Survey Paper on Traffic Flow Control using Cellular Automata

Transcription

1 1 Survey Paper on Traffic Flow Control using Cellular Automata Swati Chauhan, Dept. of Computer Science & Engg., Krishna Institute of Engg. And Technology,Ghaziabad, India Lokesh Kumar, Dept. of Computer Science & Engg.,TULAS Institute of Technology,Dehradun,India ABSTRACT As freeway traffic is increasing in exponential rate day by day need an correct and practical methods to model and control the traffic flow.a cellular Automata (CA) is a system of finite automata that provide a discrete computational model to under the complex behaviour system. This article provides a survey on how researchers can use Cellular Automata to control the traffic on highway including walkers with the cellular automata rules. Many researchers have provided different-different models on different traffic flow (Microscopic, Macroscopic, Mesoscopic, CATS...) to control traffic. CATS(cellular automata model for traffic flow simulation) capable to handle various difficult situations where it is related to discretized traffic into homogeneous cells of equal length, and time is discretized into time steps of equal duration and permit the users to identify locations within the road topology. Keywords CATS, Microscopic, Macroscopic, Mesoscopic, FRESIM, NETSIM, stochasticity, FHWA,NETCELL. I. INTRODUCTION To control the transportation systems Traffic flow modelling is an important step. Traffic can be controlled by analysing the richness and complexity of real traffic. Cellular automata (CA), which has emerged in the last few years as a very promising alternative to existing traffic flow models [1, 2, 3, 4]. With the help of cellular automata we can represent the interaction among individual vehicles including different factors such as throughput, travel time, and vehicle speed. Define the different rules to each vehicle by allowing different vehicles to own different driving rules (acceleration/deceleration, lane change rules, reaction times, etc.), CA models can detain the complexity of real traffic. Using deterministic or stochastic CA model, it can be more effective in secretarial for the inherent variability in generally real traffic. To provide a modelling of highway traffic control CA models are capable to demonstrating both single and multi-lane traffic. Due to the exponential growth of traffic flow, it need an accurate and realistic method to model and predicts the traffic flow. In populated areas it has most probability to create frequent traffic jams and congestions because of a significant profitable damage. In such situations it is harder to build the new rods cause of lack of land. So it may be controlled by using of the resource traffic infrastructure. An example of such a populated area, where roads become overcrowded during the rush-hours is The German state North Rhine -Westphalia (NRW). Every day there occur congestions on the autobahns (the German freeways) in the Rhine-Ruhr region (Dortmund, Duisburg, D usseldorf, Essen, etc.). So it is very needed to make a reliable traffic information systems and traffic management concepts. To control the traffic on the autobahns the German federal Ministry of Transport, Building and Housing endows. CA used to control all traffic models, was developed and tested on topologically simple road networks and the translation to large and topologically complex real road networks, like the autobahn network of NRW, is nontrivial. Cellular automata models used to quantize complex behaviour of traffic by simple individual components. Generally Traffic models provide the address to different traffic problems. Traffic Models have different categories as either macroscopic, Mesoscopic, or microscopic. To describe these types of traffic models cellular automata model for traffic flow simulation CATS model used. II. CELLULAR AUTOMATA Cellular automata were originally introduced by von Neumann and Ulam in the 1960s to perform the study of self-reproduction in biological [5,6,7]. They have been used broadly for physics applications such as particle transport simulations and thermodynamics studies. Cellular automaton model used in the form of a Boolean simulation of traffic flow in Creamer and Ludwig [8].In Boolean model individual vehicles are represented by 1- bit variables that are placed in computer memory locations equivalent to the locations of vehicles on the roadway. Thus, the pattern of cars relate to the rules of cellular automata within a lane of a roadway and represented at a discrete time instant in a chain of logical 0's (representing free space) and 1's (marking the position of a vehicle).cellular automata have become a well-

