G/M/1 queue with server hyperexponential vacation

Abstract

In this paper, we consider the G/M/1 queue with multiple vacation and exhaustive service discipline where the vacation time has n stages hyperexponential distribution. For this model, By using the methods of the shift operater and supplementary variable, we obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously. In addition, we show that our results for n=1 reduce to the corresponding known results obtained by imbedded Markob chain approach.