The dynamic pricing problem of a freeway corridor with high-occupancy toll (HOT) lanes was formulated and solved based on a point queue abstraction of the traffic system [1]. However, existing pricing strategies cannot guarantee that the closed-loop system converges to the optimal state, in which the HOT lanes' capacity is fully utilized but there is no queue on the HOT lanes, and a well-behaved estimation and control method is quite challenging and still elusive.This paper attempts to fill the gap by making three fundamental contributions: (i) to present a simpler formulation of the point queue model based on the new concept of residual capacity, (ii) to propose a simple feedback control theoretic approach to estimate the average value of time and calculate the dynamic price, and (iii) to analytically and numerically prove that the closed-loop system is stable and guaranteed to converge to the optimal state, in either Gaussian or exponential manners.
The development of traffic models based on macroscopic fundamental diagrams (MFD) enables many real-time control strategies for urban networks, including cordon-based pricing schemes. However, most existing MFD-based pricing strategies are designed only to optimize the traffic-related performance, without considering the revenue collected by operators. In this study, we investigate cordon-based pricing schemes for mixed networks with urban networks and freeways. In this system, heterogeneous commuters choose their routes based on the user equilibrium principle. There are two types of operational objective for operating urban networks: (1) to optimize the urban network’s performance, that is, to maximize the outflux; and (2) to maximize the revenue for operators. To compare those two objectives, we first apply feedback control to design pricing schemes to optimize the urban network’s performance. Then, we formulate an optimal control problem to obtain the revenue-maximization pricing scheme. With numerical examples, we illustrate the difference between those pricing schemes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.