2 2 established method of traffic flow modelling. Cellular automata have a low computational cost of CA models and provide a possibility to conduct large-scale realties simulations of urban traffic in the cities of Duisburg and Dallas/Fort Worth. [9, 10] Car following models are based on formulas of interaction. CA models function as discrete idealizations of the partial differential equations that describe flows and allow simulation of flows and interactions that are used in intractable (Wolfram, 1994). In CA simulations it is based on very simple rules which are capable of capturing essential system features of extraordinary complexity [11]. Modelling vehicular flows and traffic networks, CA micro simulation has been successfully applied. It has been proven that cellular automata provide an excellent estimate for complex traffic flow patterns over a populated area [12, 13, 14].Over the past several years, researchers have established the applicability of CA to model car-following and vehicular flows. The flow control strategies come out from the significance of the rule set to the individual travellers.ca methods has the ability to capture the fundamental properties of walker movements using a small set of fairly simple rules. It is investigated of flow periodicity for deterministic systems. Generally, traffic flow is considered as a episodic with a finite period of length. This finite period is found to be highly sensitive to traffic density in a no monotonic fashion. To design and control automated roadway systems knowledge of this periodic behaviour play a useful role. III.TRAFFIC FLOW MODELLING USING CELLULAR AUTOMATA In general way traffic flow models are divided into two major parts: 1) Microscopic 2) Macroscopic. 3) Mesoscopic. Microscopic models describe traffic behaviour when vehicles interacting to each other from discrete entities. They could be achieved by analytical models as car following models [15] that was used to complete simulation models, FRESIM [17] and NETSIM [17] simulation software. On the other hand CA micro simulation used to create a model for vehicular flows on roadways which provides thrust for discovering its appropriateness to modelling walker flows as well. Cellular Automata provides as instinctively and experimental model with minimum rules set to control the flow of traffic. Rule set eliminates critical behavioural factors from complex situations and micro simulation provide a clear understanding dynamical system. There are three elements of walker movements that a bidirectional microscopic model have: 1) Side stepping 2) Forward movement 3) Conflict mitigation. [19] Side stepping is defined by the desire of a walker to switch-lanes where movement is laterally to either enable increased velocity or avoid head-on conflicts. Forward movement consider the desired speed of the walker including the position of the immediate neighbourhood. Conflict mitigation considers the opposite direction and avoids the head-on deadlock. There is a description where use of place exchange for extenuating head-on conflicts defined [18].The CA rules set is applied at every time stamp with two parallel updates. 1. Lane assignment 2. forward motions All walkers change their positions in two parallel stages using local rules for each walker. Macroscopic models describe the aggregate behaviour of traffic by describing the relationships between vehicle speed, flow and density. Example macroscopic models include input/output, simple continuum, and higher order range ([15]). It has a limitation that they presume uniform behaviour for all vehicles. The models with cellular automata are deterministic cannot detain the inherent stochastic behaviour in real traffic. Microscopic models generally difficult to extend to multi-lane systems. A key limitation of macroscopic models is their aggregate nature. Because they consider traffic flow continuously and they are incapable of capturing the discrete dynamic behaviour that arises from the interaction of individual vehicles. Macroscopic has a disadvantage that this model cannot calculate approximately travel time, turning movements at intersections, fuel consumption, and control parameters on a short time scale [19]. Mesoscopic models describe the cooperation between the exactness of a microscopic model and computational efficiency of a macroscopic model. When high level of detail is needed then these models are used in real-time simulation [21]. A. One-Lane Traffic Flow using Cellular Automata In Cellular automata space and time are considered discrete and it provides mathematical idealizations of physical systems. A cellular automaton has a regular uniform lattice with finite in amount and discrete variables occupying the various sites. The state of cellular automata is completely specified by the values of rules at each site. The variables at each site update simultaneously based on the values of the own variables and in their

