负顾客到达造成服务率变化的可修排队系统

为了解决由于在工作中操作失误引起机器服务速率减慢或是由于病毒入侵引起计算机速率减慢这一类问题,采用拟生灭过程和矩阵几何解的方法研究了具有正、负两类顾客服务速率可变的可修排队系统,其中负顾客到达带走正顾客的同时使服务速率减低.结果表明:负顾客到达率越高系统中平均等待的顾客数越少.给出了系统稳态平衡所需条件,推导出了系统稳态概率向量和系统的一些稳态排队和可靠性指标.最后给出了相关的数值实例为实际应用提供理论参考.

Repairable queuing system with customers service rate variation caused by negative customers

In order to solve the problems that operating errors result in the machine service rate to slow down or computer viruses cause the computer to slow the rate down,this study uses quasi-birth-and-death process and matrix-geometric solution method to investigate a repairable queuing system with a variable service rate for two kinds of customers:positive and negative.In the system,a negative customer’s arrival offsets a positive customer and makes the service rate variable.The results show that the average number of customers decreases as the arrival rate of negative customer increases.Concise expressions of the steady-state distribution are obtained and some queuing and reliability indexes are subsequently derived.A numerical example provides a theoretical reference for its practical application.