Finite bufferGI/Geo/1 batch servicing queue with multiple working vacations

Abstract

This paper analyzes a discrete-time finite buffer renewal input queue with multiple working vacations where services are performed in batches of maximum size “b ”. The service times both during a regular service period and vacation period and vacation times are geometrically distributed. Employing the supplementary variable and imbedded Markov chain techniques, we derive the steady-state queue length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. Based on the queue length distributions, some performance measures and waiting time distribution in the queue have been discussed. Finally, numerical results showing the effect of model parameters on the key performance measures are presented.