3 3 neighbourhood at the previous time step with definite set of local rule [2, 4]. Traffic model is defined by one dimensional array with C cells including boundary conditions, where N numbers of vehicles maintained in constant way. Each cell (site) may be contained one vehicle or it may be empty [22]. Vehicles Figure 1: one lane in the form of cells which contain one or none vehicle Each cell related to a road segment with a length c equal to the average movement taken in a traffic jam. So traffic density will be = N/C. and Each vehicle has a velocity range from 0 to Vmax. The movement of vehicles within the cells is determined by set of updating rules. These rules are applied to each vehicle in a parallel fashion iteratively. [22] following notations to describe each system state: p(i): exact location of the ith vehicle, s(i): speed of ith vehicle, g(i): gap between the ith and the (i+1)th vehicle Given by g(i) = x(i + 1) - x(i) [22] With Cellular Automata, vehicle motion is calculated by set of updating rules: 1. Acceleration of free vehicles: If V(i) < Vmax and g(i) V(i) + 1, Then V(i) = V(i) + 1.[22] 2. Slowing down because of other vehicles: If V(i) > g(i) - 1, Then V(i) = g(i). 3. Vehicle motion: Vehicle is advanced V(i) sites.[22] These updating rules were first suggested by Nagel [2] and then used in many variations by others [23, 24, 3, and 4]. According to these rules, all vehicles have identical behaviours and follow the same maximum speed. It could have fix maximum speed and then obtained the time slot at each iteration. CA can be useful in gaining insights into the fundamental behaviour of traffic flow. Deterministic CA provides a modelling theory for automated highway systems, where vehicle speeding and vehicle deceleration are externally controlled. An automated highway system would work very much like a deterministic cellular automaton with rules that specify total number of vehicles allowed in the system and the set of allowable vehicle behaviours [22]. B. Stochastic Cellular Automata for Two-Lane Traffic Flow The deterministic fails to report for non-deterministic acceleration and deceleration, inherent variability in vehicle speed. This stochasticity may be the solution that is captured by adding a randomization rule to the three updating rules of the CA model [23]. When after the first two rules apply and reducing the speed result of each vehicle then randomization rules will be applied by some probability [4, 22, 24]. p (i.e., if V > 0 then V = V - 1 with probability p, p 1). Following this randomization step, all vehicles are advanced V cells. The simulation is conducted over 10,000 iterations. The results are similar to those which are obtained in deterministic case and provide a consistent behaviour in real world traffic. It also measures the effect of uncertainty in vehicle behaviour. There are three deceleration probabilities are compared: p = 0, p = 0.1 and p = 0.5. It is seen that increased variability in vehicle behaviour reduces the throughput in the system. Variability also reduces average speed and the duration of the phase of laminar flow [22]. Most highways provide two or more lanes for traffic. CA models are particularly useful in modelling multi-lane traffic so they can unambiguously detain changing rules of lane varying. This approach use a minimal set of acceleration, deceleration, and lane varying rules that are capable of acquiescent practical macroscopic traffic behaviour. Firstly CA model considered for two lane traffic [24].Its initial model was deterministic and used a Vmax = 1. But in this model led to situations where cells (site) of several vehicles move backwards and forwards among lanes without any of the vehicles moving forward. This problem later solved by initiating randomness into lane changing [13] which has a model with Vmax 1. In modelling lane varying behaviour it makes two important assumptions:[22] (1) During lane conversion, only transversal movement are allowed.

