A mutual overflow system with simultaneous occupation of resources

In this paper, we consider a special mutual overflow system for the analysis of RTNR (Real Time Network Routing) dynamic routing networks. The system has three multiserver service facilities and no waiting room is available. The first-offered traffic to a facility is generated to form an independently and identically distributed Poisson process. If all the servers of a facility are busy, blocking occurs. Blocked customer overflows to the other facilities and service is required from both of the rest facilities simultaneously. If the service can be provided immediately, then two servers that belong to their respective facility are assigned to the customer and start or finish service at the same time. Otherwise, the overflows will be cleared from the system. For such a system, we describe an algorithm to compute exactly the joint state probabilities by considering the server reservation for first-offered traffic. Following this result, we give a series of steady-state performance measures including blocking probability, carried traffic, utilization of facilities and so on. Numerical examples will also be discussed for understanding of the behavior of load balance mechanism in such a system and to show the effectiveness of the presented performance evaluation method.