关键词: 服务员假期;p进入规则;队长;瞬态分布;稳态分布;随机分解

Abstract:

This paper considers the M/G/1 queueing system with server vacations in whi ch the customers who arrive during server vacations enter the system with probab ility  p(0≤p≤1). By introducing the server busy period and using the Lapla ce or Laplace Stieltjes transform, both the recursion expression of the Laplace  transform of the transient distribution and the recursion expression of the equ ilibrium distribution for the queue length are obtained. Furthermore, the stocha s tic decomposition of the queue length at a random point in equilibrium and some  corresponding results under special cases are also given.

Key words: Server vacation, p entering discipline, Queue length, Transient distribution, Equilibrium distribution, Stochastic decomposition