IX International Workshop “ Applied Problems in Theory of Probabilities and Mathematical Statistics related to modeling of information systems ”

Consideration is given to long-term staffing problem in highlevel telecommunication service systems in which rates of processes that govern their behaviour depend on time. We assume that except for arrivals of requests and their respective service there happen periodic breakdowns when system drops all active requests. The staffing objective is “immediate service of a given percentage of incoming requests”. Such service systems typically have strongly time-varying arrivals and services. Noticing that a natural model for such an time-varying processes is an innhomogeneous birth-death process we propose some general theoretical results concerning its ergodicity conditions and limiting behaviour. As an example we show that if service system may be modelled by multiserver queue Mt/Mt/S with one input flow, periodic arrivals, services and breakdowns (catastrophes) rates which may depend on the state of the system, one can calculate (approximately) the quantities needed for the solution of optimization problem with specified accuracy.