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Approximations for the performance evaluation of a discrete-time two-class queue with an alternating service discipline

Author

Listed:
  • Arnaud Devos

    (Department of Telecommunications and Information Processing)

  • Joris Walraevens

    (Department of Telecommunications and Information Processing)

  • Dieter Fiems

    (Department of Telecommunications and Information Processing)

  • Herwig Bruneel

    (Department of Telecommunications and Information Processing)

Abstract

We consider a discrete-time queueing system with two queues and one server. The server is allocated in each slot to the first queue with probability $$\alpha $$ α and to the second queue with probability $$1-\alpha $$ 1 - α . The service times are equal to one time slot. The queues have exponentially bounded, but general, arrival distributions. The mathematical description of this system leads to a single functional equation for the joint probability generating function of the stationary system contents. As the joint stochastic process of the system contents is not amenable for exact analysis, we focus on an efficient approximation of the joint probability generating function. In particular, first we prove that the partial probability generating functions, present in the functional equation, have a unique dominant pole. Secondly, we use this information to approximate these partial probability generating functions by truncating an infinite sum. The remaining finite number of unknowns are estimated from a noise perturbed linear system. We illustrate our approach by various numerical examples and verify the accuracy by means of simulation.

Suggested Citation

  • Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2022. "Approximations for the performance evaluation of a discrete-time two-class queue with an alternating service discipline," Annals of Operations Research, Springer, vol. 310(2), pages 477-503, March.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03776-5
    DOI: 10.1007/s10479-020-03776-5
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    References listed on IDEAS

    as
    1. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    2. Blanc, J.P.C., 1993. "Performance Analysis and Optimization with the Power- Series Algorithm," Papers 9347, Tilburg - Center for Economic Research.
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    5. Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
    6. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
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