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Analysis of a two-class single-server discrete-time FCFS queue: the effect of interclass correlation

Author

Listed:
  • Herwig Bruneel

    (Ghent University-UGent)

  • Tom Maertens

    (Ghent University-UGent)

  • Bart Steyaert

    (Ghent University-UGent)

  • Dieter Claeys

    (Ghent University-UGent
    Ghent University-UGent)

  • Dieter Fiems

    (Ghent University-UGent)

  • Joris Walraevens

    (Ghent University-UGent)

Abstract

In this paper, we study a discrete-time queueing system with one server and two classes of customers. Customers enter the system according to a general independent arrival process. The classes of consecutive customers, however, are correlated in a Markovian way. The system uses a “global FCFS” service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their classes. The service-time distribution of the customers is general but class-dependent, and therefore, the exact order in which the customers of both classes succeed each other in the arrival stream is important, which is reflected by the complexity of the system content and waiting time analysis presented in this paper. In particular, a detailed waiting time analysis of this kind of multi-class system has not yet been published, and is considered to be one of the main novelties by the authors. In addition to that, a major aim of the paper is to estimate the impact of interclass correlation in the arrival stream on the total number of customers in the system, and the customer delay. The results reveal that the system can exhibit two different classes of stochastic equilibrium: a “strong” equilibrium where both customer classes give rise to stable behavior individually, and a “compensated” equilibrium where one customer type creates overload.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:26:y:2018:i:3:d:10.1007_s11750-018-0480-9
    DOI: 10.1007/s11750-018-0480-9
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    References listed on IDEAS

    as
    1. 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.
    2. I. J. B. F. Adan & A. Sleptchenko & G. J. Van Houtum, 2009. "Reducing Costs Of Spare Parts Supply Systems Via Static Priorities," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(04), pages 559-585.
    3. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.
    4. Tom Maertens & Joris Walraevens & Herwig Bruneel, 2008. "Performance comparison of several priority schemes with priority jumps," Annals of Operations Research, Springer, vol. 162(1), pages 109-125, September.
    5. Walraevens, Joris & Steyaert, Bart & Bruneel, Herwig, 2004. "Performance analysis of a GI-Geo-1 buffer with a preemptive resume priority scheduling discipline," European Journal of Operational Research, Elsevier, vol. 157(1), pages 130-151, August.
    6. Feng, Wei & Umemura, Masataka, 2009. "Analysis of a finite buffer model with two servers and two nonpreemptive priority classes," European Journal of Operational Research, Elsevier, vol. 192(1), pages 151-172, January.
    7. Walraevens, Joris & Fiems, Dieter & Wittevrongel, Sabine & Bruneel, Herwig, 2009. "Calculation of output characteristics of a priority queue through a busy period analysis," European Journal of Operational Research, Elsevier, vol. 198(3), pages 891-898, November.
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