Modeling elasticity, similarity, stochasticity, and congestion in a network equilibrium framework using a paired combinatorial weibit choice model

In the traffic assignment problem for predicting traffic flow patterns in a transportation network, it is important to account for route overlap and non-identical perception variance in route choice analysis. In this study, we establish a novel route choice model, named the paired combinatorial weibit (PCW) model, to capture the route overlap and route-specific perception variance. The PCW model retains a closed-form probability solution, which allows the development of an equivalent mathematical programming (MP) formulation for the PCW-based stochastic user equilibrium (PCW-SUE) model. Specifically, we propose two equivalent MP formulations for modeling the fixed demand (FD) and elastic demand (ED), named PCW-SUE-FD and PCW-SUE-ED, respectively. The PCW-SUE-ED model can address the abovementioned two issues in route choice for the FD scheme, but also can consider the effect level-of-service (LOS) in travel choice for the ED scheme. The equivalency and uniqueness of the PCW-SUE-FD and PCW-SUE-ED models are rigorously proved. In addition, a path-based partial linearization algorithm combined with a self-regulated averaging line search strategy is developed to solve the two SUE models. Numerical results are presented to illustrate the features of the PCW-SUE-FD and PCW-SUE-ED models and applicability of the solution algorithm to a real transportation network.