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A Scalable Game-theoretic Approach to Urban Evacuation Routing and Scheduling

Kazi Ashik Islam, Da Qi Chen, Madhav Marathe, Henning Mortveit, Samarth Swarup, Anil Vullikanti

TL;DR

A strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure and a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition.

Abstract

Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. However, finding jointly optimal evacuation routes and schedule that minimizes the average evacuation time or evacuation completion time, is a computationally hard problem. As a result, large-scale evacuation routing and scheduling continues to be a challenge. In this paper, we present a game-theoretic approach to tackle this problem. We start by formulating a strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure. We show that: (i) every instance of EGRES has at least one pure strategy Nash equilibrium, and (ii) an optimal outcome in an instance will always be an equilibrium in that instance. We then provide bounds on how bad an equilibrium can be compared to an optimal outcome. Additionally, we present a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition. We use Virginia Beach City in Virginia, and Harris County in Houston, Texas as study areas and construct two EGRES instances. Our results show that, by utilizing SAA, we can efficiently find equilibria in these instances that have social objective close to the optimal value.

A Scalable Game-theoretic Approach to Urban Evacuation Routing and Scheduling

TL;DR

A strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure and a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition.

Abstract

Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. However, finding jointly optimal evacuation routes and schedule that minimizes the average evacuation time or evacuation completion time, is a computationally hard problem. As a result, large-scale evacuation routing and scheduling continues to be a challenge. In this paper, we present a game-theoretic approach to tackle this problem. We start by formulating a strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure. We show that: (i) every instance of EGRES has at least one pure strategy Nash equilibrium, and (ii) an optimal outcome in an instance will always be an equilibrium in that instance. We then provide bounds on how bad an equilibrium can be compared to an optimal outcome. Additionally, we present a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition. We use Virginia Beach City in Virginia, and Harris County in Houston, Texas as study areas and construct two EGRES instances. Our results show that, by utilizing SAA, we can efficiently find equilibria in these instances that have social objective close to the optimal value.
Paper Structure (28 sections, 7 theorems, 14 equations, 8 figures, 6 algorithms)

This paper contains 28 sections, 7 theorems, 14 equations, 8 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Problem Formulation
  4. Theoretical Analysis of egres
  5. Existence of Pure Strategy Nash Equilibrium
  6. Bound on Price of Anarchy
  7. Finding Pure Strategy Nash Equilibrium
  8. Calculating Best Response
  9. Calculating Equilibria
  10. Empirical Evaluation
  11. Quality of the Equilibria
  12. Scalability of saa
  13. Conclusion
  14. Proof of Lemma \ref{['lemma:cmpletion_time_upper_bound']}
  15. brsa Details and Proofs
  16. ...and 13 more sections

Key Result

Lemma 1

Given an evacuation network $\mathcal{G}(\mathcal{V}, \mathcal{A})$, there exists an outcome where all evacuees arrive at some safe node within time $(n\tau + M - 1)$ without any edge capacity violation. Here, $n$ is the number of nodes in $\mathcal{G}$, $M$ is total number of evacuees, and $\tau =

Figures (8)

  • Figure 1: egres example instance with $T_{max}=4$.
  • Figure 2: egres instance where price of anarchy is $O(n)$. The edges are labelled with their travel time. All of the edges have capacity $1$. Each source node has $d$ number of evacuees.
  • Figure 3: Example of confluent and non-confluent routes.
  • Figure 4: Proof sketch for brsa. The green edges denote the routes in $a_{-i}$.
  • Figure 5: Virginia Beach City game instance.
  • ...and 3 more figures

Theorems & Definitions (23)

  • Definition 1
  • Definition 2
  • Lemma 1
  • Definition 3
  • Definition 4
  • Definition 5
  • Example 1
  • Theorem 1
  • proof
  • Corollary 1
  • ...and 13 more