In this paper an assumption made by almost every traffic model in use today in transportation planning is relaxed, that is the assumption of the stationarity of the traffic flow where the input flows are assumed constant through time. It is important to refine the presently used traffic models which are supposed to simulate the reality to the case of non stationary models. The study of the dynamic aspect of the traffic flow patterns, their evolution with time and location is a key to a better understanding of the transportation phenomena. We present in this study an approach to the realization of this goal by adapting the probabilistic multipath assignment model to the case of non stationary input flows. The probabilistic multipath assignment model introduced by dial (transpn res. 5, 83-111, 1972) is a multipath generalization of the all-or-nothing model and subsumes it as a particular case. Given non stationary input flows the assignment model evaluates for each point of the transportation network, the flow distribution through time. This allows to study the formation and the evolution of congestion and gives a more precise image of the reality. The algorithm implementing this dynamic model uses repeatedly an adapted version of the algorithm for the stationary case and a fast fourier transform procedure.
Abstract