N-strategy Multi-adaptive Vacation M/g/1 Queuing System

In order to realize the conversion between busy period and leisure period, it usually needs some cost.It is generally believed that it is not wise to do the conversion frequently. Thus, to set a threshold value, N, to maximize the benefit is necessary. At the same time, the length of the vocation of a server depends on the process of customer'arrival and auxiliary work. In real life, there exists some queuing system conforming to both two situations. At present, many researchers have studied lots of models with single vacation, multiple vacation, N-policy and mixed vacations and calculated the index of queue length by using some methods. Therefore, this paper studies the model of N policy and multi-level adaptive vocation of M/G/1 queuing system.This paper use total probability decomposition technique, L- transformation and LS-transformation to analyze queue length in busy period, vacation and leisure period.Finally, we obtain the recursion formula of the steady-state queue length and the steady -state equal queue length.