### Abstract

Original language | English |
---|---|

Number of pages | 17 |

Journal | arXiv |

Volume | ARXIV 1701.02872v1 |

Publication status | Published - 11 Jan 2017 |

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### Cite this

*arXiv*,

*ARXIV 1701.02872v1*.

}

*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.

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 -