A study on MX/G(a, b)/1 queue with server breakdown without interruption and controllable arrivals during multiple adaptive vacations. (5th August 2019)

• Record Type: Journal Article
• Authors: Jeyakumar, S.; Rameshkumar, E.
• Is Part Of: International journal of mathematics in operational research. Volume 15:Number 2(2019)
• Page Start: 137
• Page End: 155
• Publication Date: 2019-08-05
• Subjects: multiple adaptive vacation -- closedown times -- server breakdown -- renovation times -- controllable arrival -- queue -- bulk service -- supplementary variables -- dormant period -- probability generating function -- PGF; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

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.