The stochastic decomposition for M/G/1 queue with p-entering discipline during server vacations

This paper considers the M/G/1 queueing system with server vacations in which the customers who arrive during server vacations enter the system with probability p. By introducing the server busy period and using the Laplace or Laplace–Stieltjes transform, both the recursion expression of the Laplace transform of the transient distribution and the recursion expression of the equilibrium distribution for the queue length are obtained. Furthermore, the stochastic decomposition of the queue length at a random point in equilibrium and some corresponding results under special cases are also given.