Analysis of MX/G/1MX/G/1 queue with pp-entering discipline during adaptive multistage vacations

This paper studies the MX/G/1MX/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.