Bounding the Rate of Convergence for One Class of Finite Capacity Time Varying Markov Queues

Consideration is given to the two finite capacity time varying Markov queues: the analogue of the well-known time varying M/M/S/0 queue with S servers each working at rate, no waiting line, but with the arrivals happening at rate only in batches of size 2; the analogue of another well-known time varying queue, but with the server, providing service at rate if and only if there are at least 2 customers in the system, and with the arrivals happening only in batches of size 2. The functions and are assumed to be non-random non-negative analytic functions of t. The new approach for the computation of the upper bound for the rate of convergence is proposed. It is based on the differential inequalities for the reduced forward Kolmogorov system of differential equations. Feasibility of the approach is demonstrated by the numerical example. © 2020, Springer Nature Switzerland AG.