In this paper, we display methods for the computation of convergence and perturbation bounds for $$/$$/1 system with balking, catastrophes, server failures and repairs. Based on the logarithmic norm of linear operators, the bounds on the rate of convergence, perturbation bounds, and the main limiting characteristics of the queue-length process are obtained. Finally, we consider the application of all obtained estimates to a specific model.
Keywords: Applied probability, ergodicity bounds; perturbation bounds, $$/$$/1 system with balking, catastrophes, server failures and repairs, limiting characteristics for the queue-length process
@article{RO_2021__55_4_2223_0,
author = {Zeifman, Alexander and Satin, Yacov and Kovalev, Ivan and Ammar, Sherif I.},
title = {Ergodicity and perturbation bounds for $M_t/M_t/1$ queue with balking, catastrophes, server failures and repairs},
journal = {RAIRO. Operations Research},
pages = {2223--2240},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/ro/2021101},
mrnumber = {4292304},
zbl = {1476.60178},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021101/}
}
TY - JOUR AU - Zeifman, Alexander AU - Satin, Yacov AU - Kovalev, Ivan AU - Ammar, Sherif I. TI - Ergodicity and perturbation bounds for $M_t/M_t/1$ queue with balking, catastrophes, server failures and repairs JO - RAIRO. Operations Research PY - 2021 SP - 2223 EP - 2240 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021101/ DO - 10.1051/ro/2021101 LA - en ID - RO_2021__55_4_2223_0 ER -
%0 Journal Article %A Zeifman, Alexander %A Satin, Yacov %A Kovalev, Ivan %A Ammar, Sherif I. %T Ergodicity and perturbation bounds for $M_t/M_t/1$ queue with balking, catastrophes, server failures and repairs %J RAIRO. Operations Research %D 2021 %P 2223-2240 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021101/ %R 10.1051/ro/2021101 %G en %F RO_2021__55_4_2223_0
Zeifman, Alexander; Satin, Yacov; Kovalev, Ivan; Ammar, Sherif I. Ergodicity and perturbation bounds for $M_t/M_t/1$ queue with balking, catastrophes, server failures and repairs. RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2223-2240. doi: 10.1051/ro/2021101
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