TRAFFIC SIMULATION ON THE BASIS OF THE QGD SYSTEM OF EQUATIONS USING SUPERCOMPUTERS
Pavel A. Sokolov, Moscow Automobile and Road Construction State Technical University (MADI), Moscow, Russia, firstname.lastname@example.org
Irina V. Shkolina, Moscow Automobile and Road Construction State Technical University (MADI), Moscow, Russia, email@example.com
Marina A. Trapeznikova, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia, firstname.lastname@example.org
Antonina A. Chechina, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia, email@example.com
Natalia G. Churbanova, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia, firstname.lastname@example.org
The work is devoted to the relevant problem of mathematical modeling of vehicular traffic flows on road networks of large cities and on highways. To describe the flows, a macroscopic model based on the continuous medium approximation is used. The quasi-gas-dynamic (QGD) system of equations is adapted to the specifics of traffic problems. Main objects of the study are fields of the average vehicle speed and the density of vehicle flow. A one-dimensional version of the QGD model, that allows efficient implementation on high-performance computing systems using logically simple numerical methods, is considered. In many cases, a one-dimensional description may be sufficient to obtain qualitatively correct results of simulation of vehicles’ behavior on complex elements of road networks. In this paper, the QGD model was first supplemented by source terms that represented changes in the number of lanes, due to which traffic on roads with the variable lane number was predicted within the framework of a one-dimensional description. For the purpose of verification, the obtained numerical results are compared with results given by the Lighthill-Whitham-Richards model and with other results presented in the literature. The density dynamics was studied in the case of rarefied as well as fairly dense flow of vehicles. The results of modeling of the passage of regulated and unregulated T-shaped intersections are also presented. The calculations are carried out in KIAM at the MVS-Express supercomputer, which has a distributed memory architecture; a high speed-up of computations has been achieved. In the future, the QGD model equations will be supplemented with functions describing the influence of entrances/exits on the dynamics of traffic flow. Consequently it will be possible to simulate traffic at road junctions that imply minimization of intersections in order to increase the traffic capacity of roads.
Keywords: traffic flow, macroscopic model, quasigasdynamic system of equations, explicit difference schemes, parallel computing.
1. Treiber, M. and Kesting, A. (2013). Traffic Flow Dynamics. Data, Models and Simulation. Springer, Berlin-Heidelberg.
2. Trapeznikova, M.A., Chechina, A.A., Churbanova, N.G. and Polyakov, D.B. (2014). Mathematical simulation of traffic flows based on the macro- and microscopic approaches. Vestnik of Astrakhan state technical university, Series “Management, computer science and informatics”, no. 1, pp. 130-139.
3. Buslaev, A.P., Tatashev, A.G. and Yashina, M.V. (2018). On cellular automata, traffic and dynamical systems in graphs. International Journal of Engineering & Technology, vol. 7, no. 2.28, pp. 351-356.
4. Sukhinova, A.B., Trapeznikova, M.A., Chetverushkin, B.N. and Churbanova, N.G. (2009). Two-Dimensional Macroscopic Model of Traffic Flows. Mathematical Models and Computer Simulation, vol. 1, no. 6, pp. 669-676.
5. Chetverushkin, B.N. (2004). Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenij [Kinetic schemes and quasigasdynamic system of equations]. Moscow: MAKS Press.
6. Samarskij, A.A. (1983). Teoriya raznostnyh skhem [The theory of difference schemes]. Moscow: Nauka.
7. Lighthill, M.H. and Whitham, G.B. (1955). On kinematic waves: A theory of traffic flow on long crowded roads. Proceedings of the Royal Society A: Mathematical, physical and engineering sciences, vol. 229, no. 1178, pp. 317-345.
8. The official site of Keldysh Institute of applied mathematics. Hybrid computational cluster MVS-Express” available at: http://www.kiam.ru/MVS/resourses/mvse.html (Accessed 26 February 2019).
Information about authors:
Pavel A. Sokolov, master student, Moscow Automobile and Road Construction State Technical University (MADI), Moscow, Russia
Irina V. Shkolina, master studentMoscow Automobile and Road Construction State Technical University (MADI), Moscow, Russia
Marina A. Trapeznikova, Senior Researcher, Ph.D., Keldysh Institute of Applied Mathematics RAS, Moscow, Russia
Antonina A. Chechina, Junior Researcher, Keldysh Institute of Applied Mathematics RAS, Moscow, Russia
Natalia G. Churbanova, Senior Researcher, Ph.D., Keldysh Institute of Applied Mathematics RAS, Moscow, Russia