4 4 (2) When a vehicle changes lanes, it remains in same lane until it becomes more desirable to move back to the other lane. The lane changing rules, which are applied in parallel to each vehicle, can be summarized as follows:[22,24] 1. Look ahead:- a vehicle looks in front to check the existing gap and can accommodate its current speed - i.e., V(i) g(i). If not, then go to rule Look sideways:- the vehicle seems at the other lane to check if the forward gap on that lane will allow it to maintain or increase its current speed. 3. Look back:- the vehicle seems at the other lane to check if the backward gap on that lane is large enough not to affect the speed of other vehicles. If so, then perform a lane change. Determine gap and check the possibility to change the lane Figure 2: two lanes in the form of cells which contain one or none vehicle with all possibilities Figure 2: Unpredictability can be initiated into lane changing with a probability. C. Vehicular Interaction Traffic Control System based on Cellular Automata It consider the eight way interaction in the form of x1,x2,x3,x4,x5,x6,x7and x8 where every lane is divided in to two lane one is used for forward and another is used for backward direction. This interaction is based on the moore neighbourhood where state of update based on the state of its own and its neighbourhoods [26]. X7 X6 X5 X8 X4 X1 X2 X3 Figure 3: Interaction problem based on moore neighbourhood X6 67 X5 57 X7 77 X8 87 X4 47 X3 37 X1 17 X2 27 Figure 4: Eight way interaction lane

5 5 According to moore neighbourhood states changed based of update function F: S(t+1)=F(S i1 (t), S i2 (t), S i3 (t), S i4 (t), S i (t), S i5 (t), S i6 (t), S i7 (t), S i8 (t) ) This function is based on cellular automata rules [26]. D. Description of and Comparison to Existing Traffic Simulation Models A microscopic urban traffic simulation model was developed by the U.S. Federal Highway Administration (FHWA)[27,28]. It was able of simulating a variety of operational conditions where nodes represent urban intersections or points at which a geometric property changes [27]. Every vehicle has an individual entity whose position must be updated every second. The effect of pedestrian traffic (which can delay vehicles at intersections) is also considered in the simulation because it considers the intersections with vehicles. NETSIM distinguishes between public and private vehicles [27] where CATS is used only used to simulate freeway traffic so it does not provide difference between private and public vehicles and the effects of walker traffic. A CAT does not make any guess about the drivers of the individual vehicles. FRESIM is the complement of NETSIM and most powerful microscopic freeway strip simulation model developed by the FHWA [27, 29]. The road topology is defined as same to that of NETSIM but FRESIM support complete topological types. The difference between FRESIM and CATS is that the FRESIM model concludes the number of vehicles into the road with a probability distribution that is based on traffic volumes, whereas CATS uses real size data occupied from embedded traffic sensors in the freeway. The cell transmission model developed as a Mesoscopic traffic flow model where vehicles moves on the basis of averaged macroscopic conditions but the cell size kept small enough to confine the microscopic state of individual vehicles [22, 30, 31]. This model is equivalent to the hydrodynamic model according to this model; traffic is described as fluid with relationships between flow, concentration and speed [22]. The implementation Mesoscopic traffic flow model used NETCELL, a freeway network simulation package and represents the road topology by a series of cells and arcs [32]. CATS model follows the steps for developing traffic simulation models in first step, input data and vehicle motion models are explained which are followed by a discussion of the vehicle position update algorithm [39]. The cellular automaton model for freeway traffic developed a CATS model [33, 34, 9, 35, 36, and 37] and this model is used to create traffic with open road boundary conditions. The CATS model is firstly used to simulate road sections with open boundary conditions. Creamer and Ludwig have used a