Abstract
We study a single-channel queuing system with an arbitrary distribution of the duration of service requirements, on the input of which there are n Poisson processes. The requirements of the various processes come in different queues. The task is to determine the rule for selecting service requirements and to determine the optimal strategy for establishing dynamic priorities. We consider a case \(n=2\).
To this end, a controlled semi-Markov process is defined, on the trajectories of which a functional is constructed that determines the quality of management and takes into account the number of lost requirements, the number of serviced requirements, the time of the requirement stay in the system, and so on. An algorithm for determining the optimal strategy is formulated.
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References
Kashtanov, V.A., Zaytseva, O.B.: Operations Research: Textbook, 256 p. INFRA-M, Moscow (2016)
Barzilovich, E.Yu., Belyaev, Yu.K., Kashtanov, V.A., et al.: Questions of a Mathematical Reliability Theory, 376 p. Radio i svaz’, Moscow (1983)
Mine, H., Osaki, S.: Markovian Decision Processes. Nauka, Moscow (1977)
Kondrashova, E.V.: Optimizing income function in controlled Markov queueing model. Upravlenie Bol’simi Sistemami 36, 93–105 (2011)
Kashtanov, V.A., Kondrashova, E.V.: Optimization of the CBSMAP-queueing model. In: Lecture Notes in Engineering and Computer Science, pp. 69–73. NL International Association of Engineers (2013)
Kondrashova, E.V., Kashtanov, V.A.: Research of optimum strategy for semi-Markov queueing models at control of CBSMAP-flow. Algorithmization. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. LNCS, vol. 10187, pp. 439–447. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57099-0_49
Kashtanov, V.A., Medvedev, A.: Reliability Theory of the Composite Systems (Theory and Practice). Fizmatlit, Moscow (2010)
Ivchenko, G.I., Kashtanov, V.A., Kovalenko, I.N.: Theory of a Queuing. LIBROCOM, Moscow (2012)
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Zaytseva, O.B., Kondrashova, E.V. (2017). Priority Management in a Semi-Markov Queuing Model. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_7
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DOI: https://doi.org/10.1007/978-3-319-71504-9_7
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