Title: An M^[X]/G^{(1, K)}/1 queue with unreliable server and Bernoulli vacation

Authors: P. Nagarajan; R. Kalyanaraman

Addresses: Department of Mathematics, SCSVMV University, Enathur, Kanchipuram-631561, India ' Department of Mathematics, Annamalai University, Annamalai Nagar-608002, India

Abstract: A Poisson arrival queue with batch arrival, service in a batch of variable size with a minimum of '1' and a maximum of 'K' customers is considered. After completion of service to the customers the server takes on Bernoulli vacation, also during the service of customers the server may breakdown. The supplementary variable technique is applied. The probability generating function of number of customers in the queue at different server states, mean queue size, and probability of server being idle are obtained. Some particular models are deduced. The amenability of the numerical treatment of this study is carried out. The numerical results are given in the form of tables and figures.

Keywords: Poisson process; batch arrival; batch service; Bernoulli vacation; unreliable server; supplementary variable technique; operating characteristics.

DOI: 10.1504/IJMOR.2023.132836

International Journal of Mathematics in Operational Research, 2023 Vol.25 No.4, pp.492 - 510

Received: 25 Apr 2022
Accepted: 03 Jun 2022
Published online: 11 Aug 2023 *

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