Truncation bounds for a class of inhomogeneous birth and death queueing models with additional transitions

The paper considers the computation of limiting characteristics for a class of inhomogeneous birth-death processes with possible transitions from and to origin. The authors study the general situation of the slower (nonexponential) decreasing of intensities of transitions from state $0$ to state $k$ as $k \to \infty$. The authors consider the situation of weak ergodicity and obtain bounds on the rate of convergence in weighted norm and, moreover, uniform in time bounds on the rate of approximations by truncated processes. The inhomogeneous $M/M/S$ queueing model with additional transitions is studied as an example.