Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity

Abstract

In this paper we investigate a bottleneck model in which the capacity of the bottleneck is assumed stochastic and follows a uniform distribution. The commuters' departure time choice is assumed to follow the user equilibrium principle according to mean trip cost. The analytical solution of the proposed model is derived. Both the analytical and numerical results show that the capacity variability would indeed change the commuters' travel behavior by increasing the mean trip cost and lengthening the peak period. We then design congestion pricing schemes within the framework of the new stochastic bottleneck model, for both a time-varying toll and a single-step coarse toll, and prove that the proposed piecewise time-varying toll can effectively cut down, and even eliminate, the queues behind the bottleneck. We also find that the single-step coarse toll could either advance or postpone the earliest departure time. Furthermore, the numerical results show that the proposed pricing schemes can indeed improve the efficiency of the stochastic bottleneck through decreasing the system's total travel cost.

Pareto-improving policies for an idealized two-zone city served by two congestible modes

“…(4) represents the queuing delay. It is a pure deadweight loss, and can be eliminated by a time-varying system-optimal toll (Gonzales and Daganzo, 2012;Amirgholy and Gonzales, 2016;Xiao et al, 2015aXiao et al, , 2015b. Note that substituting the queue delay cost with an optimal toll does not change the highway travel cost, thus will not change the mode choice and the equilibrium travel costs.…”

Stochastic bottleneck capacity, merging traffic and morning commute

“…In this case, the equilibrium departure rate from origin equals to its arrival rate at downstream bottleneck. The analytical solutions for the equilibrium pattern for this case can be seen in Xiao et al, (2013). Then, the total travel cost can be formulated as follows:…”

Bottleneck Models and Departure Time Problems

“…Let us also mention that stochasticity may play other roles in the bottleneck models. This is the case when considering stochastic capacities, as in Xiao, Huang and Liu (2015), or stochastic travel times, as in Xiao, Coulombel and de Palma (2017).…”