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

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The fixed-cycle traffic-light (FCTL) queue is the standard 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. Building on the recent work of Oblakova et al. [1], we obtain a contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. We also show that similar contour integrals arise for generalizations of the FCTL queue introduced in [1] that relax some of the classical assumptions. Our results allow to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures. References: [1] A. Oblakova, A. Al Hanbali, R.J. Boucherie, J.C.W. van Ommeren, and W.H.M. Zijm. Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. Memorandum Faculty of Mathematical Sciences University of Twente, September 2016.
TaalEngels
Pagina's89-111
TijdschriftQueueing Systems
Volume91
Nummer van het tijdschrift1-2
DOI's
StatusGepubliceerd - 1 feb 2019

Vingerafdruk

Telecommunication traffic
Queue
Integral

Trefwoorden

  • math.PR

Citeer dit

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abstract = "The fixed-cycle traffic-light (FCTL) queue is the standard 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. Building on the recent work of Oblakova et al. [1], we obtain a contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. We also show that similar contour integrals arise for generalizations of the FCTL queue introduced in [1] that relax some of the classical assumptions. Our results allow to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures. References: [1] A. Oblakova, A. Al Hanbali, R.J. Boucherie, J.C.W. van Ommeren, and W.H.M. Zijm. Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. Memorandum Faculty of Mathematical Sciences University of Twente, September 2016.",
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Pollaczek contour integrals for the fixed-cycle traffic-light queue. / Boon, Marko (Corresponding author); Janssen, A.J.E.M.; Leeuwaarden, Johan S.H. van; Timmerman, Rik W.

In: Queueing Systems, Vol. 91, Nr. 1-2, 01.02.2019, blz. 89-111.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

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