Stochastic congestion and pricing model with endogenous departure time selection and heterogeneous travelers.

This paper proposes a stochastic congestion and pricing model that combines a bottleneck model with stochastic queuing to study roadway congestion and pricing. Employing this model, two pricing schemes are developed: one is omniscient pricing for which the transportation administrative agency is assumed to be aware of each and every traveler's cost structure (i.e., their detailed valuation of journey cost as well as early and late penalties), and the other is observable pricing, for which only queuing delay is considered. Travelers are characterized by their late-acceptance level and the effects of various compositions of late-averse, late-tolerant and late-neutral travelers on congestion patterns with and without pricing are discussed.  Numerical simulation indicates that omniscient pricing scheme is most effective in suppressing peak hour congestion and distributing demands over longer time horizon. Also, congestion pricing is found to be more effective when travelers have diversified cost structures than identical cost structures, and congestion is better reduced with heterogeneous traveler composition than with single composition. This is consistent with earlier studies in the literature. In addition, the simulation results indicate that omniscient pricing in general reduces Expected Total Social Cost<(with or without the return of the congestion fee). However, the ultimate benefits of a certain pricing scheme depend on travelers' cost structure as well as the composition of late-tolerant, late-averse and late-neutral travelers in the entire population; extreme situations such as 100% late-averse or 100% late-tolerant traveler composition deserves extra attention when analyzing different pricing schemes.