A Traffic Overflow System With a Large Primary Queue

Abstract

We analyze a traffic overflow system that consists of two groups of trunks, with waiting spaces for each group, and some overflow capability from the primary to the secondary group. We consider the case in which the number of waiting spaces in the primary queue is large compared to the corresponding number in the secondary queue and to the number of trunks in the secondary group. The case of an infinite number of waiting spaces in the primary queue is also allowed. We contrast the approach presented with some previous approaches that are suitable when the number of waiting spaces in the primary queue is not comparatively large. As with previous approaches, the aim is to reduce the dimensions of the system of equations to be solved in order to calculate various steady-state quantities of interest. Our results include expressions for the loss probabilities, the probability of overflow from the primary to the secondary group, and the average waiting times in the queues. We also obtain the stability condition under which the results are valid when the number of waiting spaces in the primary queue is infinite.