Abstract
The forward Kolmogorov system for a general nonstationary Markovian queueing model with possible batch arrivals, possible catastrophes and state-dependent control at idle time is considered. We obtain upper bounds on the rate of convergence for corresponding models (nonstationary \(M^X/M_n/1\) queue without catastrophes with the special resurrection intensities and general nonstationary \(M^X/M_n/1\) queue with mass arrivals and catastrophes) and apply these estimates for some specific situations. Examples with given parameters are considered and corresponding plots are constructed.
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The research has been supported by the Russian Science Foundation under grant 19-11-00020.
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Zeifman, A., Satin, Y., Kryukova, A., Shilova, G., Kiseleva, K. (2020). Convergence Rate Estimates for Some Models of Queuing Theory, and Their Applications. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_4
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