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Capacity Allocation and Pricing of High Occupancy Toll Lane Systems with Heterogeneous Travelers

Haripriya Pulyassary, Ruifan Yang, Zhanhao Zhang, Manxi Wu

TL;DR

This paper addresses joint capacity allocation and toll design for High Occupancy Toll (HOT) lanes, where the authority selects the HOT capacity fraction $\rho \in [0,1]$ and toll $\tau>0$ to influence traveler choices. Travelers are modeled as nonatomic agents with heterogeneous values of time $\beta$ and carpool disutility $\gamma$, distributed uniformly on $\mathcal{P}=[0,\overline{\beta}]\times[0,\overline{\gamma}]$, who choose among paying, forming carpools, or using the ordinary lane, with lane latencies $C_o$ and $C_h$ driving costs. The authors derive a complete Wardrop equilibrium characterization, identifying two regimes (Regime A: all HOT users pool; Regime B: some HOT users pay) and providing fixed-point equations for equilibrium shares, plus comparative static results showing how increasing $\rho$ shifts traffic toward the HOT lane. They calibrate the model to California’s I-880 using a BPR-like latency model and compute a Pareto frontier over travel time and toll revenue to guide capacity and toll design. The work offers a practical framework for HOT lane design with heterogeneous travelers and suggests extensions to nonuniform preference distributions and multi-origin–destination networks.

Abstract

In this article, we study the optimal design of High Occupancy Toll (HOT) lanes. In our setup, the traffic authority determines the road capacity allocation between HOT lanes and ordinary lanes, as well as the toll price charged for travelers who use the HOT lanes but do not meet the high-occupancy eligibility criteria. We build a game-theoretic model to analyze the decisions made by travelers with heterogeneous values of time and carpool disutilities, who choose between paying or forming carpools to take the HOT lanes, or taking the ordinary lanes. Travelers' payoffs depend on the congestion cost of the lane that they take, the payment and the carpool disutilities. We provide a complete characterization of travelers' equilibrium strategies and resulting travel times for any capacity allocation and toll price. We also calibrate our model on the California Interstate highway 880 and compute the optimal capacity allocation and toll design.

Capacity Allocation and Pricing of High Occupancy Toll Lane Systems with Heterogeneous Travelers

TL;DR

This paper addresses joint capacity allocation and toll design for High Occupancy Toll (HOT) lanes, where the authority selects the HOT capacity fraction and toll to influence traveler choices. Travelers are modeled as nonatomic agents with heterogeneous values of time and carpool disutility , distributed uniformly on , who choose among paying, forming carpools, or using the ordinary lane, with lane latencies and driving costs. The authors derive a complete Wardrop equilibrium characterization, identifying two regimes (Regime A: all HOT users pool; Regime B: some HOT users pay) and providing fixed-point equations for equilibrium shares, plus comparative static results showing how increasing shifts traffic toward the HOT lane. They calibrate the model to California’s I-880 using a BPR-like latency model and compute a Pareto frontier over travel time and toll revenue to guide capacity and toll design. The work offers a practical framework for HOT lane design with heterogeneous travelers and suggests extensions to nonuniform preference distributions and multi-origin–destination networks.

Abstract

In this article, we study the optimal design of High Occupancy Toll (HOT) lanes. In our setup, the traffic authority determines the road capacity allocation between HOT lanes and ordinary lanes, as well as the toll price charged for travelers who use the HOT lanes but do not meet the high-occupancy eligibility criteria. We build a game-theoretic model to analyze the decisions made by travelers with heterogeneous values of time and carpool disutilities, who choose between paying or forming carpools to take the HOT lanes, or taking the ordinary lanes. Travelers' payoffs depend on the congestion cost of the lane that they take, the payment and the carpool disutilities. We provide a complete characterization of travelers' equilibrium strategies and resulting travel times for any capacity allocation and toll price. We also calibrate our model on the California Interstate highway 880 and compute the optimal capacity allocation and toll design.
Paper Structure (5 sections, 4 theorems, 11 equations, 5 figures)

This paper contains 5 sections, 4 theorems, 11 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. Model
  3. Equilibrium characterization
  4. Optimal design of HOT on California I-880
  5. Concluding remarks

Key Result

Lemma 1

For a given $\sigma$, define $\Lambda_i(\sigma) \subseteq \mathcal{P}$ to be the subset of agents whose best response to $\sigma$ is $R_i$, for $i \in \{toll, pool, o\}$. Then,

Figures (5)

  • Figure 1: Characterization of best response strategies
  • Figure 2: Equilibrium outcome in regime A
  • Figure 3: Equilibrium outcome in regime B
  • Figure 4: Interstate 880 (I-880) Highway (Encircled in Red)
  • Figure 5: Pareto Front of $T(\tau, \rho)$ and $R(\tau, \rho)$.

Theorems & Definitions (6)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • proof
  • Theorem 1
  • Theorem 2