On the Existence of Pricing Strategies in the Heterogeneous Single Bottleneck Model

Since the single bottleneck with homogeneous and heterogeneous commuters was formulated as a linear complementarity problem (LCP), it has enabled the research community to look at important extensions. Based on the LCP formulations, this paper will explore useful extensions to contribute to the single bottleneck literature. First, the congestion pricing for homogeneous and heterogeneous commuters is studied. This paper shows that the system optimal for single bottleneck model with heterogeneous commuters might be obtained by an appropriate pricing scheme. Second, the models with flexible arrival time for both homogeneous and heterogeneous models are formulated. It is shown that the system optimal for heterogeneous commuter model might be obtained with a proper toll scheme. Finally, the LCP formulation is extended to study the elastic capacity problem for the homogeneous case. The result shows that, in the particular condition, the existence and uniqueness for homogeneous model with elastic capacity can be guaranteed.