A Semi-Analytical Approach for Solving the Bottleneck Model with General User Heterogeneity

This paper proposes a novel semi-analytical approach for solving the dynamic user equilibrium of a bottleneck model with general heterogenous users. The proposed approach makes use of the analytical solutions from the bottleneck analysis to create an equivalent assignment problem that admits closed-form commute cost functions. More specifically, the underlying assignment problem is a static, multi-class and asymmetric traffic assignment problem, which may be formulated and solved as a variational inequality problem (VIP). The proposed approach provides a new tool to understand the analytical properties of the bottleneck model with general heterogeneity, and to design efficient numerical procedures for its solution. The results of numerical experiments show that a primitive projection algorithm is able to quickly solve the equivalent VIP with a reasonable number of user groups. Thus, the proposed approach may be used to perform numerical analysis for the bottleneck models that are analytically intractable. It can also be easily extended to address simultaneous departure time and route choice in a single O-D (origin-destination) network with multiple parallel routes.

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