Transient analysis of an M/M/1 queue with a repairable server and multiple vacations. (1st January 2014)

• Record Type: Journal Article
• Authors: Kalidass, K.; Gnanaraj, J.; Gopinath, S.; Kasturi, Ramanath
• Is Part Of: International journal of mathematics in operational research. Volume 6:Number 2(2014)
• Page Start: 193
• Page End: 216
• Publication Date: 2014-01-01
• Subjects: Markovian queue -- time dependent analysis -- multiple vacations -- a repairable server -- busy period analysis; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

Abstract

In this paper, we discuss the time dependent behaviour of an M / M /1 queueing system with multiple vacations. We assume that the system is subject to sudden breakdowns and that during this period the system is flushed out. After the repair, the server waits for the arrival of the next customer. We have obtained analytical expressions for the transient state probabilities of the system size. We also obtain expressions for the transient expected value and variance of the system length. The corresponding steady state results are derived. We have performed a busy period analysis of this system in the steady state. We have obtained analytical expressions for the expected duration of a busy period and the expected duration of the vacation period. We present numerical examples to illustrate the sensitivity of the performance measures of the system to the changes in the parameters of the system.