Abstract
This paper deals with a finite-buffer renewal input queueing system, where the arrivals occur in batches of random size and the server serves the customers singly. The successive service times are correlated and its representation is expressed through the continuous-time Markovian service process (C-MSP). As the buffer capacity is finite, the partial batch rejection policy and the total batch rejection policy are considered in this paper. The blocking probabilities and mean waiting time of the first, last, and an arbitrary customer of a batch are determined using the steady-state system-length distribution at pre-arrival epoch. Further, the probability of k or more consecutive customer loss (i.e., k-CCL) during a busy period is computed. The results are illustrated by some tables and graphs for different inter-batch-arrival distributions as well as different C-MSP representations.
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The third author was supported partially by NSERC under research grant number RGPIN-2014-06604.
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Banik, A.D., Ghosh, S., Chaudhry, M.L. (2019). On the Consecutive Customer Loss Probabilities in a Finite-Buffer Renewal Batch Input Queue with Different Batch Acceptance/Rejection Strategies Under Non-renewal Service. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 816. Springer, Singapore. https://doi.org/10.1007/978-981-13-1592-3_4
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