Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form

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Abstract

In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages34
Publication statusPublished - Sep 2016

Publication series

NameMemorandum
PublisherUniversity of Twente, Department of Applied Mathematics
No.2056
ISSN (Print)1874-4850

Keywords

  • MSC-60J22
  • Fixed-cycle traffic light model
  • IR-101081
  • EWI-27174
  • METIS-317688
  • contour integration
  • bulk service queue
  • roots

Cite this

Oblakova, A., Al Hanbali, A., Boucherie, R. J., van Ommeren, J. C. W., & Zijm, W. H. M. (2016). Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. (Memorandum; No. 2056). Enschede: University of Twente, Department of Applied Mathematics.
Oblakova, Anna ; Al Hanbali, Ahmad ; Boucherie, Richardus J. ; van Ommeren, Jan C.W. ; Zijm, Willem H.M. / Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. Enschede : University of Twente, Department of Applied Mathematics, 2016. 34 p. (Memorandum; 2056).
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abstract = "In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.",
keywords = "MSC-60J22, Fixed-cycle traffic light model, IR-101081, EWI-27174, METIS-317688, contour integration, bulk service queue, roots",
author = "Anna Oblakova and {Al Hanbali}, Ahmad and Boucherie, {Richardus J.} and {van Ommeren}, {Jan C.W.} and Zijm, {Willem H.M.}",
note = "Submitted version",
year = "2016",
month = "9",
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series = "Memorandum",
publisher = "University of Twente, Department of Applied Mathematics",
number = "2056",

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Oblakova, A, Al Hanbali, A, Boucherie, RJ, van Ommeren, JCW & Zijm, WHM 2016, Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. Memorandum, no. 2056, University of Twente, Department of Applied Mathematics, Enschede.

Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. / Oblakova, Anna; Al Hanbali, Ahmad; Boucherie, Richardus J.; van Ommeren, Jan C.W.; Zijm, Willem H.M.

Enschede : University of Twente, Department of Applied Mathematics, 2016. 34 p. (Memorandum; No. 2056).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form

AU - Oblakova, Anna

AU - Al Hanbali, Ahmad

AU - Boucherie, Richardus J.

AU - van Ommeren, Jan C.W.

AU - Zijm, Willem H.M.

N1 - Submitted version

PY - 2016/9

Y1 - 2016/9

N2 - In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.

AB - In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.

KW - MSC-60J22

KW - Fixed-cycle traffic light model

KW - IR-101081

KW - EWI-27174

KW - METIS-317688

KW - contour integration

KW - bulk service queue

KW - roots

M3 - Report

T3 - Memorandum

BT - Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Oblakova A, Al Hanbali A, Boucherie RJ, van Ommeren JCW, Zijm WHM. Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form. Enschede: University of Twente, Department of Applied Mathematics, 2016. 34 p. (Memorandum; 2056).