An Overflow System in Which Queuing Takes Precedence

In this paper a particular overflow system with queuing is analyzed. The system consists of two groups, a primary and a secondary, with nk servers and qk waiting spaces, which receive demands from independent Poisson sources Sk with arrival rates A* > 0, k = 1 and 2, respectively, as depicted in Fig. 1. The service times of the demands are independent, and exponentially distributed with mean service rate /i, > 0. If all n2 servers in the secondary are busy when a demand from S2 arrives, the demand is queued if one of the q2 waiting spaces is In Memoriam: Joanne B. Fry, Associate Editor of The Bell System Technical Journal since 1978, died in an automobile accident January 2, 1981.