cellular automaton model with a Boolean simulation of traffic flow [8] where Boolean model signifies individual vehicles by 1-bit variables to the locations of vehicles on the roadway. CA model used to perform large-scale real-time simulations of urban traffic in the cities of Duisburg and Dallas/Fort Worth [10]. The simulated data used to compare for establishing theoretical results and the simulated data are compared to real data [38]. Distance between successive vehicles in a traffic lane is measured from some common reference point on the vehicles as the front bumpers or front wheels [39]. Represent the breakdown of traffic flow [40]. It can be measured the shape of the flow density curve is from the linear speeddensity model [41, 42, 43]. IV.CONCLUSION This survey paper represents the different techniques, models to control the traffic flow. The model uses cellular automaton theory to form complex traffic behaviour. Seen the advantage of cellular automata approach which define roadway is quantized into simple homogeneous cells, time is quantized into discrete time steps. CATS can imitate traffic flow on the road of the actual time period. Models predicts traffic flow on mainlines. Provide a key difference between CATS and existing models. The solution for one lane and two lane traffics providing using cellular automata s rules. For deterministic systems, traffic flow is determined by acquiring a finite period which is highly sensitive to density. CA models are more acquiescent to modelling multi-lane traffic based on Moore neighbourhood concept and lane changing rules and behaviour can be accounted for in the model. It is shown that frequent lane changing means an increase in the possibility of traffic accidents so traffic should be activated at lower densities using ramp meters. Cellular automata provide different rules for acceleration, deceleration, and lane changing to different vehicles also include the model which is based on a single entry/single exit system as well as multiple entries and exits. V.ACKNOWLEDGMENT The authors would like to thank Prof. Anand Prakash Shukla for providing the relevant information to the training of cellular automata. VI.REFERENCES [1] Blue, V., Bonetto, F. and M. Embrechts, A Cellular Automata of Vehicular Self Organization and Nonlinear Speed Transitions, Transportation

6 6 Research Board Annual Meeting, Washington, DC, [2] Nagel, K., Particle Hopping Models and Traffic Flow Theory, Physical Review E,"Vol. 3, No. 6, pp , [3] Schadschneider, A. and M. Schreckenberg, Cellular Automaton Models and Traffic Flow, Journal of Physics A, Vol. 26, pp , [4] Villar, L. and A. de Souza, Cellular Automata Models for General Traffic Conditions on a Line, Physica A, Vol. 211, pp , [5] Wolfram, S., Theory and Applications of Cellular Automata, World Scientific, [6] Von Neumann, Collected Works, [7] Fathy, S., Some ideas and prospects in biomathematics. Ann. Rev. Bio., page 255, [8] Creamer, M. and J. Ludwig, A fast simulation model for traffic flow on the basis of Boolean operations, Mathematical and Computers in Simulation, Vol 28, pp ,1986. [9] Esser, J. and M. Schreckenberg. Microscopic simulation of urban traffic based on cellular Automata, International Journal of Modern Physics C, Vol. 8, No. 5, pp ,1997. [10] Fuks, H, Exact Results for deterministic cellular automata traffic models,physical Review E, Vol 60, No. 1, pp , [11] Bak, P., How Nature Works: The Science Of Self-Organized Criticality. Springer, New York. [12] Nagel, K., Rasmussen, S., 1994, Traffic at the edge of chaos, In: Artificial Life IV: Proceedings of the Fourth International workshop on the Synthesis and Simulation of Living Systems. pp. 222±225. [13] Paczuski, M., Nagel, K., Self-Organized criticality and 1/f noise in traffic. Los Alamos Unclassified Report 95:4108, Los Alamos National Laboratory, Los Alamos, New Mexico; In: Wolf, D.E., Schreckenberg, M., Bachem (Eds.), Traffic and Granular Flow, Singapore: World Scientific, 1996, p. 41. [14] Nagel, K., 1998, From particle hopping models to traffic flow theory, Transportation Research Record 1644, 1±9. [15] Gerlough, D. L. and M. J. Hunber, Traffic Flow Theory - A Monograph, Transportation Research Board National research