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Computer Research and Modeling, 2021, Volume 13, Issue 2, Pages 365–379
DOI: https://doi.org/10.20537/2076-7633-2021-13-2-365-379
(Mi crm888)
 

This article is cited in 3 scientific papers (total in 3 papers)

SPECIAL ISSUE
MODELING OF TRAFFIC IN INTELLIGENT TRANSPORTATION SYSTEMS

Finding equilibrium in two-stage traffic assignment model

E. V. Kotlyarovaa, A. V. Gasnikovabc, E. V. Gasnikovaa, D. V. Yarmoshika

a National Research University Moscow Institute of Physics and Technology, 9 Institute lane, Dolgoprudny, 141701, Russia
b Institute for Information Transmission Problems RAS, 9 B. Karetny lane, Moscow, 127051, Russia
c Caucasus Mathematical Center, 208 Pervomaiskaia st., Maikop, 385000, Russia
References:
Abstract: Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of a model for calculating a correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model calculates a matrix of correspondences using a matrix of transport costs (it characterizes the required volumes of movement from one area to another, it is time in this case). To solve this problem, authors propose to use one of the most popular methods of calculating the correspondence matrix in urban studies — the entropy model. The second model describes exactly how the needs for displacement specified by the correspondence matrix are distributed along the possible paths. Knowing the ways of the flows distribution along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage model is a fixed point in the sequence of these two models. In practice the problem of finding a fixed point can be solved by the fixed-point iteration method. Unfortunately, at the moment the issue of convergence and estimations of the convergence rate for this method has not been studied quite thoroughly. In addition, the numerical implementation of the algorithm results in many problems. In particular, if the starting point is incorrect, situations may arise where the algorithm requires extremely large numbers to be computed and exceeds the available memory even on the most modern computers. Therefore the article proposes a method for reducing the problem of finding the equilibrium to the problem of the convex non-smooth optimization. Also a numerical method for solving the obtained optimization problem is proposed. Numerical experiments were carried out for both methods of solving the problem. The authors used data for Vladivostok (for this city information from various sources was processed and collected in a new dataset) and two smaller cities in the USA. It was not possible to achieve convergence by the method of fixed-point iteration, whereas the second model for the same dataset demonstrated convergence rate $k^{-1.67}$.
Keywords: correspondence matrix calculation model, multi stage model, equilibrium distribution model of traffic flow.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-00337-20-03
0714-2020-0005
Russian Foundation for Basic Research 18-29-03071
The work of E. V. Gasnikova was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation (goszadaniye) No. 075-00337-20-03, project No. 0714-2020-0005. The work of A. V. Gasnikov was supported by the RFBR grant No. 18-29-03071 mk.
Received: 08.12.2020
Revised: 29.12.2020
Accepted: 15.01.2021
Document Type: Article
UDC: 519.8
Language: Russian
Citation: E. V. Kotlyarova, A. V. Gasnikov, E. V. Gasnikova, D. V. Yarmoshik, “Finding equilibrium in two-stage traffic assignment model”, Computer Research and Modeling, 13:2 (2021), 365–379
Citation in format AMSBIB
\Bibitem{KotGasGas21}
\by E.~V.~Kotlyarova, A.~V.~Gasnikov, E.~V.~Gasnikova, D.~V.~Yarmoshik
\paper Finding equilibrium in two-stage traffic assignment model
\jour Computer Research and Modeling
\yr 2021
\vol 13
\issue 2
\pages 365--379
\mathnet{http://mi.mathnet.ru/crm888}
\crossref{https://doi.org/10.20537/2076-7633-2021-13-2-365-379}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Computer Research and Modeling
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