Control Theoretic Approaches to Congestion Pricing for High-occupancy Toll Lanes

High-occupancy vehicle (HOV) lanes are those reserved for cars with a minimum of two or three occupants and other qualified vehicles. However, some HOV lanes could be
underutilized, even when the corresponding general purpose (GP) lanes on the same roads are congested. A type of relatively recent congestion pricing strategy is realized with the high-occupancy toll (HOT) lane, where single-occupancy vehicles (SOVs) can pay a price to use HOV lanes during peak periods. The purpose of this study is to propose control theoretic approaches to congestion pricing for HOT lanes. This dissertation focuses on three operation objectives: (1) maintaining a certain level of service on the HOT lanes; (2) improving the overall system performance; and (3) maximizing revenue for the operators. Inspired by the work of (Yin and Lou, 2009), this study first proposes a simultaneous estimation and control method for a freeway with HOT and GP lanes. An integral controller is applied to estimate the average value of time (VOT) of SOVs, and the dynamic prices are calculated based on the logit model. The closed-loop system is proved to be stable and guaranteed to converge to the optimal state both analytically and numerically. Two convergence patterns, Gaussian or exponential, are revealed. The effect of the scale parameter in the logit model is also examined.

The heterogeneity of SOVs is essential for determining pricing schemes for HOT lanes. A vehicle-based user equilibrium (UE) principle is proposed to incorporate heterogenous SOVs. A general lane choice model is derived based on the characteristics of the logit and the vehicle-based UE principle. We obtain an insight regarding
the pricing schemes by analytically solving the optimal dynamic prices with constant demands of HOVs and SOVs. Then, we design a feedback controller to determine the dynamic prices without knowing SOVs' lane choice models, but to satisfy the two control objectives: maximizing the flow-rate but not forming a queue on the HOT lanes.
Agencies have stated that revenue maximization should generally coincide with the optimization of freeway performances. In order to verify this statement, an optimal control problem is formulated to find the pricing scheme that maximizes the revenue for HOT lane operators. Numerical results show that there is conflict between those two
objectives. Operators need to make different strategies based on the traffic demand patterns. It has long been known that drivers' departure time choice behavior is one fundamental cause of congestion. Further in this dissertation, pricing schemes are proposed to consider both lane choice equilibrium and departure time equilibrium. It turns out that flat pricing schemes are able to meet the following three constraints: (1) the nontransfer disutility (NTD) is minimized; (2) the cost for each HOV is not worse-off; and (3) the costs for each nonswitching and switching SOV are the same. We show that different revenue requirements lead to different pricing schemes.