Previous works on CA traffic models focused on pure cars only.
Some of which defined the cell unit with a rather coarse scale, thus the particles might have unrealistic speed jumps or drops. This is obviously not consistent with what we can observe in the mixed traffic contexts. To overcome these shortcomings, we define a common cell unit with much finer square grid as 1.25~1.25 meters. Based on the field observation, a motorcycle in our proposed CA models always occupies 2x 1 cells and a passenger car always takes away 6x2 cells. The maximum speeds for the motorcycle and car are of the same, which are set as 13 cell units per time step with no deviation in our deterministic CA models. The simulation results have shown reasonable interacting relationships among particles in the mixed traffic environments. To validate the deterministic CA models, we use another set of field data where maximum speeds of motorcycle and car are not the same; thus, the CA rules have been slightly modified to accommodate the distinct maximum speeds between these two vehicle types.
In line with the real world situations, we further develop stochastic CA models by considering the deviations of maximum speeds for individual particles of the same type. Compared with the deterministic CA models, we examine the effects of maximum speed deviations on the maximum flow rates and the corresponding critical speeds. It is found that both maximum flow rates and critical speeds have declined with an increase of maximum speed deviations. It is due to the slow-vehicle effect that deteriorates the cell utilization efficiency; however, such decline effect is less significant as the road (lane) gets wider.
346 L. W. Lan and C- K Chang
The present study does not mark the lane to guide the motorcyclists and car drivers, thus the vehicles may occupy the lateral cells in an inefficient manner. Marking the lanes and revising the CA rules accordingly deserve further investigation. The paper deals only with the interacting movements of two vehicle types, motorcycle and car, on the road section where flows are not interrupted by curb parking, crossing vehicles or pedestrians, traffic signals or the like. Future studies can consider more types of vehicles, such as bus and bicycle, with interruptions or traffic lights on the road section or at intersection.
However, it requires introducing more complicated CA rules that can govern the particles stopping, starting, moving or turning behaviors.
Special attentions must be paid to control the particles acceleration or deceleration to avoid any unrealistic abrupt speed jumps or drops. Since the motorcyclists and car drivers may act in a different way in other cities or countries, more empirical case studies from different field environments also deserve further explorations.
Acknowledgements
This paper is moderately revised from the original work [Lan and Chang, 2004al presented at the International Conference on Application of Information and Communication Technology in Transport Systems in Developing Countries, Kalutara, Sri Lanka. The research was granted by the National Science Council of ROC (NSC93-2211-E-009-033). The authors are indebted to two reviewers for giving very good suggestions to ameliorate the original paper.
References
Bham, G. H. and Benekohal, R. F., 2004. A high fidelity traffic simulation model based on cellular automata and car-following concepts. Transportation Research 12C, 1-32.
Bierley, R. L., 1963. Investigation of an inter-vehicle spacing display.
Highway Research Record 25,58-75.
Brackstone, M. and McDonald, M., 1999. Car-following: a historical review. Transportation Research 2F, 18 1 - 196.
Chakroborty, P. and Kikuchi, S., 1999. Evaluation of the general motors based car-following models and a proposed fuzzy inference model.
Transportation Research 7C, 209-235.
Inhomogeneous Cellular Automata ... 347
Chowdhury, D., Wolf, D. E. and Schreckenberg, M., 1997.
Particle-hopping models for two-lane traffic with two kinds of vehicles: effects of lane-changing rules. Physica 235A, 41 7-439.
Daganzo, C. F., 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research 28B, 269-287.
Daganzo, C. F., 2002a. A behavioral theory of multi-lane traffic flow.
Part I: Long homogeneous freeway sections. Transportation Research 36B, 131-158.
Daganzo, C. F., 2002b. A behavioral theory of multi-lane traffic flow.
Part 11: Merges and the onset of congestion. Transportation Research Evans, L. and Rothery, R., 1977. Perceptual thresholds in car following
-
a recent comparison. Transportation Science 1 1,60-72.
Gipps, P. G., 1981. A behavioral car following model for computer simulation. Transportation Research 15B, 105-1 1 1.
Helbing, D., 2001. T&c and related selfkhiven many-particle systems.
Reviews of Modern Physics 73,1067- 1 14 1.
Herman, R., Montroll, E. W., Potts, R. B. and Rothery, R. W., 1959.
Traffic dynamics: analysis of stability in car following. Operations Research 7, 86- 106.
