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

TL;DR

The paper addresses equity-aware congestion pricing by comparing credit-based (CBCP) and discount-based (DBCP) policies on networks with tolled express lanes. It develops a mixed-economy routing model, establishes existence of $Nash$ equilibria for both policy types, and provides convex-program formulations to compute equilibria efficiently (under time-invariant VoTs for CBCP). On single-edge networks, it derives analytical conditions under which DBCP or CBCP better expands eligible users’ express-lane access and identifies parameters driving policy effectiveness. Empirical validation via a San Mateo pilot corroborates the theoretical findings and demonstrates how tolls, budgets, and discount levels shape express-lane usage and societal costs, guiding policy design toward equitable efficiency gains.

Abstract

Congestion pricing offers a promising traffic management policy for regulating congestion, but has also been criticized for placing outsized financial burdens on low-income users. Credit-based congestion pricing (CBCP) and discount-based congestion pricing (DBCP) policies, which respectively provide travel credits and toll discounts to subsidize low-income users' access to tolled roads, are promising mechanisms for reducing traffic congestion without worsening societal inequities. However, the optimal design and relative merits of CBCP and DBCP policies remain poorly understood. This work studies the effects of deploying CBCP and DBCP policies to route users on multi-lane highway networks with tolled express lanes. We formulate a non-atomic routing game in which a subset of eligible users is granted toll relief via a fixed budget or toll discount, while all other users must pay out-of-pocket. We prove that Nash equilibrium traffic flow patterns exist under any CBCP or DBCP policy. Under the assumption that eligible users have time-invariant values of time (VoTs), we provide a convex program to efficiently compute these equilibria. For single-edge networks, we identify conditions under which DBCP policies outperform CBCP policies, in the sense of improving eligible users' express lane access, an equity objective often neglected in existing congestion pricing schemes. We identify user and network-dependent parameters whose values play a key role in determining whether DBCP or CBCP policies are more effective at expanding eligible users' express lane access. Finally, we present empirical results from a CBCP pilot study of the San Mateo 101 Express Lane Project in California. Our empirical results corroborate our theoretical analysis of the impact of deploying credit-based and discount-based policies.

Figures (5)

• Figure 1: $y^C$ vs. $\alpha$ and $y^D$ vs. $\alpha$, under Assumptions \ref{['Assumption: Latency Function']} and \ref{['Assumption: For 1 eligible group, 0 ineligible group']}, for the setting where $\ell(x) = x^4/16$, $\tau = 0.6$, and $v^E = 1$, in which case $\alpha_1 = 0.120$, $\alpha_2 = 0.156$.
• Figure 2: $y^C(\alpha)$ and $y^D(\alpha)$, under Assumptions \ref{['Assumption: Latency Function']} and \ref{['Assumption: For 1 eligible group, 1 ineligible group']}, for the settings where $\ell(x) = x^4/16$ and (Left) $\tau = 0.4$, $v^E = 1$, $v^I = 1.25$, in which case $\tau < 2v^E \ell'(1)$, (Middle) $\tau = 0.7$, $v^E = 1$, $v^I = 1.25$, in which case $\tau > 2v^E \ell'(1)$, $1 - v^E/v^I = 0.2 < \alpha_3 = 0.368$, (Right) $\tau = 0.7$, $v^E = 1$, $v^I = 2.5$, in which case $\tau > 2v^E \ell'(1)$, $1 - v^E/v^I = 0.6 > \alpha_3 = 0.368$.
• Figure 3: $\bar{y}^C$ (red) and $\bar{y}^D$ (blue) vs. $\alpha$ at $v^I = 1.25, 1.5, 1.75, 2.0$.
• Figure 4: $y^C$ (red) and $y^D$ (blue) vs. $\alpha$, at $d^I = 0, 0.5, 1, 1.5$.
• Figure 5: (Left) Percent of eligible users and (Right) Average eligible users' travel time at (Top) $(\tau, B)$-CBCP and (Bottom) $(\tau, \alpha = B/(\tau T))$-DBCP equilibria with toll $\tau$ and allotted credit $B$.

Theorems & Definitions (27)

• Definition 3.1: DBCP Equilibrium
• Remark 1
• Remark 2
• Definition 3.2: CBCP Equilibrium
• Proposition 4.1
• proof
• Proposition 4.2
• Theorem 4.3
• proof
• Theorem 4.4