带有Bernoulli反馈的多级适应性休假的Geo/G/1排队系统分析

Analysis of Geo/G/1 queueing system with multiple adaptive vacations and Bernoulli feedback

考虑带有Bernoulli反馈的多级适应性休假的Geo/G/1离散时间排队系统.通过引入服务员忙期和使用一种简洁的分解方法,讨论了队长的瞬时分布,得到了在任意时刻n队长为j的概率关于时刻n的z-变换的递推式,及队长平稳分布的递推式,且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.

This paper considers a discrete-time Geo/G/1 queue with multiple adaptive vacations and Bernoulli feedback.By introducing the server busy period and using a concise decomposition method,the transient distribution of the queue length is studied.Both the recursion expression of the z-transform about epoch n of the probability that the queueing length equals to j at any epoch n and the recursion formulae of the stationary distribution for the queue length are obtained.The stochastic decomposition property of steady-state queue length has been proved.Finally,some corresponding results and numerical examples under special cases are also given.