The Queue Length Distribution of $M^X/G/1$ with Adaptive Multistage Vacation
多级适应性休假$M^X/G/1$排队系统的队长分布

In the paper, the bulk-arrival $M^X/G/1$ queue with adaptive multistage vacation is studied. By using a simple method, the recursion expression of the Laplace transform of the transient queue-length distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Furthermore, the distribution of the server idle period and the circular server busy period are obtained. Especially, some corresponding results for some special queueing systems can be derived directly by the results obtained in this paper.