A Control Theoretic Approach to Simultaneously Estimate Average Value of Time and Determine Dynamic Price for High-occupancy Toll Lanes

TL;DR

This paper introduces a control theoretic method for estimating average value of time and setting dynamic prices in HOT lanes, ensuring system stability and optimal capacity utilization.

Contribution

It presents a simplified point queue model, a feedback control approach for estimation and pricing, and proves system stability and convergence.

Findings

The proposed model guarantees convergence to the optimal state.

The control approach is stable under Gaussian and exponential conditions.

The method effectively utilizes HOT lane capacity without queues.

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 [Yin and Lou, 2009]. 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.