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Precomputing Multi-Agent Path Replanning using Temporal Flexibility: A Case Study on the Dutch Railway Network

Issa Hanou, Eric Kemmeren, Devin Wild Thomas, Mathijs de Weerdt

TL;DR

The paper addresses rapid replanning for a single delayed agent in a multi-agent path planning setting by leveraging temporal flexibility in other agents. It formalizes Flexible Multi-Agent Delay Replanning and introduces FlexSIPP, which precomputes an any-start-time plan for the delayed agent using flexible arrival-time functions that reflect other agents' allowed delays, and identifies tipping points that signal when agent ordering should swap. The approach yields safer, more cost-efficient plans than fixing others or delaying the delayed agent alone, demonstrated on a dense Dutch railway network with real timetable data. Practically, FlexSIPP enables automated, real-world re-timetabling by extracting tipping points and producing precomputed, actionable plans within polynomial-time bounds, albeit with higher upfront computation compared to some baselines.

Abstract

Executing a multi-agent plan can be challenging when an agent is delayed, because this typically creates conflicts with other agents. So, we need to quickly find a new safe plan. Replanning only the delayed agent often does not result in an efficient plan, and sometimes cannot even yield a feasible plan. On the other hand, replanning other agents may lead to a cascade of changes and delays. We show how to efficiently replan by tracking and using the temporal flexibility of other agents while avoiding cascading delays. This flexibility is the maximum delay an agent can take without changing the order of or further delaying more agents. Our algorithm, FlexSIPP, precomputes all possible plans for the delayed agent, also returning the changes for the other agents, for any single-agent delay within the given scenario. We demonstrate our method in a real-world case study of replanning trains in the densely-used Dutch railway network. Our experiments show that FlexSIPP provides effective solutions, relevant to real-world adjustments, and within a reasonable timeframe.

Precomputing Multi-Agent Path Replanning using Temporal Flexibility: A Case Study on the Dutch Railway Network

TL;DR

The paper addresses rapid replanning for a single delayed agent in a multi-agent path planning setting by leveraging temporal flexibility in other agents. It formalizes Flexible Multi-Agent Delay Replanning and introduces FlexSIPP, which precomputes an any-start-time plan for the delayed agent using flexible arrival-time functions that reflect other agents' allowed delays, and identifies tipping points that signal when agent ordering should swap. The approach yields safer, more cost-efficient plans than fixing others or delaying the delayed agent alone, demonstrated on a dense Dutch railway network with real timetable data. Practically, FlexSIPP enables automated, real-world re-timetabling by extracting tipping points and producing precomputed, actionable plans within polynomial-time bounds, albeit with higher upfront computation compared to some baselines.

Abstract

Executing a multi-agent plan can be challenging when an agent is delayed, because this typically creates conflicts with other agents. So, we need to quickly find a new safe plan. Replanning only the delayed agent often does not result in an efficient plan, and sometimes cannot even yield a feasible plan. On the other hand, replanning other agents may lead to a cascade of changes and delays. We show how to efficiently replan by tracking and using the temporal flexibility of other agents while avoiding cascading delays. This flexibility is the maximum delay an agent can take without changing the order of or further delaying more agents. Our algorithm, FlexSIPP, precomputes all possible plans for the delayed agent, also returning the changes for the other agents, for any single-agent delay within the given scenario. We demonstrate our method in a real-world case study of replanning trains in the densely-used Dutch railway network. Our experiments show that FlexSIPP provides effective solutions, relevant to real-world adjustments, and within a reasonable timeframe.
Paper Structure (18 sections, 2 theorems, 3 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 18 sections, 2 theorems, 3 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Safe Interval Path Planning
  4. Any-Start-Time Planning
  5. Multi-Agent Execution Delay Replanning
  6. Problem Description: Flexible Multi-Agent Delay Replanning
  7. Method
  8. Search
  9. Tipping points
  10. Case Study: Rotterdam to Schiphol
  11. Railway Replanning with Flexibility
  12. Evaluation
  13. Experimental Setup
  14. Running Example
  15. Case Study
  16. ...and 3 more sections

Key Result

Proposition 1

Given a Flexible Multi-Agent Delay Replanning problem, we can derive the flexibility of all agents in polynomial time.

Figures (5)

  • Figure 1: Example of a corridor MAPF problem.
  • Figure 2: An ATF with parameters $\zeta,\alpha,\beta$, and $\Delta$.
  • Figure 3: Railway Network in the Netherlands showing the maximum speed on each segment. Zoom-in of the area between Rotterdam and Amsterdam, both the regular track over Leiden in yellow, as well as the high-speed section between Rotterdam and Schiphol in red ProRail2022a[p.199].
  • Figure 4: Two blocking time staircases of two trains along the same track. The rightmost block is the critical block. Adapted from Pachl2021.
  • Figure 5: (Continuous) ATFs from FlexSIPP to solve the corridor example.

Theorems & Definitions (9)

  • Example 1
  • Definition 1: Flexibility
  • Proposition 1: Flexibility
  • Example 2: Flexibility
  • Definition 2: Tipping Point
  • Example 3: Tipping Point
  • Example 4: ATF
  • Example 5: Search with flexibility
  • Proposition 2