Analysis of some overflow problems with queuing

When calls offered to a primary group of trunks find all of them busy, provisions are often made for these calls to overflow to other groups of trunks. Such traffic overflow systems have been of interest for a long time, but recently overflow systems that allow for some calls to be queued have been of importance. In this paper we analyze a traffic overflow system with queuing. The system consists of two groups, a primary and a secondary. We consider two cases which differ in the treatment of demands waiting in the primary queue. We adopt a novel analytical approach, which considerably reduces the dimensions of the problem and simplifies the calculation of various steady-state quantities of interest. Our theoretical results include expressions for the loss probabilities, the probability of overflow from the primary to the secondary, and the average waiting times in the queues.