This paper studies an M/G/1 queueing system with a finite waiting room and with server vacation times consisting of periods of time that the server is away from the queue doing additional work. Service at the queue is exhaustive, in that a busy period at the queue ends only when the queue is empty. At each termination of a busy period, the server takes an independent vacation. In the case that the system is still empty upon return from vacation the server waits for the first customer to arrive when an ordinary M/G/1 busy period starts. The queue length process is studied using the embedded Markov chain. Using a combination of the supplementary variable and sample biasing techniques, we derive the general queue length distribution of the time continuous process, as well as the blocking probability of the system, due to the finite waiting room in the queue. We also obtain the busy period and waiting time distributions. The results for this model are compared with the those for queueing system with vacation studied by Tony T. Lee, which has different vacation policy; if the server finds the system empty at the end of a vacation, he immediately takes another vacation.
본 논문에서는 휴가 규칙이 취급자가 휴가 시간을 마치고 왔을때 대기 체계가 비어있을경우 첫 번째 고객이 올 때까지 기다리는 대기체계에 관하여 연구하였으며, 특히 평형 상태하에 대기 체계에 있는 고객수의 확률 분포와 대기체계에 들어 갈수 없는 확률을 구하고 대기 체계에 도착해서 대기 체계를 떠날때까지 걸리는 시간의 확률 분포를 구하였다.
또한 Tony T. Lee가 연구한 다른 휴가 규칙(휴가 시간을 마치고 돌아온 취급자는 대기체계가 비어있을 경우 다시 휴가를 떠남)을 갖는 대기체계와 비교하였다.
