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Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control

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Route choice and traffic signal control : A study of the stability and instability of a new dynamical model of route choice and traffic signal control. / Liu, Ronghui; Smith, Mike.

In: Transportation Research Part B: Methodological, Vol. 77, 01.07.2015, p. 123-145.

Research output: Contribution to journalArticle

Harvard

Liu, R & Smith, M 2015, 'Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control', Transportation Research Part B: Methodological, vol. 77, pp. 123-145. https://doi.org/10.1016/j.trb.2015.03.012

APA

Liu, R., & Smith, M. (2015). Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control. Transportation Research Part B: Methodological, 77, 123-145. https://doi.org/10.1016/j.trb.2015.03.012

Vancouver

Liu R, Smith M. Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control. Transportation Research Part B: Methodological. 2015 Jul 1;77:123-145. https://doi.org/10.1016/j.trb.2015.03.012

Author

Liu, Ronghui ; Smith, Mike. / Route choice and traffic signal control : A study of the stability and instability of a new dynamical model of route choice and traffic signal control. In: Transportation Research Part B: Methodological. 2015 ; Vol. 77. pp. 123-145.

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@article{99c1bdbb464b4db1a8aeb923e5f63753,
title = "Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control",
abstract = "This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar-Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the {"}pressure{"} formula fits the special control policy P0 (see Smith, 1979a,b), then the combined flow-swapping/green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilised. The dynamical models described here do not represent blocking back effects.",
keywords = "Convergence, Day to day, Dynamics, Routeing, Signal control, Stability",
author = "Ronghui Liu and Mike Smith",
year = "2015",
month = "7",
day = "1",
doi = "10.1016/j.trb.2015.03.012",
language = "English",
volume = "77",
pages = "123--145",
journal = "Transportation Research Part B: Methodological",
issn = "0191-2615",
publisher = "Elsevier Limited",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Route choice and traffic signal control

T2 - A study of the stability and instability of a new dynamical model of route choice and traffic signal control

AU - Liu, Ronghui

AU - Smith, Mike

PY - 2015/7/1

Y1 - 2015/7/1

N2 - This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar-Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the "pressure" formula fits the special control policy P0 (see Smith, 1979a,b), then the combined flow-swapping/green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilised. The dynamical models described here do not represent blocking back effects.

AB - This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar-Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the "pressure" formula fits the special control policy P0 (see Smith, 1979a,b), then the combined flow-swapping/green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilised. The dynamical models described here do not represent blocking back effects.

KW - Convergence

KW - Day to day

KW - Dynamics

KW - Routeing

KW - Signal control

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84928153185&partnerID=8YFLogxK

U2 - 10.1016/j.trb.2015.03.012

DO - 10.1016/j.trb.2015.03.012

M3 - Article

AN - SCOPUS:84928153185

VL - 77

SP - 123

EP - 145

JO - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

SN - 0191-2615

ER -