A splitting rate model of traffic re-routeing and traffic control

Mike Smith*, Richard Mounce

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)
4 Downloads (Pure)

Abstract

The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control. (C) 2010 Published by Elsevier Ltd.

Original languageEnglish
Pages (from-to)316-340
Number of pages25
JournalProcedia – Social and Behavioral Sciences
Volume17
DOIs
Publication statusPublished - 2011
Event19th International Symposium on Transportation and Traffic Theory (ISTTT) in honor of Carlos F. Daganzo - Berkeley, Canada
Duration: 18 Jul 201120 Jul 2011

Keywords

  • user equilibrium assignment
  • variational-inequalities
  • signal control
  • road network
  • algorithms
  • transportation
  • enumeration
  • stability

Cite this

A splitting rate model of traffic re-routeing and traffic control. / Smith, Mike; Mounce, Richard.

In: Procedia – Social and Behavioral Sciences, Vol. 17, 2011, p. 316-340.

Research output: Contribution to journalArticle

@article{bc9c867ad0c24ee398180d6237f1b41c,
title = "A splitting rate model of traffic re-routeing and traffic control",
abstract = "The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control. (C) 2010 Published by Elsevier Ltd.",
keywords = "user equilibrium assignment, variational-inequalities, signal control, road network, algorithms, transportation, enumeration, stability",
author = "Mike Smith and Richard Mounce",
year = "2011",
doi = "10.1016/j.sbspro.2011.04.520",
language = "English",
volume = "17",
pages = "316--340",
journal = "Procedia – Social and Behavioral Sciences",
issn = "1877-0428",
publisher = "Elsevier BV",

}

TY - JOUR

T1 - A splitting rate model of traffic re-routeing and traffic control

AU - Smith, Mike

AU - Mounce, Richard

PY - 2011

Y1 - 2011

N2 - The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control. (C) 2010 Published by Elsevier Ltd.

AB - The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control. (C) 2010 Published by Elsevier Ltd.

KW - user equilibrium assignment

KW - variational-inequalities

KW - signal control

KW - road network

KW - algorithms

KW - transportation

KW - enumeration

KW - stability

U2 - 10.1016/j.sbspro.2011.04.520

DO - 10.1016/j.sbspro.2011.04.520

M3 - Article

VL - 17

SP - 316

EP - 340

JO - Procedia – Social and Behavioral Sciences

JF - Procedia – Social and Behavioral Sciences

SN - 1877-0428

ER -