Analysis of single working vacation in GI/M/1/N and GI/M/1/∞ queueing systems

We consider a finite-buffer GI/M/1 queue with exhaustive service discipline and single working vacation. Service time in a vacation, in a service period and vacation time all are exponentially distributed random variables independent of each other. Queue length distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system, etc. have been obtained using the method of embedded Markov chain and supplementary variable. The corresponding infinite-buffer GI/M/1 queue with exhaustive service discipline and single working vacation has also been analysed. For this model, we also obtain pre-arrival and arbitrary epoch probability along with some important performance measures. These queueing models have potential application in the area of computer and communication network where a single channel is allotted for more than one type of job.