Use of Deterministic Traffic Assignment Algorithms in Stochastic Networks: Analysis of Equivalent Link Disutility Functions

At present, in practice, most traffic assignment tasks are performed by using deterministic network (DN) models, which assume that the link travel time is uniquely determined by the link volume and link capacity. In reality, for the same link volume and link capacity, a link may have different travel times. However, the corresponding stochastic network (SN) models are not widely used because they are much more computationally complex than the DN models. In the past research, it was shown that in the important particular case, when the link travel time follows Gamma distribution, the traffic assignment problem for SN can be reformulated in terms of deterministic equivalent link disutility function. Thus in this case the traffic assignment can be solved by the standard Frank-Wolfe algorithm. In this paper, we show that a similar equivalent link disutility function exists in the general case of an arbitrary distribution of link travel time. Therefore, we can use the Frank-Wolfe algorithm in the general SN case, both for the risk averse and risk prone driver route choice behavior. We also provide an explicit expression for this equivalent link disutility function in terms of the link volume and link capacity