Hermann, M. and Kerner, B. S., 1998. Local cluster effect in different traffic flow models. Physica 255A, 163-188.
Knospe, W., Santen, L., Schadschneider, A. and Schreckenberg, M., 1999. Disorder effects in cellular automata for two-lane traffic.
Physica 265A, 6 14-633.
Kometani, E. and Sasaki, T., 1959. A safety index for traffic with a linear spacing. Operations Research 7,707-720.
Krug, J. and Spohn, H., 1988. Universality classes for deterministic surface growth. Physical Review 83A, 427 1-4286.
Lan, L. W., Wang, J. C. and Chiang, C. I., 1994. On the car following model with fizzy control. Transportation Quarterly 25,43-55.
Lan, L. W. and Yeh, H. H., 2001. Car following behavior for drivers with non-identical risk aversion: ANFIS approach. Journal of the Chinese Institute of Civil & Hydraulic Engineering 13,427-434.
Lan, L. W. and Chang, C. W., 2004a. Inhomogeneous particles hopping models for mixed traffic with motorcycles and cars. International Conference on Application of Information and Communication Technology in Transport Systems in Developing Countries, Kalutara, Sri Lanka, August 5-7.
Lan, L. W. and Chang, C. W., 2004b, Motorcycle-following models of 36B, 159-169.
348 L. W. Lan and C- W. Chang
General Motors (GM) and adaptive neuro-fuzzy inference system (ANFIS). Transportation Planning Journal 33, 51 1-536.
Lighthill, M. H. and Whitham, G. B., 1955. On kinematic waves: a theory of traffic flow on long crowed roads. Proceedings of the Royal Society, Series A 229,3 17-345.
Liu, G., Lyrintzis, A. S . , and Michalopoulus, P. G., 1998. Improved high-order model for freeway traffic flow. Transportation Research Record 1644,37-46.
May, A. D., 1990. Traffic Flow Fundamentals. Prentice-Hall Inc., New Jersey.
Michaels, R.M. and Cozan, L. W., 1963. Perceptual and field factors causing lateral displacement. Highway Research Record 25, 1
-
13.Nagel, K. and Schreckenberg, M., 1992. A cellular automaton model for freeway traffic. Journal de Physique I France 2,222 1-2229.
Nagel, K., 1996. Particle-hopping models and traffic flow theory.
Physical Review 53E, 4655-4672.
Nagel, K., 1998. From particle-hopping models to traffic flow theory.
Transportation Research Record, 1644, 1-9.
Nagel, K., Wolf, D. E., Wagner, P. and Simon, P., 1998. Two-lane traffic rules for cellular automata: A systematic approach. Physical Review
Payne, H. J., 1971. Model of &way traf€ic and control. Mathematics of Public Systems 1,51-61.
Pipes, L. A., 1967. Car following models and the fundamental diagram of road traffic. Transportation Research Record 1 , 2 1-29.
Pottmeier, A., Barlovic, R., Knospe, W. and Schadschneider, A., 2002.
Localized defects in a cellular automaton model for traffic flow with phase separation. Physica 308A, 47 1-482.
Richards, P. I., 1956. Shock waves on highway. Operations Research 4, Rickert, M., Nagel, K., Schreckenberg, M. and Latour, A., 1996. Two lane traffic simulation using cellular automata. Physica 23 1 A, Rockwell, T. H. and Treiterer, J., 1968. Sensing and communication
between vehicles. NCHRP Report 5 1, HRB, Washington, D.C.
Wang, B. H., Wang, L., Hui, P. M. and Hu, B., 2000. The asymptotic steady states of deterministic one-dimensioned traffic flow models.
Physica 27B, 237-239.
Wei, C. H. and Lin, H. C., 1999. Construction of car-following models using artificial neural networks and genetic algorithms.
Transportation Planning Journal 28,353-378.
58E, 1425-1437.
42-5 1 .
534-550.
Inhomogeneous Cellular Automata.. . 349
Wolf, D. E., 1999. Cellular automata for traffic simulations. Physica Wolfram, S., 1986. Theory and Applications of Cellular Automata. Word
Scientific, Singapore.
Wong, G . C. K. and Wong, S. C., 2002. A multi-class traffic flow model -
an extension of L W R model with heterogeneous drivers. Transportation Research 36A, 827-841.
Zhang, H. M., 1998. A theory of nonequilibrium traffic flow.
Transportation Research 32B, 485-498.
263A, 438-45 1.