Investigation of traffic flow dynamic processes using discrete model

• Autorzy: Bogdevicius M. , Junevicius R.

Identyfikatory

DOI

10.5604/12314005.1130421

• Języki publikacji: EN

Abstrakty

EN

Modelling the process of traffic flow was previously studied from different points of view and different mathematical methods where used to describe the same process. All authors have an agreement on basic traffic flow parameters like, traffic flow density, traffic flow rate or the average speed of traffic flow. Besides, a lot of different investigations into the use of traffic flow models to deal with various problems of engineering are carried out. A comparison of different continuum models has drawn that a number of scientific works were based on fluid dynamic theory and gas - kinetic traffic flow theory. The kinetic traffic flow theory is used in ‘microscopic’ or “macroscopic”, traffic flow models. The kinetic traffic flow theory is used in Flötteröd G., Nagel K., Ging A., Li L., Li-qun X., Prigogine I., Herman R. works where various approaches to the similar method are discussed. The ‘macroscopic’ theory of traffic flows also can be developed as the hydrodynamic theory of fluids that was first introduced by Lighthill-Whitham and Richards’s model. Plenty of traffic flow models are based on car–following theories supported by the analogues to Newton’s equation for each individual vehicle interacting in a system of vehicles on the road. Different forms of the equation of motion give different versions of car–following models. This work presents research of traffic flow dynamic processes, as nonlinear dynamic system, by using a discrete model of traffic flow (DMTF). The main variables in DMTF are traffic flow density and speed. DMTF can be used to describe various traffic flow situations in the roads. The mathematical simulation of traffic flow is made when constant value of traffic flow speed and traffic flow rate is entered. Numerical results of traffic flow dynamics are obtained.

Słowa kluczowe

EN

traffic flow; method; dynamics; numerical results

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2014
• Tom: Vol. 21, No. 4
• Strony: 15--19
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Bogdevicius M.

• Vilnius Gediminas Technical University, Department of Transport and Technological Equipment Plytinės 27, LT–10105, Vilnius, Lithuania tel.:[phone]

autor

Junevicius R.

• Vilnius Gediminas Technical University, Department of Transport and Technological Equipment Plytinės 27, LT–10105, Vilnius, Lithuania tel.:[phone]

Bibliografia

• [1] Chalons, C., Gotin, P., Godunov scheme and sampling technique for computing phase transitions in traffic flow modelling, Interface and Free Boundaries, pp. 197-221, 2008.
• [2] Safanof, L. A., Tomer, E., Strygin, V.V., Havlin, S., Periodic solutions of a non-linear traffic model. Phyica A, pp.147-155, 2000.
• [3] Kim, Y., Keller H., On-line traffic flow model applying the dynamic flow – density relation, Road transport information and control, P. 105, 2002.
• [4] Liu, T., Jia, L., Zhu, W-x., A New traffic flow Model with the Effects of backward Looking and Relative Current, Fuzzy Systems and Knowledge Discovery, FSKD, Fifth International Conference on 5(DOI 10.1109/FSKD.2008.113), pp. 438-442, Jinan Shandong 2008.
• [5] Flotterod, G., Nagel K., High Speed Combined Micro/Macro Simulation of Traffic Flow, Proccedings of the 2007 IEEE Intelligent Transportation Systems conference, P. 6, 2007.
• [6] Bonzani I., Hyperboliciy analyzis of a class of dynamical systems modelling traffic flow, Applied Mathematics Letters, Vol. 20(8), pp. 933-937, 2007.
• [7] Nikolov, E., Traffic flow model based on the Green – function, Intelligent Systems, IS'08, 4th International IEEE Conference 1 (DOI 10.1109/IS.2008.4670421), pp. 4-25-4-32, Varna 2008.
• [8] Gning, A., Mihaylova, L., Boel, R., An interval compositional vehicular traffic model for Real –time applications, IEEE Inteligent Vehicle symposium, pp. 494-499, Eindhoven 2008.
• [9] Li, L., Li-qun, X., Linear stability analysis of a multi-vehicle car-following traffic flow model, Management Science and Engineering, ICMSE 2008, 15th Annual Conference Proceedings, International Conference on (DOI 10.1109/ICMSE.2008.4669125), pp. 1642-1647, Long Beach, CA 2008
• [10] Prigogine, I., Herman, R., Kinetic Theory of Vehicular Traffic, p. 101, New York 1971.
• [11] Tampere, C. M. J., Human-kinetic multiclass traffic flow theory and modelling: with application to advanced driver assistance systems in congestion, Netherlands TRAIL Research School, p. 309, 2004.
• [12] Helbing, D., Greiner A., Modelling and Simulation of Multi-Lane Traffic Flow, (arXiv:condmat/9806126), 1998.
• [13] Karner, B. S., Klenov, S. L., Deterministic three-phase traffic flow models, Journal of Physics A: Mathematical And General, Vol. 39, pp. 1775-1809, 2006.
• [14] Junevičius R., Bogdevičus, M., Mathematical modelling of network traffic flow, Transport Vol. 24(4): 333-338, 2009.