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arXiv · 2408.15990

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

Xuting Wang·Wen-Long Jin·Yafeng Yin
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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.

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Xuting Wang, Wen-Long Jin, Yafeng Yin. 2024-08-28. A Control Theoretic Approach to Simultaneously Estimate Average Value of Time and Determine Dynamic Price for High-occupancy Toll Lanes. https://doi.org/10.1109/tits.2020.3007160

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