Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

Abstract

This paper considers the Geom / G / 1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state N(0+) = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n+ and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n−, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M / G / 1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network.