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A multi-class discrete-time queueing system under the FCFS service discipline

Author

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  • Sofian De Clercq
  • Koenraad Laevens
  • Bart Steyaert
  • Herwig Bruneel

Abstract

The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn’t actually determine what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into ‘during the same time-slot’. In other words, it doesn’t specify in which order such customers are served. When we consider multiple types of customers, each requiring different service time distributions, the precise order of service even starts to affect quantities such as queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a multi-class discrete-time queueing system with a general independent arrival process and generally distributed service times. The service discipline is FCFS and customers entering during the same time-slot are served in random order. It will be our goal to search for the steady-state distribution of queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the random order of service is equivalent to FCFS if different customers have different arrival epochs within this time-slot and if the arrival epochs are independent of customer class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a slot as a bounded continuous time frame. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Sofian De Clercq & Koenraad Laevens & Bart Steyaert & Herwig Bruneel, 2013. "A multi-class discrete-time queueing system under the FCFS service discipline," Annals of Operations Research, Springer, vol. 202(1), pages 59-73, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:59-73:10.1007/s10479-011-1051-8
    DOI: 10.1007/s10479-011-1051-8
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    References listed on IDEAS

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    1. 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.
    2. Joris Walraevens & Bart Steyaert & Herwig Bruneel, 2006. "A preemptive repeat priority queue with resampling: Performance analysis," Annals of Operations Research, Springer, vol. 146(1), pages 189-202, September.
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    Cited by:

    1. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    2. Herwig Bruneel & Tom Maertens & Bart Steyaert & Dieter Claeys & Dieter Fiems & Joris Walraevens, 2018. "Analysis of a two-class single-server discrete-time FCFS queue: the effect of interclass correlation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 403-436, October.
    3. Sofian Clercq & Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2016. "Analysis of a discrete-time queue with time-limited overtake priority," Annals of Operations Research, Springer, vol. 238(1), pages 69-97, March.
    4. Yongjiang Guo & Xiyang Hou & Yunan Liu, 2021. "A functional law of the iterated logarithm for multi-class queues with batch arrivals," Annals of Operations Research, Springer, vol. 300(1), pages 51-77, May.
    5. Sofian Clercq & Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2016. "Analysis of a discrete-time queue with time-limited overtake priority," Annals of Operations Research, Springer, vol. 238(1), pages 69-97, March.

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