Modeling of Adaptive Traffic Lights. Using Basic Petri Net Marking

Transcription

1 Journal of Innovative Technology and Education, Vol. 3, 26, no., HIKARI Ltd,.m-hikari.com Modeling of Adaptive Traffic Lights Using Basic Petri Net Marking Tomi Tristono Department of Management Informatic of Universitas Merdeka Madiun Serayu Road 79 Madiun East Java Indonesia Setiyo Daru Cahyono Civil Engineering of Universitas Merdeka Madiun Serayu Road 79 Madiun East Java Indonesia Copyright 25 Tomi Tristono and Setiyo Daru Cahyono. This article is distributed under the Creative Commons Attribution License, hich permits unrestricted use, distribution, and reproduction in any medium, provided the original ork is properly cited. Abstract Petri net is a general modeling frameork for the problem solving that associated ith formal analysis, design and coordination logic control of discrete event systems. The block diagram structures provide a high-level overvie of the major system of the components that use basic Petri net marking to construct the behavior of traffic lights model. The common role of the traffic lights is as signal systems to control transportation an intersection at urban netorks. Events in a real case, the major road demand changes periodically. This paper proposes an appropriate schedule model to address these problems. The models analysis using coverability tree, invariant, and simulation. The basic Petri net marking had designed a complex phase for creating profitable the adaptive traffic lights models. Keyords: Petri net, Modeling, Traffic lights Introduction Petri Net (PN) is a general modeling frameork to solve many kinds of problems that associated ith formal analysis, design, and coordination logic control of discrete event systems also [], [2], [7]. The Petri net model has many

2 7 Tomi Tristono and Setiyo Daru Cahyono advantages. The model can present the analysis of behavioral properties and performance evaluations of the system [2], [3]. The traffic lights have a common role as signal systems that control transportation due safety for the road users and efficiency planning [4], [5]. The main classifications of traffic signal systems are [8]:. Fixed time systems and, 2. Traffic responsive systems. Fixed time system is the implementation of the simple control signal that based on historical data. It assumes that the demand is constant, and the actual events in the real orld cannot influence the systems. Otherise, the traffic responsive systems are the real-time systems that use measurements gathering by detectors [9]. The territories have the left-hand traffic [], []. The traffic movement keeps on the left side of the road. The major road traffic demands that prioritized changes periodically. The empirical data has recorded heavy traffic at the first cycle, and lo traffic at the next cycle [6]. This event is the effect of previous signalized intersection that located about three kilometers from the subject intersection. To build the coordination of the both traffic lights schedules are not possible because the distance is too far [5], []. This paper proposes dual schedules of traffic lights model consisting of long (first) and short (second) cycles. These dual schedules are interchangeably active as a transverse ave. The aim of this paper is to build a high-level model using basic Petri net that commonly complicated. Many researchers had presented models, but they applied timed Petri net models using colored tokens. We have built the analysis on the basic Petri net model easily, and some analysis becomes difficult on a timed Petri net model that use colored tokens. Traffic Lights N 2 ta g h 2 2 tb pa ta pb g- pa h- pb pc Traffic Lights Figure.Traffic Stream of A Signalized Intersection. Figure. 2. The block diagram of Petri net structure using single buffer place and its reduction. Figure. 3. The block diagram of Petri net structure using double buffer places (pb and pc) and its reduction

