Credit-Based vs. Discount-Based Congestion Pricing: A Comparison Study

TL;DR

The paper analyzes equitable congestion pricing by comparing credit-based (CBCP) and discount-based (DBCP) policies for tolled express lanes. It introduces a mixed-economy transport model with eligible and ineligible user groups, and proves that Nash equilibrium flows exist and can be computed via convex programs. Under a chain-network topology and a revenue-weighted societal-cost objective, DBCP is shown to outperform CBCP in minimizing the equilibrium cost, with strict improvement under additional conditions; when revenue weighting is reversed, CBCP can outperform DBCP in some scenarios. The authors validate the theory with a San Mateo 101 Express Lanes case study, showing higher toll revenue and lower societal costs under DBCP, informing policy design for equitable and efficient congestion pricing. The work also discusses broader implications and potential extensions to hybrid subsidies and welfare programs in other sectors.

Abstract

Credit-based congestion pricing (CBCP) and discount-based congestion pricing (DBCP), which respectively allot travel credits and toll discounts to subsidize low-income users' access to tolled roads, have emerged as promising policies for alleviating the societal inequity concerns of congestion pricing. However, since real-world implementations of CBCP and DBCP are nascent, their relative merits remain unclear. In this work, we compare the efficacy of deploying CBCP and DBCP in reducing user costs and increasing toll revenues. We first formulate a non-atomic congestion game in which low-income users receive a travel credit or toll discount for accessing tolled lanes. We establish that, in our formulation, Nash equilibrium flows always exist and can be computed or well approximated via convex programming. Our main result establishes a set of practically relevant conditions under which DBCP provably outperforms CBCP in inducing equilibrium outcomes that minimize a given societal cost, which encodes user cost reduction and toll revenue maximization. Finally, we validate our theoretical contributions via a case study of the 101 Express Lanes Project, a CBCP program implemented in the San Francisco Bay Area.

Figures (3)

• Figure 1: (Left) Schematic for the 101 Express Lanes Project CBCP-SanMateo, a CBCP policy deployed on the Northbound US-101 freeway between Palo Alto and San Bruno. (Right) Chain network representation of the 101 Express Lanes Project, consisting of consecutive edges representing cities (in green) within the 101 Express Lanes Project's jurisdiction. Each edge comprises an express lane that may be tolled (red, $k=1$) and a toll-free GP lane (black, $k=2$).
• Figure 2: Percent increase in the following metrics at equilibrium under the optimal DBCP policy, compared to the optimal CBCP policy, for (a) each $\boldsymbol{\lambda} \in S_{\boldsymbol{\lambda}}^{({1})}$, and (b) each $\boldsymbol{\lambda} \in S_{\boldsymbol{\lambda}}^{({2})}$: Overall, eligible, and ineligible users' express lane usage, average travel time on the express and GP lanes over $T = 5$ weekdays, eligible and ineligible users' costs, toll revenues, and societal costs.
• Figure 3: Piecewise affine approximations (orange) of the latency functions $\ell_e$ across edges $e \in E_\text{ELP}$ in our network model $\mathcal{N}_\text{ELP}$ for the 101 Express Lanes Project, calibrated using flow and travel latency data from Caltrans' Performance Measurement System (PeMS) database.

Theorems & Definitions (31)

• Remark 1
• Definition 3.1
• Definition 3.2
• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• Remark 2
• Proposition 4.4
• Definition 4.5
• Proposition 4.6