Optimal strategies for traffic flow management on the transportation network of parallel links

A. Yu. Krilatov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2014), pp. 120-129

Résumé

Traffic flows management is one of the major problems of modern cities. Urbanization in conjunction with the development of the automotive industry has led to huge flows of vehicles moving through the streets of modern cities. An impressive cluster of cars in reduced — largely already established — road transport infrastructure leads to congestion on the roads, and consequently, force to delay the supply chains. The latter, in turn, entails serious losses in the economy. Thus, there is an objective demand for the development of a methodology for traffic management and reassignment. In this paper the problem of finding of the optimal traffic flow assignment strategies on a network of parallel channels is studied. Wardrop equilibrium assignment of traffic flows is considered as optimal strategies. Network of parallel channels is studied due to research, according to which a network of arbitrary topology should be presented as a set of pairs of departure-arrival areas interconnected by a set of parallel routes. Using linear BPR-delay function in the formulated problem user-equilibrium and system optimal strategies are found explicitly. Explicit form of found strategies allows us to realize the effective application for the road navigation systems or systems of intelligent infrastructure management in large cities. In fact, obtained explicit user equilibrium can form the basis for high-speed applications in car navigation systems when evaluation of traffic flows based on the Wardrop's principles. In turn, system optimal solutions can be used for finding the optimal topology of transportation networks in big cities. Bibliogr. 16.

Détail

Keywords: Wardrop equilibrium, traffic flows assignment.

Bibliographie

[1] Wardrop J. G., “Some theoretical aspects of road traffic research”, Proc. Institution of Civil Engineers, 2 (1952), 325–378

[2] Beckmann M. J., McGuire C. B., Winsten C. B., Studies in the Economics of Transportation, Yale University Press, New Haven, CT, 1956, 359 pp.

[3] Sheffi Y., Urban transportation networks: equilibrium analysis with mathematical programming methods, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1985, 416 pp.

[4] Yang H., Huang H.-J., “The multi-class, multi-criteria traffic network equilibrium and systems optimum problem”, Transportation Research. Pt B, 38 (2004), 1–15 | DOI

[5] V. A. Drujinina, I. A. Volkova (eds.), Introduction to mathematical modeling of traffic flows, Moscow Institute of Physics and Technology, M., 2010, 360 pp.

[6] Aliev A. S., Strelnikov A. I., Shvetsov V. I., Shershevskii Yu. Z., “Modeling of the city transport flows as applied to the Moscow agglomeration”, Avtomatika i telemehanika, 2005, no. 11, 113–125 | MR

[7] Tong C. O., Wong S. C., “A predictive dynamic traffic assignment model in congested capacity-constrained road networks”, Transportation Research. Pt B, 34 (2000), 625–644 | DOI

[8] Korilis Y. A., Lazar A. A., Orda A., “Architecting noncooperative networks”, IEEE Journal on selected areas in communications, 13:7 (1995), 1241–1251 | DOI

[9] Zakharov V. V., Krilatov A. Yu., “System optimum of traffic flows in megapolis and strategies of navigation providers: theoretic game approach”, Matematicheskaya teoriya igr i eyo prilozheniya, 4:4 (2012), 23–44

[10] Zakharov V., Krylatov A., Ivanov D., “Equilibrium traffic flow assignment in case of two navigation providers”, Collaborative Systems for Reindustrialization, Proc. of the 14thIFIP Conference on Virtual Enterprises PRO-VE 2013, Springer, Dresden, 2013, 156–163 | DOI

[11] Shvetsov V. I., “Mathematical modeling of traffic flows”, Avtomatika i telemehanika, 2003, no. 11, 3–46

[12] Frank M., Wolfe P., “An algorithm for quadratic programming”, Naval Research Logistics Quarterly, 3 (1956), 95–110 | DOI | MR

[13] Shvetsov V. I., “Algorithms for distributing traffic flows”, Avtomatika i telemehanika, 2009, no. 10, 148–157

[14] Daganzo C. F., “The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory”, Transpn. Res. B, 28 (1994), 269–287 | DOI

[15] Korilis Y. A., Lazar A. A., Orda A., “Avoiding the Braess paradox in non-cooperative networks”, J. Appl. Prob., 36 (1999), 211–222 | DOI | MR | Zbl

[16] Horowitz A. J., Delay/Volume Relations for Travel Forecasting Based upon the 1985 Highway Capacity Manual, Department of Civil Engineering and Mechanics University of Wisconsin-Milwaukee, Milwaukee, 1991, 87 pp.