Transient solution for queue-length distribution of Geometry/G/1 queueing model

Abstract

In this paper, the Geometry/G/1 queueing model with inter-arrival times generated by a geometric(parameter p) distribution according to a late arrival system with delayed access and service times independently distributed with distribution {gj}, j ≥ 1 is studied. By a simple method (techniques of probability decomposition, renewal process theory) that is different from the techniques used by Hunter (1983), the transient property of the queue with initial state i(i ≥ 0) is discussed. The recursion expression for u-transform of transient queue-length distribution at any time point n+ is obtained, and the recursion expression of the limiting queue length distribution is also obtained.