On the bounds of the rate of convergence for $M_t/M_t/1$ model with two different requests

The author deals with a nonstationary queuing model $M_t/M_t/1$ with one server and two different types of requests. For this model, the author obtains a one-dimensional birth and death process that describes the number of requirements in the original system. By applying the standard method of the logarithmic norm of the operator of a linear function, corresponding estimates for the rate of convergence and ergodicity are obtained. A numerical example with exact given values of intensities showing the application of the studied approach is constructed and corresponding graphic illustrations are provided. The author uses the general algorithm to build graphs, it is associated with solving the Cauchy problem for the forward Kolmogorov system on the corresponding interval which has already been used by the authors in previous papers.