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Equitable Congestion Pricing under the Markovian Traffic Model: An Application to Bogota

Alfredo Torrico, Natthawut Boonsiriphatthanajaroen, Nikhil Garg, Andrea Lodi, Hugo Mainguy

TL;DR

This study develops a data-driven framework for equitable congestion pricing within a Markovian traffic equilibrium framework. By extending the Markovian Traffic Equilibrium to multiple agent types with monetary costs and an external option (e.g., public transit), the authors prove the existence and uniqueness of a single equilibrium and provide a practical algorithm to compute it under given prices. Applying the framework to Bogotá with real OD and strata data, they compare uniform, per-stratum, and area pricing schemes and show that personalized per-stratum pricing can achieve higher welfare and revenue, while area pricing offers a robust middle ground that closely matches per-stratum gains with simpler implementation. The results highlight strong equity and efficiency benefits from spatially informed pricing and offer policy guidance for cities aiming to balance revenue with fairness, including the potential for revenue recycling or transit investments to reinforce equity goals.

Abstract

Congestion pricing is used to raise revenues and reduce traffic and pollution. However, people have heterogeneous spatial demand patterns and willingness (or ability) to pay tolls, and so pricing may have substantial equity implications. We develop a data-driven approach to design congestion pricing given policymakers' equity and efficiency objectives. First, algorithmically, we extend the Markovian traffic equilibrium setting introduced by Baillon & Cominetti (2008) to model heterogeneous populations and incorporate prices and outside options such as public transit. Second, we empirically evaluate various pricing schemes using data collected by an industry partner in the city of Bogota, one of the most congested cities in the world. We find that pricing personalized to each economic stratum can be substantially more efficient and equitable than uniform pricing; however, non-personalized but area-based pricing can recover much of the gap.

Equitable Congestion Pricing under the Markovian Traffic Model: An Application to Bogota

TL;DR

This study develops a data-driven framework for equitable congestion pricing within a Markovian traffic equilibrium framework. By extending the Markovian Traffic Equilibrium to multiple agent types with monetary costs and an external option (e.g., public transit), the authors prove the existence and uniqueness of a single equilibrium and provide a practical algorithm to compute it under given prices. Applying the framework to Bogotá with real OD and strata data, they compare uniform, per-stratum, and area pricing schemes and show that personalized per-stratum pricing can achieve higher welfare and revenue, while area pricing offers a robust middle ground that closely matches per-stratum gains with simpler implementation. The results highlight strong equity and efficiency benefits from spatially informed pricing and offer policy guidance for cities aiming to balance revenue with fairness, including the potential for revenue recycling or transit investments to reinforce equity goals.

Abstract

Congestion pricing is used to raise revenues and reduce traffic and pollution. However, people have heterogeneous spatial demand patterns and willingness (or ability) to pay tolls, and so pricing may have substantial equity implications. We develop a data-driven approach to design congestion pricing given policymakers' equity and efficiency objectives. First, algorithmically, we extend the Markovian traffic equilibrium setting introduced by Baillon & Cominetti (2008) to model heterogeneous populations and incorporate prices and outside options such as public transit. Second, we empirically evaluate various pricing schemes using data collected by an industry partner in the city of Bogota, one of the most congested cities in the world. We find that pricing personalized to each economic stratum can be substantially more efficient and equitable than uniform pricing; however, non-personalized but area-based pricing can recover much of the gap.
Paper Structure (48 sections, 5 theorems, 43 equations, 19 figures, 5 tables, 1 algorithm)

This paper contains 48 sections, 5 theorems, 43 equations, 19 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Algorithmic and Methodological Contributions.
  3. Empirical Applied Contributions.
  4. Network Equilibrium and Efficiency.
  5. Congestion Pricing.
  6. Equity in Congestion Pricing.
  7. Equity and Pricing in Operations.
  8. Model
  9. Notation.
  10. Background: The Markovian Traffic Equilibrium Model
  11. Our Model: Multiple Agent Types and Monetary Costs
  12. MTE: Existence and Uniqueness.
  13. Modeling Details and Algorithm
  14. Choice Models
  15. Adding an Outside Option
  16. ...and 33 more sections

Key Result

Theorem 1

Assume $\mathbf{t}^0\in\mathcal{C}$ where $t_a^0 = \ell_a(0)$ for all $a\in{\mathcal{A}}$. Then, there exists a unique MTE given by $f_a^\star = \ell_a^{-1}(t^\star_a)$, where $\mathbf{t}^\star$ is the unique solution of the smooth strictly convex program

Figures (19)

  • Figure 1: Meta-network with two layers. Layer in red indicates the road network (cars) and the layer in blue indicates the outside option network (e.g., public transit). The demand $g_{i,d}^s$ splits according to probabilities $1-\mathring{P}_{i,d}^{s}$ and $\mathring{P}_{i,d}^{s}$.
  • Figure 2: Road Network: Nodes are in red and dashed lines indicate area splits.
  • Figure 3: Instance Summary. Last 3 rows: The value in parentheses indicate the number of OD pairs.
  • Figure 3: Instance Demand Data
  • Figure 4: The effects of Uniform Pricing, with each metric calculated under the equilibrium for the associated pricing. Overall, uniform pricing has highly inequitable effects, disproportionately harming the low-income group that is most price-sensitive. This group starts fewer trips, uses the primary roads less, and has a lower average speed. Uniform pricing also severely impacts the low-income and mid-income groups in terms of welfare. We remark that we do not plot the welfare at price 0 in (e) because it is 0 by definition.
  • ...and 14 more figures

Theorems & Definitions (11)

  • Definition 1: baillon2008markovian
  • Definition 2
  • Theorem 1
  • Definition 3
  • Definition 4: Welfare
  • Remark 1
  • Lemma 1
  • Proposition 1
  • Lemma 2
  • Lemma 3
  • ...and 1 more