On the bounds of the rate of convergence for some queueing models with incompletely defined intensities

The authors consider some queuing systems with incompletely defined $1$-periodical intensities under corresponding conditions. The authors deal with $M_t/M_t/S$ queue for any number of servers $S$ and $M_t/M_t/S/S$ (the Erlang model). Estimates of the rate of convergence in weakly ergodic situation are obtained by applying the method of the logarithmic norm of the operator of a linear function. The examples with exact given values of intensities and different variations of amplitude and frequency are considered, ergodicity conditions and estimates of the rate of convergence are obtained for each model, and plots of the effect of intensities' amplitude and frequency of incoming requirements on the limiting characteristics of the process are constructed. The authors use 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.