Origin-Destination Matrix Estimation Problem in a Markov Chain Approach

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.