摘要
考虑带启动时间的N-策略M/G/1排队系统,从任意初始状态出发,直接研究了系统队长的瞬态分布和稳态分布.通过引进的"服务员忙期",使用全概率分解技术和拉普拉斯变换,导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式,进一步获得了有重要应用价值的稳态分布的具体的递推式子,以及稳态队长的随机分解结果.特别地,还直接获得了一些特殊排队系统的更实用的稳态队长分布的递推表达式.
This paper considered the M/G/1 queue with N-policy and set-up times,and directly studied both the transient distribution and equilibrium distribution of the queue length.By introducing the server busy period,and using the total probability decomposition technique and Laplace transform,the recursion expressions of the Laplace transform of the transient queue length distribution at any time t are obtained. Furthermore,the recursion expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium are also obtained,which have important value on application.Especially, some corresponding results which have more really value in some special queueing models are obtained directly.
出处
《系统工程理论与实践》
EI
CSSCI
CSCD
北大核心
2011年第1期131-137,共7页
Systems Engineering-Theory & Practice
基金
国家自然科学基金(70871084)
教育部高校博士点专项研究基金(200806360001)
关键词
N-策略排队
启动时间
队长分布
随机分解
全概率分解技术
N-policy queue
set-up
queue length distribution
stochastic decomposition
total probability decomposition technique
