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Application of a Particular Class of Markov Chains in the Assessment of Semi-actuated Signalized Intersections

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10378))

Abstract

We investigate a queuing model for a signalized intersection regulated by semi-actuated control in a urban traffic network. Modelling the queue length and the delay of vehicles for this type of traffic, characterized by variable durations of the green signal, is crucial to evaluate the performance of traffic intersections. Additionally, determining the size of the extensions of the green signal is also relevant. The traffic systems addressed in the paper have the particularity that the server remains active (green signal) for a period of time that depends on the number of vehicles waiting at the intersection. This gives rise to an M/D/1 queuing system with a server that occasionally takes vacations (red signal), for which we compute the long-run mean delay of vehicles, mean queue length and mean duration of the green signal. We consider a case study and compare the results obtained from the proposed queueing model with those obtained by using a microsimulation model. The formulas derived for the performance measures are of interest for traffic engineers, since the existing alternative formulas are subject to strong criticism.

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Acknowledgments

The first author was partially supported by CMUP under a grant of the project UID/MAT/00144/2013, financed by FCT/MEC (PIDDAC). This research was partially supported by CMUP (UID/MAT/00144/2013) and CEMAT (UID/Multi/04621/2013), funded by FCT (Portugal) with National (MEC) and European structural funds through the programs FEDER, under partnership agreement PT2020.

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Authors and Affiliations

  1. CMUP, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Francisco Macedo & Paula Milheiro-Oliveira

  2. Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    Paula Milheiro-Oliveira & Maria Lurdes Simões

  3. CEMAT and Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001, Lisboa, Portugal

    Francisco Macedo & António Pacheco

  4. CONSTRUCT, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    Maria Lurdes Simões

Authors
  1. Francisco Macedo
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  2. Paula Milheiro-Oliveira
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  3. António Pacheco
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  4. Maria Lurdes Simões
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Corresponding author

Correspondence to Paula Milheiro-Oliveira .

Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Nigel Thomas

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Matthew Forshaw

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Macedo, F., Milheiro-Oliveira, P., Pacheco, A., Simões, M.L. (2017). Application of a Particular Class of Markov Chains in the Assessment of Semi-actuated Signalized Intersections. In: Thomas, N., Forshaw, M. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2017. Lecture Notes in Computer Science(), vol 10378. Springer, Cham. https://doi.org/10.1007/978-3-319-61428-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-61428-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61427-4

  • Online ISBN: 978-3-319-61428-1

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