Abstract
Consideration was given to the multi-server queuing system with unlimited buffer, Markov input flow, and Markov (general) process of servicing all customers on servers with the number of process states and intensities of the inter-phase passage depending on the number of customers in the system. Additionally, a Markov flow of negative customers arrives to the system, the arriving negative customer killing the last queued positive customer. A recurrent algorithm to calculate the stationary probabilities of system states was obtained, and a method of calculation of the stationary distribution of the waiting time before starting servicing of a positive customer was proposed.
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Original Russian Text © P.P. Bocharov, C. d’Apice, R. Manzo, A. V. Pechinkin, 2007, published in Automatika i Telemekhanika, 2007, No. 1, pp. 93–104.
This work was supported by the Russian Foundation for Basic Research, project no. 06-07-89056.
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Bocharov, P.P., d’Apice, C., Manzo, R. et al. Analysis of the multi-server Markov queuing system with unlimited buffer and negative customers. Autom Remote Control 68, 85–94 (2007). https://doi.org/10.1134/S0005117907010080
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DOI: https://doi.org/10.1134/S0005117907010080