Abstract
A multiserver queueing system with finite buffer, Markov input flow, and Markov (general) service process of all customers on servers with the number of process states and intensities of inter-phase transitions depending on the number of customers in the system is considered. A Markov flow of negative customers arrives to the system; one negative customer “kills” one positive customer at the end of the queue. A recurrent algorithm for computing stationary probabilities of system states is obtained; and a method for calculating stationary distribution of waiting time before starting service of a positive customer is proposed.
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Original Russian Text © A.V. Pechinkin, 2007, published in Informatsionnye Protsessy, 2007, Vol. 7, No. 2, pp. 138–152.
This work was supported by the Russian Foundation for Basic Research, projects nos. 06-07-89056 and 05-07-90103.
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Pechinkin, A.V. Markov queueing system with finite buffer and negative customers affecting the queue end. Autom Remote Control 68, 1104–1117 (2007). https://doi.org/10.1134/S0005117907060173
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DOI: https://doi.org/10.1134/S0005117907060173