Queueing systems with vacations—a survey
Queueing Systems: Theory and Applications
Stochastic models in queueing theory
Stochastic models in queueing theory
On the additional delay in an M/G/1 queue with generalized vacations and exhaustive service
Operations Research - Supplement to Operations Research: stochastic processes
Markovian bulk service queue with delayed vacations
Computers and Operations Research
Analysis of a bulk queue with N-policy multiple vacations and setup times
Computers and Operations Research
On the batch arrival batch service queue with finite buffer under server's vacation: MX/GY/1/N queue
Computers & Mathematics with Applications
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Numerical investigation of finite-source multiserver systems with different vacation policies
Journal of Computational and Applied Mathematics
A batch-service queueing model with a discrete batch Markovian arrival process
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Tail distribution of the delay in a general batch-service queueing model
Computers and Operations Research
Analysis of a versatile batch-service queueing model with correlation in the arrival process
Performance Evaluation
Computers and Operations Research
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This paper deals with an M/G/1 batch service queue where customers are served in batches of maximum size b with a minimum threshold value a. The server takes a single vacation when he finds less than a customers after the service completion. The vacation time of the server is arbitrarily distributed. Using the supplementary variable method we obtain the probability generating functions of the queue length distributions at various epochs. We also obtain relations among queue length distributions at arbitrary, service (vacation) termination epochs. Further their evaluation is also discussed. Finally, some numerical results and graphs are presented.