Dynamic congestion pricing in within-day and day-to-day network equilibrium models

This dissertation explores two kinds of dynamic pricing models which react to within-day and day-to-day variation in traffic. Traffic patterns vary within each day due to uncertainty in the supply-side that is caused by non-recurring sources of congestion such as incidents, poor weather, and temporary bottlenecks. On the other hand, significant day-to-day variations in traffic patterns also arise from stochastic route choices of travelers who are not fully rational. Using slightly different assumptions, we analyze the network performance in these two scenarios and demonstrate the advantages of dynamic pricing over static tolls. In both cases, traffic networks are characterized by a set of stochastic states. We seek optimal tolls that are a function of the network states which evolve within each day or across days.

In the within-day equilibrium models, travelers are assumed to be completely rational and have knowledge of stochastic link-states, which have different delay functions. At every node, travelers observe the link-states of downstream links and select the next node to minimize their expected travel times. Collectively, such behavior leads to an equilibrium, which is also referred to as user equilibrium with recourse, in which all used routing policies have equal and minimal expected travel time. In this dissertation, we improve the system performance of the equilibrium flows using state-dependent marginal link tolls. These tolls address externalities associated with non-recurring congestion just as static marginal tolls in regular traffic assignment reflect externalities related to recurring congestion.

The set of tolls that improve system performance are not necessarily unique. Hence, in order to make the concept of tolling more acceptable to the public, we explore alternate pricing mechanisms that optimize social welfare and also collect the least amount of revenue in expectation. This minimum revenue toll model is formulated as a linear program whose inputs are derived from the solution to a novel reformulation of the user equilibrium with recourse problem.

We also study day-to-day dynamic models which unlike traditional equilibrium approaches capture the fluctuations or stochasticity in traffic due to route choice uncertainty. Travelers decisions are modeled using route choice dynamics, such as the logit choice protocol, that depend on historic network conditions. The evolution of the system is modeled as a stochastic process and its steady state is used to characterize the network performance. The objective of pricing in this context is to set dynamic tolls that depend on the state of the network on previous day(s) such that the expected total system travel time is minimized. This problem is formulated as an average cost Markov decision process. Approximation methods are suggested to improve computational tractability.

The day-to-day pricing models are extended to instances in which closed form dynamics are unavailable or unfit to represent travelers' choices. In such cases, we apply Q-learning in which the route choices may be simulated off-line or can be observed through experimentation in an online setting. The off-line methods were found to be promising and can be used in conjunction with complex discrete choice models that predict travel behavior with greater accuracy.

Overall, the findings in this dissertation highlight the pitfalls of using static tolls in the presence of different types of stochasticity and make a strong case for employing dynamic state-dependent tolls to improve system efficiency.