Abstract
Dynamic user equilibrium assignment (DUE) is known as a methodology to assign a dynamic traffic flow, while there is no known methodology that surely finds an equilibrium solution at any case. In addition, it has been mentioned that the good properties such as uniqueness of the solution may not be guaranteed. As an equilibrium point is a stationary point of a day-to-day dynamics, we may remedy the abovementioned problem of DUE solutions by calculating the day-to-day dynamics and recognising its solution trajectory as an alternative of an equilibrium solution. This study formulates a dynamic traffic assignment problem with vehicles discretised and models a day-to-day dynamics of route choices of individual vehicles as a Markov chain model. An absorbing state of the Markov chain corresponds to a Nash equilibrium point of the assignment problem if it exists. If it does not exist, we need to evaluate its stationarity by a statistical method. We performed numerical tests for a few test cases and found that the system go to an equilibrium point or have the stationarity, at least for a small network cases.