Steady state probabilities for the server vacation model with group arrivals and under control-operating policy

In this study, an efficient algorithm is developed to compute steady state probabilities for the following M^x/G/1 server vacation system under control-operating policy: At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time, and at the end of each vacation, inspects the length of the queue. If the queue length at this time is equal to or greater than a prespecified threshold value r, the server begins to serve the queue until it is empty. [In Korean.]