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 lateacceptance 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% latetolerant traveler composition deserves extra attention when analyzing different pricing schemes.

This paper deals with first-best and second-best congestion pricing of a stylised two-link network with probabilistic route choice of travellers. Travellers may have heterogeneous values of travel times and may differ in their idiosyncratic route preferences. We derive first-best and second-best tolls taking into account how the overall network demand responds to generalized costs including the tolls that are levied. We show that with homogeneous values of times the welfare losses of second-best pricing, of one link only, may be smaller if route choice is probabilistic. Furthermore, we show that with heterogeneous values of times, common second-best tolls and group-differentiated tolls can be very close when route choice is governed by random utility maximisation, leading to low welfare losses from the inability to differentiate tolls.