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

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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.

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Notes

  1. We remark that \(\Delta (z)=-\sqrt{D_Y(z)}\) if \(z\in [1,\tau _T]\), due to the properties of the principal square root.

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Authors and Affiliations

  1. Department of Telecommunications and Information Processing, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Ghent, Belgium

    Arnaud Devos, Joris Walraevens, Dieter Fiems & Herwig Bruneel

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  1. Arnaud Devos
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  2. Joris Walraevens
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  3. Dieter Fiems
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  4. Herwig Bruneel
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Correspondence to Arnaud Devos.

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Devos, A., Walraevens, J., Fiems, D. et al. Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals. Queueing Syst 96, 133–152 (2020). https://doi.org/10.1007/s11134-020-09663-x

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  • DOI: https://doi.org/10.1007/s11134-020-09663-x

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