3 Modeling of adaptive traffic lights 7 2 The Intersection and the Block Diagram of Petri Net Structure Fig. shos the signalized intersection and the traffic stream in more detail. The east arm is the major road that has the vehicles arrival as transverse aves during to cycles. The signals allo the traffic that comes from the north arm to move straight to south arm only. Signals do not allo them to turn right. The old traffic lights schedule had fixed time system. It consisted of to phases i.e. phase NS (North South) and phase EW (East West) [], []. The definition of a cycle during each phase of traffic lights schedule presented the sum of the hole duration of the green period, yello, and red lights. Fig. 2 is the design of the block diagram of Petri net structures ith single buffer place. This block consists of to places pa, pb (a buffer), and a transition ta. The Fig. 3 is the block diagram of Petri net structures ith double buffers. These block diagram structures provide a high-level overvie of major system of Petri net components. GEW defines green east-est. YEW: yello east-est, REW: red east-est. GNS is green north-south, YNS: yello north-south, and RNS: red north-south. The state cgew is countdon timer of green east-est, etc. Each traffic light has three states i.e. green, yello, and red. The place state of intermediation SI and SI2 present the state hile both phases turn on red. The dual synchronized schedules of traffic lights in Fig. 4 must use places controller C2, & C4 for the first schedule and C & C3 for the second schedule. 3 Methods Traffic lights have to lit up in the correct order and do not allo deadlock. The role of traffic lights should be able to build the management of vehicle movements to avoid conflicts vehicle stream that are crossing the intersection. The sequence should be able to serve all the signal phases and returnable to the initial state. The analysis uses coverability tree, invariant, and Petri net simulator for simulation []. 4 The Coverability Tree Each token has a timestamp. A token meaning is one unit of time. The number of the tokens in the places countdon timer mean as the duration. The coverability tree presents the reachability tree because it contains all finite states may occur. It has an important role to explain three aspects i.e. boundedness, conservation, and coverability state []. The coverability tree uses column vectors consisting of telve elements. The elements are x, x( cgew ), x2, x( cyew ), x3, x( crew ), x4, x( cgns ), x x( ), 5, cyns x6, x( crns ), x7, x( csi), x8, x( csi 2), x 9, x( C ), x, x( C2), x, x( C 3 ), x2, x( C4). The coverability tree presents a sequence of the firing transitions and makes records of the number of tokens in the places of countdon timer (hich are not as buffers) and controller places.

4 72 Tomi Tristono and Setiyo Daru Cahyono The coverability tree in Fig. 5. refers to Fig. 4. The set of states X consists of telve different main states. T is a set of transitions that located outside of the block diagram of Petri net structures. T={t, t2, t3, t4, t5, t6, t7, t8, t9, t}. The coverability tree has tested its reachability. The deadlock is absence and the analysis has proved the boundedness, conservation, and its returnables to the initial state. 5 Places Invariant and Simulation Result The firing of enables transitions has presented the marking of the Petri net. The invariants provide a guarantee that the markings of a Petri net ould not vary. C C2 cgew cgns 2 t6 t t cyew cyns 2 t 3 3 C3 t7 t8 C4 3 csi csi2 crew crns t 4 t 5 t9 t Figure 4. The Top Don of Control Net Component of Phase NS and EW of Dual Synchronized Schedules of Traffic Lights Using Fixed Time System. The next discussion bases on Fig. 4. Hide all controller places and countdon timer behind the scenes. Install the traffic lights on the control net component ith

5 Modeling of adaptive traffic lights 73 the same connection. Fig. 6 shos the result that appears similar to timed place Petri net [8], [], []. This basic Petri net model has implemented block diagram structures to provide a high-level design. The existence of a token signs that a place sitches on, or off rather than one unit of time. Thus, a binary number set B={, }. The binary states mean on () or off (). The marking x(gns),x(yns), x(rns), x(gew), x(yew), x(rew), x(si), x(si2)b. x(gns) + x(yns) + x(rns) = () The invariant () asserts that could be a place only that turns on at one of three places GNS, YNS, and RNS. x(gew) + x(yew) + x(rew) = (2) x(gns)+ x(yns)+ x(rns)= x(rew) hile x(rew)= (3) The invariant (3) indicates that if place REW sitches at state on then it must turn on in either place GNS, YNS, or RNS. x(gew)+ x(yew)+ x(rew)= x(rns) hile x(rns)= (4) x(si)+ x(gns)+ x(yns) + x(si2)+ x(gew)+ x(yew) = (5) Invariant (5) contains places SI and SI2. This invariant hints that the model systems provide a guarantee of the safety and have no conflict of traffic movement. t 5 t t t t t 7 2 X X 2 X 3 X 4 X 5 X 6 X t t t 3 3 t t t 8 7 X 8 X 9 X X X X Figure 5. Markings of Coverable Tree.

6 74 Tomi Tristono and Setiyo Daru Cahyono GEW GNS t t2 t6 t6 YEW YNS SI t3 t7 t8 REW SI2 RNS t4 t5 t9 t Figure 6. Phase NS and EW Dual Synchronized Schedules of Traffic Lights Table 2. Cycles of Dual Synchronized Schedules of Traffic Lights Inter Green Green Phase Yel All red Red Cycle I II lo SI SI2 I II I II EW NS R GEW ( ) Y REW ( 3) GEW ( 2) Y REW ( 3) RNS () GNS (3) Y RNS () GNS (3) Y R SI 2 SI SI 2 SI SI 2 C 4 C 3 C 4 C 2 C C 2 An East West First cycle An East West Second cycle seconds Figure 7. Simulation Result. 6 Discussion Fig. 4 presents control net component of the basic Petri net models of traffic lights schedules. The second model in Fig. 6 that uses hidden block diagram structures have a similar characteristic to timed place Petri net. The model can design a complex phase of traffic lights schedule. Fig. 8a presents control net component that has the green long-short and red long-short durations. The schedule of Fig. 8b has five times repetition of the green short and once for long durations. The system guarantees can maintain the traffic stability in six cycles. Table 3 referring to Fig. 4 has long and short green east-est traffic lights duration that interchangeably active. Table 3 referring to Fig. 8b and to more