Council, Special Report 165, [16] FRESIM User Guide, Version 4.5, Federal Highway Administration, US Department of Transportation, Washington, DC, [17] Rathi, A. K. and and A. J. Santiago, The New NETSIM Simulation Program, Traffic Engineering and Control, pp , [18] Blue, V.J, Adler and J.L, Cellular automata micro simulation of bi-directional pedestrian flows. Presented at the 79th Annual Meeting of the Transportation Research Board, Washington, DC (forthcoming in Transportation Research Record), [19] V.J. Blue, J.L. Adler, Cellular automata micro simulation for modelling bi-directional pedestrian walkways, Transportation Research Part B 35 (2001) 293±312. [20] May, A.D. Models for Freeway Corridor Analysis, Technical Report, National Academy of Sciences, Spec. Rep. 194, [21] Ziliaskopoulos, A. and S. Lee, A Cell Transmission Based Assignment-Simulation Model For Integrated Freeway/Surface Street Systems, Transportation Research Board 76th Annual Meeting, January [22] Saifallah Benjaafar, Kevin Dooley and Wibowo Setyawan, Cellular Automata for Traffic Flow Modelling, Department of Mechanical Engineering, University of Minnesota,Minneapolis, MN [23] Nagatani, T., Jamming Transition in the Traffic Flow Model with Two-Level Crossings, Physical Review E, Vol. 48, No. 5, pp , [24] Nagatani, T., Self Organization and Phase Transition in the Traffic Flow Model of a Two- Lane Roadway, Journal of Physics A, Vol. 26, pp , [25] Rickert, M., Nagel, K., Schreckenberg, M. and A. Latour, Two Lane Traffic Simulations using Cellular Automata, Physica A, submitted, [26] Debasis Das,RajivMishra, Vehicular interaction traffic control system based on cellular automata, department of computer science, IIT Patna [27] CORSIM User Manual Version 1.01, U.S. Department of Transportation, Federal Highway Administration, Washington D.C. August [28] Prevedouros, P.D. and Y. Wang, Simulation of Large Freeway and Arterial Network with CORSIM, INTEGRATION, and WATSIM, Transportation Research Record, Vol 1678, pp , [29] Smith S., R. Worrall, D. Roden, R. Pfefer and M. Hankey, Application of Freeway Simulation Models to Urban Corridors Volume I: Final Report, U.S. Department of Transportation, Federal Highway Administration FHWA-RD , Washington D.C., [30] Daganzo, C. The Cell Transmission Model: A Dynamic Representation of Highway Traffic Consistent with Hydrodynamic Theory. Transportation Research B., Vol. 28B, No.4, pp ,1994. [31] Daganzo, C. The Cell Transmission Model Part II: Network Traffic. Transportation Research B.,Vol. 29B, No. 2, pp , [32] Cayford, R., W. Lin and C. Daganzo.The NETCELL simulation package: Technical

7 7 Description. California PATH Research Report, UCB-ITS-PRR-97-23, [33] Nagel, K. and M. Schreckenberg. A Cellular Automaton Model for Freeway Traffic, Journal de Physique I France, Vol. 2, pp , [34] Wagner, P, K. Nagel and D. Wolf. Realistic multilane traffic rules for cellular automata, Physica A, Vol. 234, pp , [35] Schreckenberg, M, A. Schadschneider, K. Nagel and N. Ito, Discrete Stochastic Models for Traffic Flow, Physical Review E, Vol. 51, No. 4, pp , [36] Nagel, K., D. Wolf, P. Wagner and P. Simon, Twolane traffic rules for cellular automata: A systematic approach. Physical Review E, Vol. 58, No. 2, pp , [37] Rickert, M., P. Wagner and Ch. Gawron, Real- Time Traffic Simulation of the German Autobahn Network, Report No , Proceedings of the 4th Workshop on Parallel. [38] Nsour, S. and A. Santiago. Comprehensive Plan Development for Testing, calibration and validation of CORSIM. Compendium of Technical Papers, 64th ITE Annual, Meeting, pp , [39] Lieberman, E. and A. Rathi, Traffic Simulation, Transportation Research Board Special Report 165, Traffic Flow Theory, [40] McShane, W.R., R.P. Roess and E.S. Prassas. Traffic Engineering Second Edition. Prentice Hall, New Jersey, [41] Highway Capacity Manual Special Report 209. Transportation Research Board, National Research Council, Washington, D.C., [42] Salter, R.J. and N.B. Hounsell, Highway Traffic Analysis and Design Third Edition, Macmillan Press, London, [43] Greenshields, B, A Study of Traffic Capacity, Proceedings of the Highway Research Board, Vol. 14, Transportation Research Board, National Research Council, Washington, D.C., 1934