithms for numerous projects. His main Ph.D. research wasdedicated to developing algorithms for VLSI Design and Optimization, where hehas explored the advantages of embedding Boolean algebra into the PolynomialRing. Currently, he is researching Fuzzy Logic and Its Applications at RyersonUniversity, Toronto, Canada.
