关键词: Server vacation, queue length, transient distribution, equilibrium distribution,
stochastic decomposition

Abstract:

This paper studies the bulk-arrival Mx/G/1 queue with single server vacation.
By introducing the server busy period and using the Laplace transform, the recursion
expression of the Laplace transform of the transient queue-length distribution is derived.
Furthermore, the distribution and stochastic decomposition result of the queue length at
a random point in equilibrium are obtained. Especially some results for the single-arrival
M/G/1 queue with single server vacation and bulk-arrival Mx/G/1 queue but with no
server vacation can be derived directly by the results obtained in this paper

Key words: Server vacation, queue length, transient distribution, equilibrium distribution,
stochastic decomposition