The analysis of a queue arising in overflow models

A methodology is presented for analyzing a queuing submodel which frequently arises in the study of overflow models. In this submodel a finite capacity, multiserver queue with exponentially distributed service times, and arriving traffic consisting of a Poisson parcel and several overflow parcels, are assumed. By modeling the overflow parcels as interrupted Poisson processes, an exact queuing analysis is possible. The analysis yields the steady-state queue length distribution, and for each input parcel: (1) the steady-state queue length distribution at arrivals; (2) the probability that an arriving call is blocked (parcel blocking); and (3) the waiting time distribution of an arriving call, in addition to a complete characterization of the overflow due to each parcel