Networks and Spatial Economics

, Volume 19, Issue 4, pp 1069–1096 | Cite as

Origin-Destination Matrix Estimation Problem in a Markov Chain Approach

  • Maryam Abareshi
  • Mehdi ZaferaniehEmail author
  • Mohammad Reza Safi


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.


Origin-destination matrix Trust-region method Markov chain Traffic counts User-equilibrium assignment 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Maryam Abareshi
    • 1
  • Mehdi Zaferanieh
    • 1
    Email author
  • Mohammad Reza Safi
    • 2
  1. 1.Department of Applied Mathematics and Computer SciencesHakim Sabzevari UniversitySabzevarIran
  2. 2.Department of MathematicsSemnan UniversitySemnanIran

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