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Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems

Author

Listed:
  • Dave Worthington

    (Lancaster University)

  • A Wall

    (Liverpool John Moores University)

Abstract

Many real-life queueing problems exhibit time-dependent behaviour, but the corresponding theoretical models are hard to handle. The overall purpose of this paper is to describe a discrete time modelling (DTM) approach to solving problems of this sort, and to outline the research opportunities and challenges associated with it. The DTM approach is placed alongside other related research and is shown in particular to have strong links with some aspects of the matrix-geometric methods. The main research issues that have arisen in applying the DTM approach to problems of the form M(t)/G/1, M(t)/G/c and M(t)/G0.c/1 are described. This then provides a basis for outlining ongoing research into systems such as M(t)/G/c/K and tandem queues. Finally DTM research opportunities and challenges for more complex problems such as priority queues, server vacation models and queueing networks are delineated.

Suggested Citation

  • Dave Worthington & A Wall, 1999. "Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(8), pages 777-788, August.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:8:d:10.1057_palgrave.jors.2600783
    DOI: 10.1057/palgrave.jors.2600783
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    Citations

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    Cited by:

    1. Wall, A.D. & Worthington, D.J., 2007. "Time-dependent analysis of virtual waiting time behaviour in discrete time queues," European Journal of Operational Research, Elsevier, vol. 178(2), pages 482-499, April.
    2. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    3. D Worthington, 2009. "Reflections on queue modelling from the last 50 years," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 83-92, May.
    4. Justus Schwarz & Judith Stoll née Matzka & Eda Özden, 2015. "A general model for batch building processes under the timeout and capacity rules," Annals of Operations Research, Springer, vol. 231(1), pages 5-31, August.
    5. Ndreca, Sokol & Scoppola, Benedetto, 2008. "Discrete time GI/Geom/1 queueing system with priority," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1403-1408, September.
    6. Xi Chen & Dave Worthington, 2017. "Staffing of time-varying queues using a geometric discrete time modelling approach," Annals of Operations Research, Springer, vol. 252(1), pages 63-84, May.

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