Flows in Transportation Networks. Spatial Distribution and its Dynamic Properties

Sławomir Dorosiewicz

doi:https://doi.org/10.59139/ps.2012.02.2

Sławomir Dorosiewicz Szkoła Główna Handlowa w Warszawie Przegląd Statystyczny. Statistical Review, vol. 59, 2012, 2, pages: 138-148 Published online: 30 June 2012 DOI https://doi.org/10.59139/ps.2012.02.2

503 Views 27 Downloads

ARTICLE

(Polish) PDF

ABSTRACT

This paper refers to Dynamic Traffic Assignment Problem. A consecutive dynamic model of traffic flows is formulated. Some of its dynamical properties (including existence of chaotic solutions and bifurcations) are examined in special cases.

KEYWORDS

Traffic Assignment, Bounded Rationality, Dynamical Systems

REFERENCES

[1] Bentkowska-Senator K., Kordel Z., Polski transport samochodowy ładunków. Wyd. Kodeks, Bydgoszcz-Gdansk-Warszawa, 2007.

[2] Bie J., Lo H.K., Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation, Transportation Research, Part B, vol. 44 (2010), pp. 90-107.

[3] Burnewicz J., Prognoza zapotrzebowania na usługi transportowe w Polsce do 2020 roku. W: Uwarunkowania rozwoju systemu transportowego Polski (red.red. B. Liberadzki, L. Mindur), Uwarunkowania rozwoju systemu transportowego Polski, str. 125-167. Wydawnictwo ITE, 2006.

[4] Cantarella G.E., Cascetta E., Dynamic processes and equilibrium in transportation networks: towards a unifying theory. Transportation Science 29 (4) 1995, pp. 305-329.

[5] Cho H.J., Hwang M.C., Day-to-day vehicular flow dynamics in intelligent transportation network. Mathematical and Computer Modelling 41 (4-5) 2005, pp. 501-522.

[6] Dorosiewicz S., Potoki w sieciach transportowych. Wydawnictwo Instytutu Transportu Samochodowego. Warszawa 2010r.

[7] Florian M., Hearn D., Networks Equilibrium Models and Algorithms, In: Network Routing. Handbooks of Operations Research and Management Science (M.O. Ball et all. eds). Volume 8. North-Holland, Amsterdam, 1995.

[8] Friesz T.L., Bernstein D., Mehta N.J., Tobin R.L., Ganjalizadeh S., Day-to-day dynamic network disequilibria and idealized traveler information systems. Operations Research 42(6), 1994, pp. 1120-1136.

[9] Horowitz J.L., The stability of stochastic equilibrium in a two link transportation network. Transportation Research Part B 18 (1) 1984, pp. 13-28.

[10] Kloeden P.E., Platten E., Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, Heidelberg, 1992.

[11] Medio A., Lines M., 2001. Nonlinear Dynamics. A Primer. Cambridge University Press, 2003.

[12] Medio A., Lines M., IDMC interactive Dynamical Model Calculator. User Quide, available at www.dss.uniud.it/nonlinear, 2004.

[13] Menes E., Dylematy rozwoju motoryzacji indywidualnej w Polsce. Wyd. Instytutu Transportu Samochodowego, Warszawa, 1998.

[14] Mounce R., Convergence in a continuous dynamic queueing model for traffic networks. Transportation Research Part B 40 (9) 2006, pp. 779-791.

[15] Smith M.J., The stability of a dynamic model of traffic assignment-an application of a method of Lyapunov. Transportation Science 18 (3) 1984, pp. 245-252.

[16] Transport. Wyniki działalnosci, Wyd. GUS. Warszawa 2008r.

[17] Watling D.P., Stability of the stochastic equilibrium assignment problem: a dynamical systems approach. Transportation Research Part B 33 (4) 1999, pp. 281-312.

[18] Watling D.P., Hazelton M.L., The dynamics and equilibria of day-to-day assignment models. Networks and Spatial Economics 3 (3) 2003, pp. 349-370.

[19] Zhang D., Nagurney A., On the local and global stability of a travel route choice adjustment process. Transportation Research Part B 30 (4) 1996, pp. 245-262.

[20] Wardrop J.G., Journey speed and flow in central urban areas. Traffic Engineering and Control, 9 1968, pp. 528-532.