Some Traffic Overflow Problems with a Large Secondary Queue

In an earlier paper, 1 we analyzed a traffic overflow system with queuing. 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 S* 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 li > 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 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. 1463 Fig. 1--Mean flow rates for an overflow system with queuing.