Pollaczek contour integrals for the fixed-cycle traffic-light queue

M. Boon, A.J.E.M. Janssen, Johan van Leeuwaarden

Research output: Contribution to journal › Article › Academic

69 Downloads (Pure)

Abstract

The fixed-cycle traffic-light (FCTL) queue is the null model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some characteristic equation. We derive a novel contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. This representation will be the basis for effective algorithms. We show that it is straightforward to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures altogether.
Original languageEnglish
Number of pages17
JournalarXiv
VolumeARXIV 1701.02872v1
Publication statusPublished - 11 Jan 2017

Fingerprint

Telecommunication traffic

Cite this

Boon, M. ; Janssen, A.J.E.M. ; van Leeuwaarden, Johan. / Pollaczek contour integrals for the fixed-cycle traffic-light queue. In: arXiv. 2017 ; Vol. ARXIV 1701.02872v1.
@article{b374ed9991184714b417042f2c51a29f,
title = "Pollaczek contour integrals for the fixed-cycle traffic-light queue",
abstract = "The fixed-cycle traffic-light (FCTL) queue is the null model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some characteristic equation. We derive a novel contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. This representation will be the basis for effective algorithms. We show that it is straightforward to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures altogether.",
keywords = "math.PR",
author = "M. Boon and A.J.E.M. Janssen and {van Leeuwaarden}, Johan",
year = "2017",
month = "1",
day = "11",
language = "English",
volume = "ARXIV 1701.02872v1",
journal = "arXiv",
publisher = "Cornell University Library",

}

Boon, M, Janssen, AJEM & van Leeuwaarden, J 2017, 'Pollaczek contour integrals for the fixed-cycle traffic-light queue', arXiv, vol. ARXIV 1701.02872v1.

Pollaczek contour integrals for the fixed-cycle traffic-light queue. / Boon, M.; Janssen, A.J.E.M.; van Leeuwaarden, Johan.

In: arXiv, Vol. ARXIV 1701.02872v1, 11.01.2017.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Pollaczek contour integrals for the fixed-cycle traffic-light queue

AU - Boon, M.

AU - Janssen, A.J.E.M.

AU - van Leeuwaarden, Johan

PY - 2017/1/11

Y1 - 2017/1/11

N2 - The fixed-cycle traffic-light (FCTL) queue is the null model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some characteristic equation. We derive a novel contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. This representation will be the basis for effective algorithms. We show that it is straightforward to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures altogether.

AB - The fixed-cycle traffic-light (FCTL) queue is the null model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some characteristic equation. We derive a novel contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. This representation will be the basis for effective algorithms. We show that it is straightforward to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures altogether.

KW - math.PR

M3 - Article

VL - ARXIV 1701.02872v1

JO - arXiv

JF - arXiv

ER -

Boon M, Janssen AJEM, van Leeuwaarden J. Pollaczek contour integrals for the fixed-cycle traffic-light queue. arXiv. 2017 Jan 11;ARXIV 1701.02872v1.

Access to Document