7 Modeling of adaptive traffic lights 75 places as controller have the green 684 times repetition of long duration hile daylight and 54 times of short duration at night in a day. The model can create multiple schedules long/ very long green durations at daytime and short/ very short green time intervals at midnight Green Yello 7 7 Green Yello Red Red a b Figure 8. Various of The Traffic Lights Petri net model on one arm. Table 3. To Phases of First and Second Duration on Green EW Inter Green Green Red Cycle Phase All red Yello s I II SI SI2 I II I II (seconds) EW NS The extension schedule models can use the third or fourth of intermediation state. The traffic light signals consist of phases North-south, east-est, south-north, and est-east. Each phase has a different time allocation. The next time, e hope Petri net model can create the setting that should not miss phase for pedestrians that commonly never have a alk signal. The duration of this complex phase of traffic lights schedule on each arm depends on the traffic demand. The model has designed the adaptive traffic lights model successfully using empirical data.

8 76 Tomi Tristono and Setiyo Daru Cahyono 7 Conclusion The Petri net model of adaptive traffic lights has dual schedules simultaneously. The basic Petri net marking implementing block diagram structures have provided a high-level design. The control net component model looks very complicated. The second model that appears similar to timed place Petri net has reduced the complicated model using hidden control net component to a simple model. The model can build multiple schedules green long/ very long durations at daytime and short/ very short time interval at midnight. Finally, the model can generate the adaptive traffic light signals consisting of phases North-south, east-est, south-north, and est-east. The Petri net model analysis of traffic light schedule on each arm is a poerful technique for creating profitable products. Acknoledgements. This ork as funded by DGHE Indonesia at competitive grant scheme No. 2/SP2H/P/K7/KM/24. References [] D. Adzkiya, Modelling Traffic Light Using Petri Net and Its Simulation, Thesis, Institut Teknologi Sepuluh Nopember, ITS, publisher ITS Digital Repository, Surabaya, (28), -3. [2] C.G. Cassandras, S. Lafortune, Introduction to Discrete Event Systems, The International Series on Discrete Event Dynamic Systems, Kluer Academic Publisher, Norell, Massachusetts, USA, 999, [3] G. Goran, Generic technolo- gies, 25. Petri-net-simulator.softare.informer.com/2. [4] IHMC, Indonesian Highay Manual Capacity, Direktorat Bina Marga Direktorat Bina Jalan Kota, Jakarta, (997), 2-. [5] ITE, Institution of Trasportation Engineers, Traffic Engineering Handbook, 6th ed., Washington, DC, 29, [6] F. Kurniaan, R. A. Al Hasibi, The Concept of Adaptive Traffic Control that Synchronized ith Density as Solutions to Minimize the Duration of the Waiting Time of Vehicles, Semesta Teknik, The Scientific Journal, Faculty of Engineering, UMY, (27), no. 2, [7] T. Murata, Petri Nets: Properties, Analysis, and Applications, Proceedings of IEEE, 77 (989),

9 Modeling of adaptive traffic lights 77 [8] M. Papageorgiou, C. Diakaki, V. Dinopoulou, A. Kotsialos, Y. Wang, Revie of Road Traffic Control Strategies, Proc. of IEEE, 9 (23), no. 2, [9] M. S. Soares, Architecture-Driven Integration of Modeling Languages for the Design of Softare-Intensive Systems, Thesis, Published and distributed by Next Generation Infrastructures Foundation, Delft The Netherlands, 2, 99-. [] T. Tristono, S. D. Cahyono, Sutomo, P. Utomo, Synchronization Model of Traffic Light at Intersection ith Train Track, Proc. of the th ICETIA 24, UMS, Surakarta, (24), [] T. Tristono, S. D. Cahyono, Sutomo, P. Utomo, Coordination Model of Traffic Lights With an Interruption, Proc. of the 22 th National Seminar on Management Technology, ITS, Surabaya, (25), Received: November 5, 25; Published: August 3, 26