Analysis of queue with -entering discipline during adaptive multistage vacations

This paper studies the M X / G / 1 queue with adaptive multistage server vacations in which the customers who arrive during server vacations enter the system with probability p ( 0 ≤ p ≤ 1 ) . Using a simple method, the recursive formulae of the transient queue-length distribution and the equilibrium queue-length distribution are obtained. Furthermore, the distributions of the server idle period and the server circular busy period are also discussed.