Abstract

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. 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 article 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.

Abstract

There are two operational objectives for operating high-occupancy toll (HOT) lanes: (i) to maintain the free-flow condition to guarantee the travel time reliability; and (ii) to maximize the HOT lanes’ throughput to minimize the system’s total delay. The traffic dynamics on both HOT and general purpose (GP) lanes are described by point queue models, where the queueing times are determined by the demands and capacities.

This article considers three types of lane-choice models: the multinomial logit model when single-occupancy vehicles (SOVs) share the same value of time, the vehicle-based user equilibrium model when SOVs’ values of time are heterogeneous and follow a distribution, and a general lane-choice model. The article demonstrates that the second objective is approximately equivalent to the social welfare optimization principle for the logit model. Observing that the dynamic price and the excess queueing time on the general purpose lanes are linearly correlated in all the lane-choice models, the article proposes a feedback control method to determine the dynamic prices based on two integral controllers. The article further presents a method to estimate the parameters of a lane-choice model once its type is known. Analytically the article proves that the equilibrium state of the closed-loop system with constant demand patterns is ideal, since the two objectives are achieved in it, and that it is asymptotically stable. With numerical examples, the article verifies the effectiveness of the solution method.

Abstract

Single-occupancy vehicles (SOVs) are charged to use the high-occupancy-toll (HOT) lanes, while high-occupancy-vehicles (HOVs) can drive in them at no cost. The pricing scheme for HOT lanes has been extensively studied at local bottlenecks or at the network level through computationally expensive simulations. However, the HOT lane pricing study on a freeway corridor with multiple origins and destinations as well as multiple interacting bottlenecks is a challenging problem for which no analytical results are available. This paper attempts to fill the gap by proposing to study the traffic dynamics in the corridor based on the relative space paradigm. In this new paradigm, the interaction of multiple bottlenecks and trips can be captured with Vickrey’s bathtub model by a simple ordinary differential equation. The paper considers three types of lane choice behavior and analyze their properties. Then, it proposes a distance-based dynamic pricing scheme based on a linear combination of I-controllers. This closed-loop controller is independent of the model and feeds back the travel time difference between HOT lanes and general-purpose lanes. Given the mathematical tractability of the system model, this study analytically studies the performance of the proposed closed-loop control under constant demand and show the existence and stability of the optimal equilibrium. Finally, the results were verified with numerical simulations considering a typical peak period demand pattern.