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When does additional information lead to longer travel time in multi-origin-destination networks?

Xujin Chen, Xiaodong Hu, Xinqi Jing, Zhongzheng Tang

TL;DR

This work provides a complete necessary-and-sufficient topological characterization of IBP-free undirected networks with multiple OD pairs under non-atomic routing. It shows IBP-free networks are exactly those where each $G_i$ is SL I and intersections of subnetworks yield only coincident blocks or cycles, with cycle networks shown to be IBP-free. The result resolves an open question and offers a structural design tool for mitigating information-induced inefficiencies in complex routing networks. The approach combines block-chain decomposition, local ICWE analyses, and a deep cycle-based sufficiency argument, strengthening connections to classical BP results while addressing the nuances of information heterogeneity. Practical impact lies in network design and information dissemination strategies to avoid paradoxical increases in travel times.

Abstract

The Informational Braess' Paradox (IBP) illustrates a counterintuitive scenario where revelation of additional roadway segments to some self-interested travelers leads to increased travel times for these individuals. IBP extends the original Braess' paradox by relaxing the assumption that all travelers have identical and complete information about the network. In this paper, we study the conditions under which IBP does not occur in networks with non-atomic selfish travelers and multiple origin-destination pairs. Our results completely characterize the network topologies immune to IBP, thus resolving an open question proposed by Acemoglu et al.

When does additional information lead to longer travel time in multi-origin-destination networks?

TL;DR

This work provides a complete necessary-and-sufficient topological characterization of IBP-free undirected networks with multiple OD pairs under non-atomic routing. It shows IBP-free networks are exactly those where each is SL I and intersections of subnetworks yield only coincident blocks or cycles, with cycle networks shown to be IBP-free. The result resolves an open question and offers a structural design tool for mitigating information-induced inefficiencies in complex routing networks. The approach combines block-chain decomposition, local ICWE analyses, and a deep cycle-based sufficiency argument, strengthening connections to classical BP results while addressing the nuances of information heterogeneity. Practical impact lies in network design and information dissemination strategies to avoid paradoxical increases in travel times.

Abstract

The Informational Braess' Paradox (IBP) illustrates a counterintuitive scenario where revelation of additional roadway segments to some self-interested travelers leads to increased travel times for these individuals. IBP extends the original Braess' paradox by relaxing the assumption that all travelers have identical and complete information about the network. In this paper, we study the conditions under which IBP does not occur in networks with non-atomic selfish travelers and multiple origin-destination pairs. Our results completely characterize the network topologies immune to IBP, thus resolving an open question proposed by Acemoglu et al.

Paper Structure

This paper contains 15 sections, 30 theorems, 4 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Routing Game
  3. Information Braess' Paradox
  4. IBP-free Networks with a Single OD Pair
  5. IBP-free Networks with Multiple OD Pairs
  6. Related Work
  7. Organization.
  8. Preliminaries
  9. Necessity Proof
  10. An IBP Instance
  11. Graphical Structures
  12. Sufficiency Proof
  13. Concluding Remark
  14. Two Critical Flaws in the Proof of Theorem 3 in roman2019multi
  15. The Proof of Theorem \ref{['thm:cycle_main']}

Key Result

Theorem 1

ibp18 A network with a single OD pair is IBP-free if and only if it is an SLI network.

Figures (10)

  • Figure 1: Three classes of networks with a single OD pair
  • Figure 2: An SLI network, which is the chain of blocks $B_1,B_2,B_3,B_4$.
  • Figure 3: A cycle network (non-coincident block) that is IBP-free
  • Figure 4: A network with two OD pairs that admits IBP
  • Figure 5: A network that can not be embedded in LI networks
  • ...and 5 more figures

Theorems & Definitions (62)

  • Definition 1: ICWE flow
  • Definition 2: IBP
  • Definition 3: SP network
  • Definition 4: LI networks
  • Definition 5: SLI network
  • Theorem 1
  • Proposition 1
  • Definition 6
  • Theorem 2
  • Theorem 3: Main Result
  • ...and 52 more