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A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline

Author

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  • Bruneel, Herwig
  • Mélange, Willem
  • Steyaert, Bart
  • Claeys, Dieter
  • Walraevens, Joris

Abstract

This paper considers a simple discrete-time queueing model with two types (classes) of customers (types 1 and 2) each having their own dedicated server (servers A and B resp.). New customers enter the system according to a general independent arrival process, i.e., the total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. Service times are deterministically equal to 1 slot each. The system uses a “global FCFS” service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. As a consequence of the “global FCFS” rule, customers of one type may be blocked by customers of the other type, in that they may be unable to reach their dedicated server even at times when this server is idle, i.e., the system is basically non-workconserving. One major aim of the paper is to estimate the negative impact of this phenomenon on the queueing performance of the system, in terms of the achievable throughput, the system occupancy, the idle probability of each server and the delay. As it is clear that customers of different types hinder each other more as they tend to arrive in the system more clustered according to class, the degree of “class clustering” in the arrival process is explicitly modeled in the paper and its very direct impact on the performance measures is revealed. The motivation of our work are systems where this kind of blocking is encountered, such as input-queueing network switches or road splits.

Suggested Citation

  • Bruneel, Herwig & Mélange, Willem & Steyaert, Bart & Claeys, Dieter & Walraevens, Joris, 2012. "A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline," European Journal of Operational Research, Elsevier, vol. 223(1), pages 123-132.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:123-132
    DOI: 10.1016/j.ejor.2012.06.031
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    References listed on IDEAS

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    1. Avishai Mandelbaum & Martin I. Reiman, 1998. "On Pooling in Queueing Networks," Management Science, INFORMS, vol. 44(7), pages 971-981, July.
    2. Maertens, Tom & Walraevens, Joris & Bruneel, Herwig, 2007. "A modified HOL priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1168-1185, August.
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    4. Laevens, Koenraad & Bruneel, Herwig, 1995. "Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers," European Journal of Operational Research, Elsevier, vol. 85(1), pages 161-177, August.
    5. Frank N. Gouweleeuw & Henk C. Tijms, 1998. "Computing Loss Probabilities in Discrete-Time Queues," Operations Research, INFORMS, vol. 46(1), pages 149-154, February.
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    Citations

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    Cited by:

    1. Jens Baetens & Bart Steyaert & Dieter Claeys & Herwig Bruneel, 2020. "System occupancy in a multiclass batch-service queueing system with limited variable service capacity," Annals of Operations Research, Springer, vol. 293(1), pages 3-26, October.
    2. Herwig Bruneel & Willem Mélange & Dieter Claeys & Joris Walraevens, 2017. "A two-class global FCFS discrete-time queueing model with arbitrary-length constant service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 164-178, April.
    3. Tao Jiang, 2018. "Analysis of a Tollbooth Tandem Queue with Two-Class Customers and Two Heterogeneous Dedicated Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-21, December.
    4. Baoxian Chang & Tao Jiang & Qingqing Ye & Xudong Chai & Liwei Liu, 2020. "Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1145-1167, September.
    5. Baoxian Chang & Qingqing Ye & Jun Lv & Tao Jiang, 2019. "Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 479-501, October.

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