Origin-Destination Matrix Estimation Problem in a Markov Chain Approach

Maryam Abareshi (), Mehdi Zaferanieh () and Mohammad Reza Safi ()
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Maryam Abareshi: Hakim Sabzevari University
Mehdi Zaferanieh: Hakim Sabzevari University
Mohammad Reza Safi: Semnan University

Networks and Spatial Economics, 2019, vol. 19, issue 4, No 3, 1069-1096

Abstract: 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.

Keywords: Origin-destination matrix; Trust-region method; Markov chain; Traffic counts; User-equilibrium assignment (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11067-019-09447-8

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