Recursive solution of queue length distribution for Geo/G/1Geo/G/1 queue with single server vacation and variable input rate

In this paper we consider discrete time Geo/G/1Geo/G/1 queue with single server vacation and variable input rate. Using renewal process, probability decomposition technique and uu-transform, we derive the recursive expressions of the queue length distributions at epochs n−,n+n−,n+, and nn. The results obtained in this paper indicate that the equilibrium queue length distribution no longer follows the stochastic decomposition discipline. Furthermore we derive the important relations between equilibrium queue length distributions at different epochs (n−,n+,nn−,n+,n).