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Preliminary Results on a Simple Approach to G/G/c-Like Queues

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5513))

Abstract

In this paper we consider a multi-server queue with a near general arrival process (represented as an arbitrary state-dependent Coxian distribution), a near general state-dependent Coxian service time distribution and a possibly finite queueing room. In addition to the dependence on the current number of customers in the system, the rate of arrivals and the progress of the service may depend on each other. We propose a semi-numerical method based on the use of conditional probabilities to compute the steady-state queue length distribution in such a queueing system. Our approach is conceptually simple, easy to implement and can be applied to both infinite and finite C m /C k /c-like queues. The proposed method uses a simple fixed-point iteration. In the case of infinite queues, it avoids the need for arbitrary truncation through the use of asymptotic conditional probabilities.

This preliminary study examines the computational behavior of the proposed method with a Cox-2 service distribution. Our results indicate that it is robust and performs well even when the number of servers and the coefficient of variation of the service times are relatively high. The number of iterations to attain convergence varies from low tens to several thousand. For example, we are able to solve queues with 1024 servers and the coefficients of variation of the service time and of the time between arrivals set to 4 within 1100 iterations.

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Author information

Authors and Affiliations

  1. Baskin School of Engineering, University of California Santa Cruz, USA

    Alexandre Brandwajn

  2. LIP6, Université Pierre et Marie Curie, France

    Thomas Begin

Authors
  1. Alexandre Brandwajn
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  2. Thomas Begin
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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, CF37 1DL, Pontypridd, UK

    Khalid Al-Begain

  2. Department TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Dieter Fiems

  3. Budapest University of Technology and Economics, P.O. Box 91, 1521, Budapest, Hungary

    Gábor Horváth

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© 2009 Springer-Verlag Berlin Heidelberg

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Brandwajn, A., Begin, T. (2009). Preliminary Results on a Simple Approach to G/G/c-Like Queues. In: Al-Begain, K., Fiems, D., Horváth, G. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2009. Lecture Notes in Computer Science, vol 5513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02205-0_12

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  • DOI: https://doi.org/10.1007/978-3-642-02205-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02204-3

  • Online ISBN: 978-3-642-02205-0

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