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Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals

Author

Listed:
  • Arnaud Devos

    (Ghent University)

  • Joris Walraevens

    (Ghent University)

  • Dieter Fiems

    (Ghent University)

  • Herwig Bruneel

    (Ghent University)

Abstract

We analyze a discrete-time two-class queueing system with a single server which is alternately available for only one customer class. The server is each time allocated to a customer class for a geometrically distributed amount of time. Service times of the customers are deterministically equal to 1 time slot each. During each time slot, both classes can have at most one arrival. The bivariate process of the number of customers of both classes can be considered as a two-dimensional nearest-neighbor random walk. The generating function of this random walk has to be obtained from a functional equation. This type of functional equation is known to be difficult to solve. In this paper, we obtain closed-form expressions for the joint probability distribution for the number of customers of both classes, in steady state.

Suggested Citation

  • Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2020. "Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 133-152, October.
    • Handle: RePEc:spr:queues:v:96:y:2020:i:1:d:10.1007_s11134-020-09663-x
    DOI: 10.1007/s11134-020-09663-x
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    References listed on IDEAS

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    1. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    2. Dieter Fiems & Bart Steyaert & Herwig Bruneel, 2002. "Randomly Interrupted GI-G-1 Queues: Service Strategies and Stability Issues," Annals of Operations Research, Springer, vol. 112(1), pages 171-183, April.
    3. 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.
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    Cited by:

    1. Arnaud Devos & Joris Walraevens & Herwig Bruneel, 2024. "Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    2. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2021. "Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue," Mathematics, MDPI, vol. 9(21), pages 1-25, October.

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