Traffic overflow in loss systems with selective trunk reservation

We consider two traffic streams competing for service at an n-server queuing system. Jobs from stream 1, the protected stream, are blocked only if all n servers are busy. Jobs from stream 2, the best effort stream, are blocked if n−r, r≥1, servers are busy. Blocked customers are diverted to a secondary group of c−n servers with, possibly, a different service rate. For the case r=1, we calculate the joint probabilities of the number of primary and secondary busy servers. For r>1, we describe a procedure for deriving the joint probabilities. These probabilities allow for the calculation of various performance measures including the overflow probabilities of the primary server and secondary server group. Our model is applicable to traffic control in communication networks that use the selective trunk reservation method.