An Element of the Performance Analysis of Path Finder and Courtesy Queuing: The Analysis of a Queue Arising in Overflow Models.

In this memorandum, we present the analysis of a queueing model which is central to the Path Finder/Courtesy Queueing performance model, and which frequently arises in the study of overflow models - a finite capacity, multiserver queue with exponentially distributed service times and arriving traffic consisting of a Poisson parcel and several overflow parcels. By modeling the overflow parcels as interrupted Poisson processes, and assuming that all incoming parcels are independent, an exact queueing analysis is possible. The analysis yield (i) the ready-state queue length distribution, and, for each input parcel, (ii) the steady-state queue length distribution as seen by arrivals in that parcel, (iii) the probability that an arriving call is blocked (parcel blocking), and (iv) the waiting time distribution of an arriving call, in addition to a complete characterization of the overflow due to each parcel.