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Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP\(^{\text {(a,b)}}/1/\infty \) Queueing System

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Abstract

This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions at other various time epochs are also derived based on prearrival epoch probabilities. A simple approach has been developed to compute the waiting-time distribution of an arriving customer. We also carried out closed-form analytical expression for the service batch size distribution of an arriving customer. Some numerical results are provided in the form of tables for a variety of interarrival-time distributions and model parameters to understand the system behaviour.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper. The first author acknowledges the Council of Scientific and Industrial Research (CSIR), New Delhi, India, for partial support from the project grant 25(0271)/17/EMR-II.

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  1. Department of Mathematics, National Institute of Technology Raipur, Raipur, -492010, India

    S. K. Samanta & R. Nandi

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  1. S. K. Samanta
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  2. R. Nandi
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Correspondence to S. K. Samanta.

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Samanta, S.K., Nandi, R. Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP\(^{\text {(a,b)}}/1/\infty \) Queueing System. Methodol Comput Appl Probab 23, 1461–1488 (2021). https://doi.org/10.1007/s11009-020-09823-9

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