Analysis of Some Overflow Problems with Queuing

In this paper, a particular overflow system with queuing is analyzed. The system consists of two groups, a primary and a secondary, with 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 H > 0. If all /12 servers in the secondary are busy when a demand from S2 arrives, the demand is queued if one of the q2 waiting spaces is available; otherwise, it is lost (blocked and cleared from the system). Demands waiting in the secondary queue enter service (in some prescribed order) as servers in the secondary become free. If all ?ii servers in the primary are busy when a demand from Si arrives and there is a free server in the secondary and no demands waiting in the secondary queue, the demand is served in the secondary. 1427 Fig. 1--Mean flow rates for an overflow system with queuing.