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A two-class global FCFS discrete-time queueing model with arbitrary-length constant service times

Author

Listed:
  • Herwig Bruneel

    (Ghent University-UGent)

  • Willem Mélange

    (Ghent University-UGent)

  • Dieter Claeys

    (Ghent University-UGent)

  • Joris Walraevens

    (Ghent University-UGent)

Abstract

We analyze a discrete-time queueing model where two types of customers, each having their own dedicated server, are accommodated in one single FCFS queue. Service times are deterministically equal to $$s \ge 1$$ s ≥ 1 time slots each. New customers enter the system according to a general independent arrival process, but the types of consecutive customers may be nonindependent. As a result, arriving customers may (or may not) have the tendency to cluster according to their types, which may lead to more (or less) blocking of one type by the opposite type. The paper reveals the impact of this blocking phenomenon on the achievable throughput, the (average) system content, the (average) customer delay and the (average) unfinished work. The paper extends the results of earlier work where either the service times were assumed to be constant and equal to 1 slot each, or the customers all belonged to the same class. Our results show that, in case of Poisson arrivals, for given traffic intensity, the system-content distribution is insensitive to the length (s) of the service times, but the (mean) delay and the (mean) unfinished work in the system are not. In case of bursty arrivals, we find that all the performance measures are affected by the length (s) of the service times, for given traffic intensity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-016-0427-y
    DOI: 10.1007/s11750-016-0427-y
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    References listed on IDEAS

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    1. 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.
    2. Tom Van Woensel & Nico Vandaele, 2007. "Modeling Traffic Flows With Queueing Models: A Review," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 435-461.
    3. Gao, Peixia & Wittevrongel, Sabine & Walraevens, Joris & Moeneclaey, Marc & Bruneel, Herwig, 2009. "Calculation of delay characteristics for multiserver queues with constant service times," European Journal of Operational Research, Elsevier, vol. 199(1), pages 170-175, November.
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    Cited by:

    1. 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.
    2. 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.
    3. 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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