The Transient Solution of an Unreliable M/G/1 Queue with Vacations

10.6186/IJIMS.2010.21.4.2

Indra；Bansal Sweety

Non-Markovian Queue ； Two-Dimensional Queueing Model ； Breakdown ； Repair ； Multiple Vacation ； Laplace Transform ； Supplementary Variable Technique ； Reliability

International Journal of Information and Management Sciences

21：4（2010 / 12 / 01）

391 - 406

英文

In this paper, we study two-dimensional time dependent probabilities of the server with some interesting particular cases for single server M/G/1 queuing model in which an unreliable server after completing the service goes on vacation with probability one when it finds no one waiting in the queue. The system when in operative state may fail due to server breakdowns and must be repaired before service can resume. Arriving customers are in poison stream. The servers' vacation times and breakdown times are having exponential distribution whereas the servers' service times and repair times are generally distributed. Explicit probabilities of exact number of arrivals & departures by a given time and, reliability and availability of the server, using supplementary variable technique and laplace transforms are derived. Number of units arrive by time t, number of units depart by time t, waiting time distribution, cumulative distribution for sojourn time, servers' breakdown time and servers' vacation time, reliability of the server are also presented numerically and graphically both.

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