Abstract
This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be dependent on the batch-size and follows a general bulk service rule. The inter-arrival times of batches are assumed to be correlated and they are represented through the batch Markovian arrival process (BMAP). Computation procedure of the queue-length distributions at the post-batch-service completion, an arbitrary, and the pre-batch-arrival epochs are discussed. Various performance measures along with the consecutive customer loss probabilities are studied considering batch-size-dependent renewal service time distributions. Further, the above finite-buffer bulk-service queueing model is also investigated considering correlated batch-service times which are presented through the Markovian service process (MSP). The phase-dependent consecutive loss probabilities for the correlated batch-service times are determined. In the form of tables and graphs, a variety of numerical results for different batch-service time distributions are presented in this paper.
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Acknowledgements
The authors are thankful to the reviewers for their valuable comments which have led to significant improvements of the paper. The first author is partially supported by the Israeli Science Foundation (Grant No. 1571/19).
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A part of this research work was presented in the 51st Annual Convention of ORSI and International Conference (ORSI-2018) in Mumbai hosted by the ORSI-Mumbai Chapter and IIT Bombay as “A Brief Note on Analytical Aspects and Consecutive Losses in Finite-buffer Queues under Batch-size-dependent/Non-renewal Bulk-service and Batch Markovian Arrival Process”
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Ghosh, S., Banik, A.D., Walraevens, J. et al. A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service. 4OR-Q J Oper Res 20, 241–272 (2022). https://doi.org/10.1007/s10288-021-00478-x
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DOI: https://doi.org/10.1007/s10288-021-00478-x
Keywords
- Finite-buffer queue
- Batch Markovian arrival process (BMAP)
- Markovian service process (MSP)
- Batch-size-dependent bulk service
- Performance measures
- Consecutive customer loss (CCL)