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The effect of green time on stochastic queues at traffic signals

Taylor, NB; Heydecker, BG; (2014) The effect of green time on stochastic queues at traffic signals. TRANSPORTATION PLANNING AND TECHNOLOGY , 37 (1) 3 - 19. 10.1080/03081060.2013.844907. Green open access

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Abstract

Many analyses of traffic signal queues use Webster and Cobbe's formula, which combines the net effect of the red/green cycle with a term representing stochastic effects, idealised as an M/D/1 queue process having random arrivals and uniform service. Several authors have noted that this component should depend not only on demand intensity but also on throughput capacity in each green period, although an extra empirical term may partially allow for this. Extending the service interval in M/D/1 (M = Markovian, i.e. random, D = deterministic, i.e. uniform, 1 = one server) enables the effect to be reproduced, but no exact expressions for its moments are found. Approximate formulae for the extended mean exist but are accurate only near saturation. The paper derives novel approximations for the equilibrium mean and also variance and utilisation, using functions linking traffic intensity with green period capacity. With three moments, equilibrium probability distributions can be estimated for which a method based on a doubly nested geometric distribution is described.

Type: Article
Title: The effect of green time on stochastic queues at traffic signals
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/03081060.2013.844907
Publisher version: http://dx.doi.org/10.1080/03081060.2013.844907
Language: English
Additional information: © 2013 The Author(s). Published by Taylor & Francis. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The moral rights of the named author(s) have been asserted.
Keywords: signal, queue, stochastic, M, D, 1, variance, probability distribution
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
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1418733
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