Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Simultaneity in discrete-time single server queues with Bernoulli inputs
Performance Evaluation
M/M/1 queues with working vacations (M/M/1/WV)
Performance Evaluation
The Discrete-Time GI/Geo/1 Queue with Multiple Vacations
Queueing Systems: Theory and Applications
Performance analysis of finite buffer discrete-time queue with bulk service
Computers and Operations Research
Vacation Models in Discrete Time
Queueing Systems: Theory and Applications
M/G/1 queue with multiple working vacations
Performance Evaluation
Discrete-time GI/Geo/1 queue with multiple working vacations
Queueing Systems: Theory and Applications
Algorithmic analysis of the discrete time GIX/GY/1 queueing system
Performance Evaluation
The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation
Performance Evaluation
On the relations among the distributions at different epochs for discrete-time GI/Geom/1 queues
Operations Research Letters
Analysis of a GI/M/1 queue with multiple working vacations
Operations Research Letters
Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B
Operations Research Letters
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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.