An $M/G/1$ Retrial Queue with Multiple Working Vacation

Abstract

We consider an $M/G/1$ retrial queue with general retrial times and multiple working vacation. During the working vacation period, customers can be served at a lower rate. Both service times in a vacation period and in a service period are generally distributed random variables. Using supplementary variable method we obtain the probability generating function for the number of customers and the average number of customers in the orbit. Further more, we carry out the waiting time distribution and some special cases of interest are discussed. Finally, some numerical results are presented.