Title: A study on M^X/G(a, b)/1 queue with server breakdown without interruption and controllable arrivals during multiple adaptive vacations

Authors: S. Jeyakumar; E. Rameshkumar

Addresses: Department of Mathematics, Government Arts College, Coimbatore – 641018, Tamilnadu, India ' Department of Mathematics, CMS College of Science and Commence, Coimbatore – 641049, Tamilnadu, India

Abstract: A single server model, after completion of a bulk service, if there is no breakdown with probability (1 − ψ) and queue length (queue) ≥ 'a', then the bulk service continues, otherwise, the server performs closedown work is analysed. At the end of bulk service, if there is a breakdown occurs with probability (ψ), then the server performs renovation process. After that, if the queue is ≥ 'a', then he performs bulk service otherwise the server perform closedown work follows a vacation. After that, if the queue is less than 'a', then he takes at most 'M' vacations successively. After 'M' vacations, if the queue is still less than 'a', then he remains in the system. However, the customers enter the service station with probability 'p' (0 ≤ p ≤ 1) during multiple adaptive vacations. The probability generating function (PGF) of queue size and performance measures are obtained and cost model is developed.

Keywords: multiple adaptive vacation; closedown times; server breakdown; renovation times; controllable arrival; queue; bulk service; supplementary variables; dormant period; probability generating function; PGF.

DOI: 10.1504/IJMOR.2019.101617

International Journal of Mathematics in Operational Research, 2019 Vol.15 No.2, pp.137 - 155

Received: 12 Dec 2016
Accepted: 08 Feb 2018
Published online: 16 Aug 2019 *

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