The Braess Paradox in a network of totally asymmetric exclusion processes

Abstract

We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-length ratios.

arXiv comment14 pages, 17 figures

References in corpus (9)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase transitions in an exactly soluble one-dimensional exclusion process
• The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
• The totally asymmetric simple exclusion process on networks
• Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport
• Exclusion processes on networks as models for cytoskeletal transport
• Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions
• Theoretical investigation of synchronous totally asymmetric exclusion processes on lattices with multiple-input-single-output junctions
• Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

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