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

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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

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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.",
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author = "M. Boon and A.J.E.M. Janssen and {van Leeuwaarden}, Johan",
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language = "English",
volume = "ARXIV 1701.02872v1",
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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 journalArticleAcademic

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

AU - van Leeuwaarden, Johan

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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.

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M3 - Article

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JO - arXiv

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