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Origin-Destination Matrix Estimation Problem in a Markov Chain Approach

Author

Listed:
  • Maryam Abareshi

    (Hakim Sabzevari University)

  • Mehdi Zaferanieh

    (Hakim Sabzevari University)

  • Mohammad Reza Safi

    (Semnan University)

Abstract

In this paper, a Markov chain origin-destination matrix estimation problem is investigated in which the average time between two incoming streams to or outgoing streams from nodes in consecutive time periods is considered as a Markov chain. Along with, a normal distribution with pre-determined parameters in each period is considered for traffic counts on links. A bi-level programming problem is introduced where in its upper level the network flow pattern in the n th period is estimated so that the probability of the estimated traffic counts is maximized, while in the lower level a traffic assignment problem with the equilibrium conditions is solved. We reduce the proposed nonlinear bi-level model to a new one level linear programming problem, where by using a trust-region method the local optimal solutions are obtained. Some numerical examples are provided to illustrate the efficiency of the proposed method.

Suggested Citation

  • Maryam Abareshi & Mehdi Zaferanieh & Mohammad Reza Safi, 2019. "Origin-Destination Matrix Estimation Problem in a Markov Chain Approach," Networks and Spatial Economics, Springer, vol. 19(4), pages 1069-1096, December.
    • Handle: RePEc:kap:netspa:v:19:y:2019:i:4:d:10.1007_s11067-019-09447-8
    DOI: 10.1007/s11067-019-09447-8
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    References listed on IDEAS

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    1. Abderrahman Ait-Ali & Jonas Eliasson, 2022. "The value of additional data for public transport origin–destination matrix estimation," Public Transport, Springer, vol. 14(2), pages 419-439, June.

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