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

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

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Article ID: iaor20114755
Volume: 61
Issue: 9
Start Page Number: 2401
End Page Number: 2411
Publication Date: May 2011
Journal: Computers and Mathematics with Applications
Authors: , , ,
Keywords: Geo/G/1 queues, vacation models
Abstract:

In this paper we consider discrete time Geo/G/1 queue with single server vacation and variable input rate. Using renewal process, probability decomposition technique and u‐transform, we derive the recursive expressions of the queue length distributions at epochs n-,n+, and n. 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+, n).

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