摘要
本文研究了顾客批量到达且服务台忙时与闲时故障率不同的多服务台可修排队系统,推导出了系统的稳态平衡方程以及稳态概率值的求解思路。由于N≥2时手工计算的复杂性,使用Mathematica软件编程实现了稳态概率值的求取,并最终得到了系统有效服务台数的稳态分布、稳态队长的母函数以及平均队长等重要的系统指标。
This paper deals with the Mx/M/N queue system subject to breakdowns where the server lifetimes are different between busy period and idle period.We derive the balance-equation of the steady-state.Because of the complexity of calculating the steady probability for N ≥ 2,we program and derive the steady probability by using the Mathematica software.After getting the steady probability,some important queueing measures are obtained：the distribution of the effective servers;the moment generating function of the effective servers; the moment generating function of the steady-state queue length; and the mean value of the queue length.
出处
《工程数学学报》
CSCD
北大核心
2009年第6期1057-1061,共5页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(70571030)
关键词
可修排队
批量到达
稳态概率值
母函数
repairable queue
batch arrival
steady probability
moment generating function
