Analysis of discrete-time batch service renewal input queue with multiple working vacations |
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Authors: | V. Goswami G.B. Mund |
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Affiliation: | aSchool of Computer Application, KIIT University, Bhubaneswar 751 024, India;bSchool of Computer Engineering, KIIT University, Bhubaneswar 751 024, India |
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Abstract: | This paper investigates a discrete-time single server batch service queue with multiple working vacations wherein arrivals occur according to a discrete-time renewal process. The server works with a different service rate rather than completely stopping during the vacation period. The service is performed in batches and the server takes a vacation when the system does not have any waiting customers at a service completion epoch or a vacation completion epoch. We present a recursive method, using the supplementary variable technique to obtain the steady-state queue-length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. The displacement operator method is used to solve simultaneous non-homogeneous difference equations. Some performance measures and waiting-time distribution in the system have also been discussed. Finally, numerical results showing the effect of model parameters on key performance measures are presented. |
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Keywords: | Discrete-time Multiple working vacations Batch service Supplementary variable Waiting-time |
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