Uniform In Time Bounds For "No-Wait" Probability In Queues Of Mt/Mt/S Type

In this paper we present new analytical results concerning long-term staffing problem in high-level telecommunication service systems. We assume that a service system can be modelled either by a classic Mt/Mt/S queue, or Mt/Mt/S queue with batch service or Mt/Mt/S with catastrophes and batch arrivals when empty. The question under consideration is: how many servers guarantee that in the long run the probability of zero delay in a queue is higher than the target probability at all times? Here the methodology is presented, which allows one to construct uniform in time upper bound for the value of S in each of the three cases and does not require the calculation of the limiting distribution. These upper bounds can be easily computed and are accurate enough whenever the arrival intensity is low, but become rougher as the arrival intensity is further increased. In the numerical section one compares the accuracy of the obtained bounds with the exact vales of S , obtained by direct numerical computation of the limiting distribution.