Dynamic pricing and long-term planning models for managed lanes with multiple entrances and exits
Creators: name: Pandey, Venktesh
Publisher: name: The University of Texas at Austin
Year: 2020
Subjects: Managed lanes
Dynamic pricing
Markov decision process
Deep reinforcement learning
User equilibrium with recourse
Network contraction

description: Express lanes or priced managed lanes provide a reliable alternative to travelers by charging dynamic tolls in exchange for traveling on lanes with no congestion. These lanes have various locations of entrances and exits and allow travelers to adapt their route based on the toll and travel time information received at a toll gantry. In this dissertation, we incorporate this adaptive lane choice behavior in improving the dynamic pricing and long-term planning models for managed lanes with multiple entrances and exits. Lane choice of travelers minimizing their disutility is affected by the real-time information about tolls and travel time through variable message signs and perceived information from past experiences. In this dissertation, we compare various adaptive lane choice models differing in their reliance on real-time information or historic information or both. We propose a decision route lane choice model that efficiently compares the disutility over multiple routes on an express lane. Assuming drivers’ disutility is only affected by tolls and travel times, we show that the decision route model generates only up to 0.93% error in expected costs compared to the optimal adaptive lane choice model, making it a suitable choice for modeling lane choice of travelers. Next, using the decision route lane choice framework, we improve the current dynamic pricing models for express lanes that commonly ignore adaptive lane choice, assume simplified traffic dynamics, and/or are based on simplified heuristics. Formulating the dynamic pricing problem as an MDP, we optimize the tolls for various objectives including maximizing revenue and minimizing total system travel time (TSTT). Three solution algorithms are evaluated: (a) an algorithm based on value-function approximation, (b) a multiagent reinforcement learning algorithm with decentralized tolling at each gantry, and (c) a deep reinforcement learning assuming partial observability of traffic state. These algorithms are shown to outperform other heuristics such as feedback control heuristics by generating up to 10% higher revenues and up to 9% lower delays. Our findings also reveal that the revenue-maximizing optimal policies follow a “jam-and-harvest” behavior where the toll-free lanes are pushed towards congestion in the earlier time steps to generate higher revenue later, a characteristic not observed for the policies minimizing TSTT. We use reward shaping methods to overcome the undesired behavior of toll policies and confirm transferability of the algorithms to new input domains. We also offer recommendations on real-time implementations of pricing algorithms based on solving MDPs. Last, we incorporate adaptive lane choice in existing long-term planning models for express lanes which commonly represent these lanes as fixed-toll facilities and ignore en route adaptation of lane choices. Defining the improved model as an equilibrium over adaptive lane choices of self-optimizing travelers and formulating it as a convex program, we show that long-term traffic forecasts can be underestimated by up to 45% if adaptive route choice is ignored. For solving the equilibrium, we develop a gradient-projection algorithm which is shown to be efficient than existing link-state algorithms in the literature. Additionally, we estimate the sensitivity of equilibrium expected costs with demand variation by formulating it as a convex program solved using a variant of the gradient projection algorithm proposed earlier. This analysis simplifies a complex express lane network as a single directed link, allowing integration of adaptive lane choice for planning of express lanes without significantly altering the components of traditional planning models. Overall these models improve the state-of-the-art of pricing and planning for managed lanes useful for evaluating future express lane projects and for operations of express lanes with multiple objectives.