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A MAP/PH/1 Queue with Setup Time, Bernoulli Schedule Vacation, Balking and Bernoulli Feedback

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Abstract

A classical model with the unique server, phase-type service distribution, inter-arrival times following the Markovian arrival process and other random variables are exponentially distributed is analyzed in this article. A single server that provides service may go on vacation at the end of each service and after the vacation period, the server undergoes the setup process. The unsatisfied customer may join the system to get the service again. The arriving customer may also balk at the system during the vacation period of the server. By using the matrix analytic method, the consequent QBD process is overlooked in the invariant circumstance. The investigation of the active period has also been accomplished. A range of system measures is listed. Finally, some graphical and numerical illustrations are presented.

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Notes

  1. These observations have been obtained after comparing the graphs of all possible combinations of arrival and service times only. Some diagrams are omitted due to page constraints.

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Acknowledgements

The authors are thankful to the Editor of the journal and the anonymous referees for their valuable suggestions for improving the standard of the article.

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This study was not funded by any agency.

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  1. Department of Mathematics, Pondicherry Engineering College, Pondicherry, Puducherry, India

    G. Ayyappan & R. Gowthami

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  1. G. Ayyappan
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  2. R. Gowthami
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The analytical results have been derived by both GA and RG and the numerical computation has been carried out by RG.

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Ayyappan, G., Gowthami, R. A MAP/PH/1 Queue with Setup Time, Bernoulli Schedule Vacation, Balking and Bernoulli Feedback. Int. J. Appl. Comput. Math 8, 62 (2022). https://doi.org/10.1007/s40819-022-01260-1

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