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Estimating probability distributions of dynamic queues

Taylor, NB; Heydecker, BG; (2015) Estimating probability distributions of dynamic queues. Transportation Planning and Technology , 38 (1) 3 - 27. 10.1080/03081060.2014.976987. Green open access

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Abstract

Queues are often associated with uncertainty or unreliability, which can arise from chance or climatic events, phase changes in system behaviour, or inherent randomness. Knowing the probability distribution of the number of customers in a queue is important for estimating the risk of stress or disruption to routine services and upstream blocking, potentially leading to exceeding critical limits, gridlock or incidents. The present paper focuses on time-varying queues produced by transient oversaturation during demand peaks where there is randomness in arrivals and service. The objective is to present practical methods for estimating a probability distribution from knowledge of the mean, variance and utilisation (degree of saturation) of a queue available from computationally efficient, if approximate, time-dependent calculation. This is made possible by a novel expression for time-dependent queue variance. The queue processes considered are those commonly used to represent isolated priority (M/M/1) and signal-like (M/D/1) systems, plus some statistical variations within the common Pollaczek-Khinchin framework. Results are verified by comparison with Markov simulation based on recurrence relations.

Type: Article
Title: Estimating probability distributions of dynamic queues
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/03081060.2014.976987
Publisher version: http://dx.doi.org/10.1080/03081060.2014.976987
Language: English
Additional information: This is an Accepted Manuscript of an article published by Taylor & Francis in Transportation Planning and Technology on November 2014, available online: http://www.tandfonline.com/10.1080/03081060.2014.976987
Keywords: dynamic, uncertainty, probability distribution, reliability, queue
UCL classification: 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/1461315
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