摘要
本文讨论了带启动时间和可变服务率的M/M/1休假排队.利用拟生灭过程与矩阵几何解方法导出了稳态队长和稳态等待时间分布.进一步,得到稳态指标的随机分解结果及附加队长和附加延迟的分布.最后,给出当启动率趋于无穷大时本文模型特例的性能指标的分析结果,以揭示本文模型应用的广泛性.
In this paper, we investigate an M/M/1 queue with single working vacation and setup times, using quasi birth and death process and matrix-geometric solution method to derive the distributions for the stationary queue length and waiting time of a customer in the system. Furthermore, we get stochastic decomposition structures of stationary indices, meanwhile, obtain the distributions of the additional queue length and additional delay. Finally, we give special cases when setup rate trends to infinity to explain its extensive applications.
出处
《应用数学学报》
CSCD
北大核心
2008年第4期692-701,共10页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(10671170)
燕山大学博士基金(B228)资助项目．
关键词
启动时间
工作休假
拟生灭过程
矩阵几何解
随机分解
setup times
vacation queue
QBD process
matrix-geometric solution
stochastic decomposition
