Mathematical model of cars distribution along the road network according to the second Wardrop principle based on the Greenshields model
https://doi.org/10.46973/0201-727X_2023_4_175
Abstract
The paper considers a review of works on the second principle of Wardrop which shows the optimal distribution of car flows for society along the transport network. The review shows that by using modern ITS technologies, the prohibition of travel through sections of the road network can stimulate the behavior of passengers and approach the “systemic optimum”. The travel time model depending on the intensity of the traffic flow was obtained for the classical Greenshields model. Based on this model, the distribution of traffic flows was obtained according to the second Wardrop principle: in the case of “narrow” and “wide” roads; two “narrow” roads. Analytical formulas are obtained for calculating the distribution of cars along two roads. A numerical example is given showing the difference between the principles of Wardrop: “competitive equilibrium” and “systemic optimum”.
About the Authors
M. E. Koryagin
Siberian State Transport University (SSTU)
Russian Federation
Russian Federation
Koryagin Mark Evgenievich, Chair «Higher Mathematics», Doctor of Engineering Sciences, Associate Professor, Head of the Chair
V. I. Medvedev
Siberian State Transport University (SSTU)
Russian Federation
Russian Federation
Medvedev Vladimir Ilyich, Chair «Life Safety», Doctor of Engineering Sciences, Professor
Ju. V. Shvets
Siberian State Transport University (SSTU); Siberian State University of Water Transport (SGUVT)
Russian Federation
Russian Federation
Shvets Julia Vladimirovna, Chair «Higher Mathematics»,
Associate Professor ; Chair «Higher Mathematics and Computer Science», Candidate of Pedagogical Sciences, Associate Professor
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Review
For citations:
Koryagin M.E., Medvedev V.I., Shvets J.V. Mathematical model of cars distribution along the road network according to the second Wardrop principle based on the Greenshields model. Vestnik Rostovskogo Gosudarstvennogo Universiteta Putej Soobshcheniya. 2023;(4):175-183. (In Russ.) https://doi.org/10.46973/0201-727X_2023_4_175
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