M~x/M/N可修排队系统

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.

M~x/M/N Repairable Queue System

This paper deals with the M~x/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 Mathematiea software. After getting the steady probability,some important queueing measures are obtained: the distribution of the effective servers; the moment generating function of the steady-state queue length; and the mean value of the queue length.