Dynamic distance-based pricing scheme for high-occupancy-toll lanes along a freeway corridor

TL;DR

The paper tackles dynamic pricing for high-occupancy-toll (HOT) lanes along a freeway corridor with multiple origins/destinations and interacting bottlenecks. It adopts Vickrey's Bathtub Model (VBM) to capture aggregated, corridor-level dynamics via two bathtubs (HOT and GP) and designs a distance-based toll as a linear combination of I-controllers, u(t) = a(t) ω(t) + b(t), driven by feedback on the per-unit-distance travel-time difference ω(t) and state variables λ(t) and ξ(t). It provides analytical results for equilibrium and stability under constant demand for several lane-choice models (UE with distributed VOT, logit, and a generalized framework), and validates the approach with numerical simulations under realistic demand and VOT assumptions. The work demonstrates that the proposed controller can achieve a stable, optimal operating point with HOT-lane utilization improved and GP congestion alleviated, offering a tractable, implementable framework for corridor-scale congestion pricing and avenues for future extensions to more general traffic models and endogenous demand.

Abstract

Single-occupancy vehicles (SOVs) are charged to use the highoccupancy-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. In this paper, we attempt 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. We consider three types of lane choice behavior and analyze their properties. Then, we propose 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, we analytically study the performance of the proposed closed-loop control under constant demand and show the existence and stability of the optimal equilibrium. Finally, we verify the results with numerical simulations considering a typical peak period demand pattern. In the future, we are interested in extending this work and testing the performance of the proposed linear combination of I-controllers for other traffic flow models.

Figures (14)

• Figure 1: Illustration of a corridor with many on- and off-ramps and subsequent pairs of origin-destination. (a) Corridor geometry with three sample trips; (b) Definition of trip distance; (c) Concept of remaining trip distance.
• Figure 2: Illustration of the in- and out-flow rates in the bathtub representation of the traffic system with HOT lanes and GP lanes.
• Figure 3: Queuing system for the bathtub model, where the outflow $g_i(t)$ depends on the active number of trips, $\delta_i(t)$, and its remaining trip distance distribution.
• Figure 4: Definition of strictly undercritical (SUC), critical (C), and strictly overcritical (SOC) phases in the NFD. For three traditional fundamental diagrams, i.e., (a) Greenshields', (b) Triangular, (c) Trapezoidal, (d) Ramp, and (e) Approximate Triangular.
• Figure 5: Assumption of (per-lane) fundamental diagram and corresponding main variables. (a) Triangular network fundamental diagram; and (b) Approximate triangular fundamental diagram (ATFD), where $c$ can range between 0 (equivalent to the triangular fundamental diagram) and $C_0$.

Theorems & Definitions (19)

• Definition 2.1
• Theorem 3.1
• Corollary 3.2
• Definition 3.3
• Lemma 3.4
• proof
• Lemma 3.5
• proof
• Lemma 3.6
• proof