A Modified Cellular Automaton Model in Lagrange Form with Velocity Dependent Acceleration Rate
Road traffic micro simulations based on the individual motion of all the involved vehicles are now recognized as an important tool to describe, understand and manage road traffic. With increasing computational power, simulating traffic in microscopic level by means of Cellular Automaton becomes a real possibility. Based on Nasch model of single lane traffic flow, a modified Cellular Automaton traffic flow model is proposed to simulate homogeneous and mixed type traffic flow. The model is developed with modified cell size, incorporating different acceleration characteristics depending upon the speed of each individual vehicle. Comparisons are made between Nasch model and modified model. It is observed that slope of congested branch is changed for modified model as the vehicle that are coming out of jam having dissimilar acceleration capabilities, therefore there is not a sudden drop in throughput near critical density Pc .
[1] Helbing, D., Herman, H.J., Schrekenberg, M. and Wolfe, D.E. Traffic and Granular Flow. Berlin: Springer, (2000).
[2] Cremer, M. and Ludwing, J. A fast simulation model for traffic flow on the basis of Boolean operations. Mathematics and Computers in Simulation, 28(4), 297-303 (1986).
[3] Wolfram, S. Theory and application of Cellular Automata. World Scientific Singapore (1986).
[4] Nagel, K. and Schrekenberg, M.. A Cellular Automata for freeway traffic. Journal of Physics I France ,2, 2221-2229 (1992).
[5] Chakroborty, P. and Maurya, A.K. Microscopic Analysis of Cellular Automata based traffic flow models and an improved model. Transport reviews, 28 (6),717-734 (2008).
[6] Chowdhery, D., Santen, and Schadschneider, A. Statistical Physics of vehicular traffic and some related systems. Physics Report, 329 (4-6), 199- 329 (2000).
[7] Brockfield, E., Barlovic, R., Schadschneider, A. and Schrekenberg, M. Optimizing traffic lights in a Cellular Automata model for city traffic. Physical Review E, 64 (5), 056132-1-12 (2001).
[8] Spyropoula, I. Modelling a signal controlled traffic stream using Cellular Automata . Transportation Research Part C, 15 (3), 175-190 (2007).
[9] Lan, W.L. and Chang, C.W. Motorbike’s moving behavior in mixed traffic: Particle hoping model with Cellular Automata. Journal of Eastern Asian Society for transportation studies, 5, 23-37 (2003).
[10] Mallikarjuna, C. and Rao, K. Identification of a suitable Cellular Automata model for mixed traffic. Journal of Eastern Asia Society for Transportation Studies 7, 2454-2468 (2007).
[11] Rawat, K., Katiyar, V. K. and Pratibha., Modeling of single lane traffic flow using Cellular Automata. International Journal of Applied Mathematics and Mechanics, 6 (5), 46- 57 (2010).
[12] Nishinari, K. A Lagrange representation of Cellular Automaton traffic flow models. Journal of Physics A: Mathematical and General, 34 (48), 10727-10736 (2001)
[13] Takayasu, M.and Takayasu, H. 1/f noise in traffic model. Fractals 1(4), 860-866 (1993).
[14] Benjamin, S., Jhonson, N. and Hui, P.. Cellular Automata models of traffic flow along a highway containing junction. Journal of Physics A: Mathematical and General, 29 (12), 3119- 3127 (1996).
[15] Barlovic, R., Santen, L., Schadschneider, A. and Schrekenberg, M. Metastable States in Cellular Automata for traffic flow. European Physical Journal B, 5(3), 793-800 (1998).