  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.
