[Paper Review] Information Design for Regulating Traffic Flows under Uncertain Network State

Manxi Wu, Saurabh Amin|arXiv (Cornell University)|Aug 19, 2019

Transportation Planning and Optimization11 references4 citations

TL;DR

This paper proposes an information design framework to minimize traffic spillover on urban routes by strategically sharing noisy signals about network states with a fraction of travelers. Using Bayesian persuasion in a two-route routing game with uncertain incident states, it analytically characterizes the optimal signal distribution that achieves minimum spillover—achieving this goal even when less than 100% of travelers receive the signal, provided the fraction exceeds a critical threshold (e.g., 13.3%).

ABSTRACT

Traffic navigation services have gained widespread adoption in recent years. The route recommendations generated by these services often leads to severe congestion on urban streets, raising concerns from neighboring residents and city authorities. This paper is motivated by the question: How can a transportation authority design an information structure to induce a preferred equilibrium traffic flow pattern in uncertain network state conditions? We approach this question from a Bayesian persuasion viewpoint. We consider a basic routing game with two parallel routes and an uncertain state that affects the travel cost on one of the routes. The authority sends a noisy signal of the state to a given fraction of travelers. The information structure (i.e., distribution of signals in each state) chosen by the authority creates a heterogeneous information environment for the routing game. The solution concept governing the travelers' route choices is Bayesian Wardrop Equilibrium. We design an information structure to minimize the average traffic spillover -- the amount of equilibrium route flow exceeding a certain threshold -- on one of the routes. We provide an analytical characterization of the optimal information structure for any fraction of travelers receiving the signal. We find that it can achieve the minimum spillover so long as the fraction of travelers receiving the signal is larger than a threshold (smaller than 1).

Motivation & Objective

• Address the practical challenge of reducing traffic congestion on neighborhood streets caused by navigation app recommendations.
• Formulate a model where a central authority designs information signals to regulate traffic flows under uncertain network states.
• Account for the reality that only a fraction of travelers receive state information, creating heterogeneous information environments.
• Minimize average traffic spillover—flow exceeding a threshold—on a target route through optimal signal design.
• Characterize the optimal information structure for any given fraction of travelers receiving the signal, under Bayesian Wardrop equilibrium.

Proposed method

• Model a two-parallel-route network with one route subject to random incidents increasing its travel cost.
• Use a Bayesian routing game where travelers choose routes based on private signals, leading to a Bayesian Wardrop equilibrium.
• Formulate the information design problem as an optimization over signal distributions (information structures) to minimize expected spillover.
• Partition feasible information structures into two classes based on their qualitative impact on equilibrium flows (Proposition 1).
• Derive analytical solutions for the optimal signal distribution using nonlinear, non-convex optimization techniques.
• Characterize the optimal signal structure as a function of the incident probability and the fraction of informed travelers (λ), identifying threshold values (e.g., λ̲ = 0.133).

Experimental results

Research questions

• RQ1 Under what conditions can a central authority minimize traffic spillover on a target route by designing information signals?
• RQ2 How does the fraction of travelers receiving the signal affect the achievable minimum spillover?
• RQ3 What is the optimal information structure (signal distribution) for any given fraction of informed travelers?
• RQ4 Can the minimum spillover be achieved without full signal access by all travelers?
• RQ5 How does the optimal information design compare to no information or complete information scenarios in terms of spillover and cost?

Key findings

• The minimum average spillover is achievable as long as the fraction of travelers receiving the signal exceeds a critical threshold (e.g., 13.3% in the example), even if not all travelers are informed.
• When the incident probability is low, it is optimal to provide no information at all, resulting in zero spillover.
• For high incident probabilities, the optimal information structure depends on the fraction of informed travelers and is analytically characterized.
• The optimal information design reduces average spillover by 18% compared to no information and by 47% compared to full information when λ > 25%.
• The equilibrium average cost under optimal information design is lower than under no information but slightly higher (1%) than under full information.
• When the authority can choose both λ and the signal structure, it is optimal to provide complete information to a fraction λ̲, minimizing both spillover and average cost.