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

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 [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.

Curbing Cruising-as-Substitution-For-Parking in Automated Mobility

“…A large value for 𝛽 corresponds to a more sensitive tolling control where the toll rate can highly fluctuate. See, e.g., Wang et al (2020), for additional discussions on this controller. The feedback control is simple yet effective, but it does not guarantee the maximization of the objective function of the MPC.…”

Ride-Sourcing Platforms with Mixed Autonomy: How will Autonomous Vehicles Affect Others on a Ride-Sourcing Network?

“…The following Table B.1 describes the correspondences between postal code and zone number: 13 We integrate the zones with postal codes 94104, 94105, 94111 as an aggregated zone with postal code 94104. 14 We integrate the zones with postal codes 94108 and 94133 as an aggregated zone with postal code 94108.…”

“…With the emergence of autonomous driving technology and intelligent transport facilities, autonomous vehicles (AVs) will bring radical changes to the business model of the ride-sourcing platforms [13]. Although Level-5 self-driving technology is still under development, Level-4 AVs operated within geofenced areas under favorable weather conditions have already been deployed in various cities nowadays (e.g., Phoenix, AZ) [14].…”

Stable dynamic pricing scheme independent of lane-choice models for high-occupancy-toll lanes

“…The solution strategies in the two studies are also the same: the VOT was first estimated dynamically with a Kalman filter, and the dynamic price was then calculated from the multinomial logit model. In (Wang and Jin, 2017;Wang et al, 2020), the HOT lane management problem for a single bottleneck was studied with the point queue traffic flow model and the multinomial logit model as in (Yin and Lou, 2009), but a simpler feedback control method was used to first estimate the VOT and then calculate the dynamic prices. Further it was shown, both analytically and numerically, that the closed-loop system is stable and converges to the ideal state.…”