초록
In this paper we consider an M/G/1 queueing system with vacation. The length of vacation period may be controlled by the waiting time of the first customer. The server goes on vacation as soon as the system is empty, and resumes service either when the waiting time of the leading customer reaches a predetermined value, or when the vacation period is expired, whichever comes first. We consider two types of vacation, say, multiple vacation type and N-policy type. We derive the steady-state distributions of the number of customers at arbitrary time and arbitrary customer's waiting time by means of decomposition property. Also, the mean lengths of busy period, idle period and a cycle time are given.
