On remaining full busy periods of GI/G/c queues and their relation to stationary point processes

Abstract

For a GI/G/c queue, a full busy period is a period commencing when an arrival finds c − 1 customers in the system and ending when, for the first time after that, a departure leaves behind c − 1 customers in the system. We show that given a full busy period is found to be in progress at a random epoch, the remaining full busy period has the equilibrium distribution. Moreover, we demonstrate that this property is typical for a broad class of stationary random processes.