Analysis of discrete-time batch service renewal input queue with multiple working vacations

作者：Goswami V^*; Mund G B

来源：Computers & Industrial Engineering, 2011, 61(3): 629-636.

DOI：10.1016/j.cie.2011.04.018

• Discrete-time
• Multiple working vacations
• Batch service
• Supplementary variable
• Waiting-time

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.

• 出版日期2011-10