On Stochastic Models of Traffic Assignment

TLDR

The paper discusses weaknesses of existing stochastic-network-loading techniques, especially Dial's multipath method, and compares them to the suggested approach. The study evaluates probabilistic traffic assignment models and proposes an alternate formulation, concluding with two techniques for approximating link flows in large networks. The authors formalize stochastic-user-equilibration, analyze the stochastic-network-loading problem, derive a route-choice probability expression from two behavioral postulates, and illustrate the approach with numerical examples on small networks. The proposed model appears reasonable and avoids the inherent weaknesses of the logit model when applied to heavily overlapping route sets.

Abstract

This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. First, the concept of stochastic-user-equilibration (S-U-E) is formalized as an extension of Wardrop's user-equilibration criterion. Then, the stochastic-network-loading (S-N-L) problem (a special case of S-U-E for networks with constant link costs) is analyzed in detail and an expression for the probability of route choice which is based on two general postulates of user behavior is derived. The paper also discusses the weaknesses of existing S-N-L techniques with special attention paid to Dial's multipath method and compares them to the suggested approach. The proposed model seems reasonable and does not exhibit the inherent weaknesses of the logit model when applied to sets of routes which overlap heavily. The discussion is supported by several numerical examples on small contrived networks. The paper concludes with the discussion of two techniques that can be used to approximate the link flows resulting from the proposed model in large networks.