article

Delay Analysis for the Fixed-Cycle Traffic-Light Queue

Author:

J. S. H. van LeeuwaardenAuthors Info & Claims

Transportation Science, Volume 40, Issue 2

Pages 189 - 199

https://doi.org/10.1287/trsc.1050.0125

Published: 01 May 2006 Publication History

Abstract

We consider the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic-light signal alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals.

Most of the research done on the FCTL queue assumes that the vehicles arrive at the intersection according to a Poisson process and focuses on deriving formulas for the mean queue length at the end of green periods and the mean delay. For a class of discrete arrival processes, including the Poisson process, we derive the probability generating function of both the queue length and delay, from which the whole queue length and delay distribution can be obtained. This allows for the evaluation of performance characteristics other than the mean, such as the variance and percentiles of the distribution.

We discuss the numerical procedures that are required to obtain the performance characteristics, and give several numerical examples.

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Ranpura PShukla VGujar R(2024)Estimation of vehicle control delay using artificial intelligence techniques for heterogeneous traffic conditionsExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123206246:COnline publication date: 15-Jul-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.123206
Verdonck FBruneel HWittevrongel S(2023)A Variable-Cycle Traffic Light QueueComputer Performance Engineering and Stochastic Modelling10.1007/978-3-031-43185-2_5(65-80)Online publication date: 20-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43185-2_5
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cover image Transportation Science

Transportation Science Volume 40, Issue 2

May 2006

126 pages

ISSN:1526-5447

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 May 2006

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Cited By

Wang DYang GTian ZWei DMao X(2024)Effects of Probabilistic Priority on Delay at Permissive Left-Turn Signalized IntersectionsIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.332958425:5(3402-3419)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.1109/TITS.2023.3329584
Ranpura PShukla VGujar R(2024)Estimation of vehicle control delay using artificial intelligence techniques for heterogeneous traffic conditionsExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123206246:COnline publication date: 15-Jul-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.123206
Verdonck FBruneel HWittevrongel S(2023)A Variable-Cycle Traffic Light QueueComputer Performance Engineering and Stochastic Modelling10.1007/978-3-031-43185-2_5(65-80)Online publication date: 20-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43185-2_5
Timmerman RMarko Boon A(2020)New vehicle-actuated access algorithms for intersections close to oversaturation2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC)10.1109/ITSC45102.2020.9294237(1-6)Online publication date: 20-Sep-2020
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Oblakova AAl Hanbali ABoucherie ROmmeren JZijm W(2019)An exact root-free method for the expected queue length for a class of discrete-time queueing systemsQueueing Systems: Theory and Applications10.1007/s11134-019-09614-192:3-4(257-292)Online publication date: 1-Aug-2019
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Boon MJanssen ALeeuwaarden JTimmerman R(2019)Pollaczek contour integrals for the fixed-cycle traffic-light queueQueueing Systems: Theory and Applications10.1007/s11134-018-9595-991:1-2(89-111)Online publication date: 1-Feb-2019
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Pacheco ASimões MMilheiro-Oliveira P(2017)Queues with Server Vacations as a Model for Pretimed Signalized Urban TrafficTransportation Science10.1287/trsc.2016.072751:3(841-851)Online publication date: 1-Aug-2017
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Mukhopadhyay SM. J. PKumar A(2017)Approximate Mean Delay Analysis for a Signalized Intersection With Indisciplined TrafficIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2017.266512118:10(2750-2762)Online publication date: 29-Sep-2017
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Janssen AVan Leeuwaarden J(2016)Dominant poles and tail asymptotics in the critical Gaussian many-sources regimeQueueing Systems: Theory and Applications10.1007/s11134-016-9499-584:3-4(211-236)Online publication date: 1-Dec-2016
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Herrera JHendrix ECasado LHaijema R(2014)Data Parallelism in Traffic Control Tables with Arrival InformationRevised Selected Papers, Part I, of the Euro-Par 2014 International Workshops on Parallel Processing - Volume 880510.1007/978-3-319-14325-5_6(60-70)Online publication date: 25-Aug-2014
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