A queueing system with two arrival streams and reserved servers with application to cellular telephone

The authors consider a service system in which n servers render service to two classes of prioritized traffic, which arrive to the system according to independent Poisson processes. Newly arriving call requests are granted server access on a first-come-first-served (FCFS) basis as long as there are fewer than g servers occupied. If fewer than g servers are free at the arrival time of a lower priority customer, the higher priority call requests are granted immediate service unless all servers are busy, in which case the call is dropped. This model has been used to study the handoff problem in a cellular telephone system, but the analytic approach taken was very complicated. The authors present a simple, novel, alternative approach to solving for the equilibrium probabilities for the number of lower priority calls in the queue and other quantities of interest. They describe two additional alternative approaches based on Neuts´ matrix analytic approach for checking results, and point out that while the results of all these approaches agree with each other, they differ from previously published results. Because these three approaches are essentially independent, it is conjectured that there are problems with the earlier numerical results. Further work has revealed that this is the case