Probit-Based Traffic Assignment: A Comparative Study between Link-Based Simulation Algorithm and Path-Based Assignment and Generalization to Random-Coefficient Approach

Probabilistic approach of traffic assignment has been primarily developed to provide a more realistic and flexible theoretical framework to represent traveler’s route choice behavior in a transportation network. The problem of path overlapping in network modelling has been one of the main issues to be tackled. Due to its flexible covariance structure, probit model can adequately address the problem. Despite that probit is one of the most appealing choice models, due to the lack of closed form expressions for evaluating choice probabilities; it has not received extensive attention by network modeling researchers. This study is set out to focus on this approach of traffic assignment. Computational difficulty of application of probit model in the large-scale network equilibrium problem has triggered development of some link-based probit network loading methods which exempt the analyst from generating and maintaining path-flow variables explicitly. To the best of our knowledge, however, the bias of these heuristic link-based methods has not been studied so far. This contribution primarily focuses on investigation of such potential bias in link-based probit assignment methods. In this research, this bias for a certain simulated link-based method proposed in the literature is empirically considered and investigated through comparison with path-based probit equilibrium solution. Our findings indicate considerable level of bias for the examined link-based algorithm. Capable of representing utility correlation and heteroscedasticity, probit model has always been one of the most theoretically attractive models for representing route choice behavior. However, this soundness of theory could further be enhanced through combining the ideas of probit and random-coefficient modeling which enables the analyst to capture random taste heterogeneity over travelers as well. To do this, the notion of mixed probit model, as a generalization to classical fixed-coefficient probit, is introduced and applied to an illustrative network in this study, in addition to the main contribution of the article.