Ergodicity and perturbation bounds for M_t/M_t/1 queue with balking, catastrophes, server failures and repairs

¹ Vologda State University, Institute of Informatics Problems, FRC CSC RAS, Vologda Research Center RAS, Vologda, Russia
² Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, Russia
³ Vologda State University, Vologda, Russia
⁴ Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom, Egypt
⁵ Department of Mathematics, College of Science, Taibah University, Medinah, Saudi Arabia

^* Corresponding author: a_zeifman@mail.ru

Received: 21 February 2021
Accepted: 8 July 2021

Abstract

In this paper, we display methods for the computation of convergence and perturbation bounds for M_t/M_t/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.