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

The purpose of this study is to propose control theoretic approaches for high-occupancy toll (HOT) lanes operation. This dissertation considers different operation objectives, and provides pricing schemes for HOT lanes accordingly.To improve the system performance, the study first proposes a simultaneous estimation and control method for the same system as that in (Yin and Lou, 2009). 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.Then, a new lane choice model, i.e., the vehicle-based user equilibrium principle, is proposed to capture the lane choice of SOVs. A general lane choice model is derived based on the characteristics of the logit and the vehicle-based UE model. An insight regarding the dynamic price is obtained by analytically solving the optimal dynamic prices with constant demands of HOVs and SOVs, and then a feedback controller is designed 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. If the type of the lane choice model is given, the distribution of VOTs of the SOVs can be estimated.Next, an optimal control problem is proposed to examine the statement that revenue maximization should generally coincide with the optimization of freeway performances, such as maximizing overall travel-time savings or throughput. Results show that operators need to make different strategies based on the traffic demand. In order to maximize the revenue, operators should set a higher price to make the HOT lanes underutilized if the demand of HOVs is low. However, if the demand of HOVs is high, operators need to set a lower price to attract more SOVs to create congestion on the HOT lanes.It has long been known that drivers’ departure time choice behavior is one fundamental cause of congestion. In the last part of this dissertation, pricing schemes are proposed to consider both lane choice and departure time choice. In the study period, the demands for the HOT and GP lanes are higher than their capacities, which means the whole freeway is congested. However, the congestion period on the HOT lanes is short than that on the GP lanes. So, the HOT lanes are “underutilized”. It turns out that flat (instead of dynamic) pricing schemes are able to meet the following two constraints: (1) the total travel time and scheduling cost is minimized; and (2) the costs for each non-switching and switching SOV are the same. We show that different revenue and tolling constrains for certain type of vehicles lead to different pricing schemes