Geodesic
Cost optimization of queueing systems with interruptions
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 371-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a queueing system $M|G|1$ with possible vacations in server operations for principal customers (for example, if a server is leased). A cost optimization problem is solved. As control parameters, we use the probability $\alpha$ of the vacation and its duration. Under fairly general assumptions about the system behavior during vacations, we show that the optimal value of the probability $\alpha$ is either 0 or 1. We also give necessary and sufficient conditions for a vacation to be carried out, i.e., $\alpha=1$. With constant vacation durations, we find conditions such that $\alpha=1$, and the vacation duration is optimal. Two examples are considered. In the first example, the revenue from the vacation is a linear function of its duration, and, in the second example, the revenue is a quadratic function.
Keywords: queueing system, queueing vacation, stationary distribution. 
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G. A. Afanasiev. Cost optimization of queueing systems with interruptions. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 2, pp. 371-382. http://geodesic.mathdoc.fr/item/TVP_2023_68_2_a8/

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