Abstract
AbstractIn the present study, we examine server breakdown, single working vacation, and catastrophic in M/M/1 queueing model with two different service rates have been considered. Service while the vacation epoch, normal working epoch together with vacation epoch are all exponentially assigned. If the queue length increases, service rate changes from slow rate to normal rate. According to the Poisson process, a catastrophe event with parameter \(\xi\) occurs only if there is a customer in the queue. Also, in this study, server may subject to sudden breakdown, and after, it should be repaired and goes to normal service. This queue model has been analyzed with the help of matrix geometric method (MGM) to find steady-state probability vectors. Using it some performance measure is also determined.KeywordsServer breakdownWorking vacation (WV)Single working vacation (SWV)CatastrophicStability conditionMatrix geometric method (MGM)AMS 2000 Classification Code60K2560K3090B22
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