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Predicting queue variability to enable analysis of overload risk

Taylor, NB; (2017) Predicting queue variability to enable analysis of overload risk. Transportation Planning and Technology , 41 (1) pp. 37-57. 10.1080/03081060.2018.1402744. Green open access

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Abstract

Predicting the risk of traffic demands and delays exceeding critical limits at road junctions, airports, hospitals, etc., requires knowing how both mean and variance of queue size vary over time. Microscopic simulation can explore variability but is computationally demanding and gives only sample results. A computationally efficient approximation to the mean is used in many modelling tools, but only empirical extensions for variance in particular situations have been available. The paper derives theoretical formulae for time-dependent and equilibrium variance, believed to be novel and to apply generally to queues covered by the Pollaczek–Khinchin mean formula, and offering possible structural insights. These are applied in an extended approximation giving mutually consistent mean and variance estimates with improved accuracy. Tests on oversaturated peak demand cases are compared with Markov probabilistic simulation, demonstrating accuracy (R2 > 0.99) for typical random, priority-like (M/M/1) and traffic-signal-like (M/D/1) queues. Implications for risk analysis, planning and policy are considered.

Type: Article
Title: Predicting queue variability to enable analysis of overload risk
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/03081060.2018.1402744
Publisher version: http://dx.doi.org/10.1080/03081060.2018.1402744
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Traffic, modelling, queue, variance, uncertainty, overload, risk
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
URI: https://discovery.ucl.ac.uk/id/eprint/10038278
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