Optimal control of an M/G/1 retrial queue with vacations

In this note,we consider an M/G/1 retrial queue with server vacations,when retrial times,service times and vacation times are arbitrary distributed.The distribution of the number of customers in the system in stationary regime is obtained in terms of generating function.Next,we give heavy traffic approximation of such distribution.We show that the system size can be decomposed into two random variables,one of which corresponds to the system size of the ordinary M/G/1 FIFO queue without vacation.Such a stochastic decomposition property is useful for the computation of performance measures of interest.Finally,we solve simple problems of optimal control of vacation and retrial policies.