Some results for inhomogeneous birth-and-death process with application to staffing problem in telecommunication service systems

This paper proposes some analytical results that may facilitate long-term staffing problem in high-level telecommunication service systems (such as information call centers) in which rates of processes, that govern their behaviour, depend on time. We assume that except for arrivals of requests and their service there happen periodic system breakdowns (possibly with very long inter-breakdown periods). The staffing objective is “immediate service of a given percentage of incoming requests”. A natural model for such a time-varying processes is an innhomogeneous birth-death process for which we propose some general theoretical results concerning its ergodicity conditions and limiting behaviour. As an example we show that if the service system is modelled by multiserver queue Mt/Mt/S with state-dependent periodic arrivals, services and breakdown rates, then using obtained results one can calculate the quantities needed for the solution of optimization problem. Accuracy of approximation is briefly discussed.