Abstract
This paper investigates a single server batch arrival and batch service queueing model with infinite waiting space. The inter-occurrence time of arrival batches with random size is distributed arbitrarily. Customers are served using the discrete-time Markovian service process in accordance with the general bulk-service rule. We compute the prearrival epoch probability vectors using the UL-type RG-factorization method based on censoring technique. The random epoch probability vectors are then obtained using the Markov renewal theory based on the prearrival epoch probability vectors. We derive analytically simple expressions for the outside observer’s, intermediate, and post-departure epochs probability vectors by evolving the relationships among them. Determining the probability mass functions of the waiting time distribution and the service batch size distribution for an arbitrary customer in an arriving batch is the most challenging aspect of this work. Finally, we discuss computational experience for the purpose of validating the analytical results presented in this paper.
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13 July 2023
A Correction to this paper has been published: https://doi.org/10.1007/s00186-023-00829-w
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Acknowledgements
The authors would like to acknowledge the anonymous reviewers and editors for their insightful comments and suggestions to improve the quality of this manuscript. The first author acknowledges the University Grant Commission (UGC), New Delhi, India for financial support from the Junior Research Fellowship (JRF) scheme.
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Das, K., Samanta, S.K. Computational analysis of \(GI^{[X]}/D\)-\(MSP^{(a,b)}/1\) queueing system via RG-factorization. Math Meth Oper Res 98, 1–39 (2023). https://doi.org/10.1007/s00186-023-00816-1
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DOI: https://doi.org/10.1007/s00186-023-00816-1
Keywords
- Batch renewal
- Discrete-time Markovian service process (D-MSP)
- General bulk service rule
- RG-factorization method
- Queueing
- Waiting time distribution