Analyzing discrete-time D-BMAP/G/1/N queue with single and multiple vacations |
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Authors: | S.K. Samanta U.C. Gupta R.K. Sharma |
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Affiliation: | 1. Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal 721 302, India;2. Department of Mathematics, Indian Institute of Technology, New Delhi 110 016, India |
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Abstract: | This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP). The service and vacation times are generally distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination, arbitrary, and prearrival epochs. The loss probabilities of the first-, an arbitrary- and the last-customer in a batch, and other performance measures along with numerical aspects have been discussed. The analysis of actual waiting time of these customers in an accepted batch is also carried out. |
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Keywords: | Discrete-time batch Markovian arrival process Finite-buffer Queueing Single vacation Multiple vacations |
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