二列模糊排队的主要指标求解的结构元方法

The structured element method for solving to the main indicators of two-server fuzzy queues

为研究顾客到达率和系统服务率均为模糊数的二列等待制排队模型,给出主要指标及其隶属函数的解析表示,在模糊分析的基础上,将模糊排队模型中主要指标的求解转化成了模糊多元函数的运算。通过模糊结构元表示方法,模糊多元函数的运算被转化成了[0,1]上多个同序单调函数的运算,避免了只利用a-截集的定义和Zadeh的扩展原理方法带来的运算困难,也给模糊多元函数的求解提供了途径。实例分析了二列模糊排队问题,其中,顾客的平均到达率和系统的平均服务率均用模糊结构元表示,求解出了顾客平均逗留时间及隶属函数,说明了方法的有效性。

This paper discusses the two-server waiting queues model and gives analytical expressions of the main indicators and their membership functions ,in which both the arrival rate of customers and the system service rate are fuzzy numbers. On the basis of fuzzy analysis,the solution to the main indicators of Fuzzy queuing model is turned into the multiple fuzzy arithmetic.By the expression based on structured element,the multiple fuzzy arithmetic is turned into the operation of multiple monotone functions with the same monotonic form on[0,1]. From this transition we avoid operation difficulties by using the definition of a -cut and Zadeh＇s extension principle and provide a means of solving of multiple fuzzy arithmetic. For instance,there is a 2-server fuzzy queues system,in which the average arrival rate and service rate are both regarded as fuzzy structuring element,the average staying time and its membership function is solved,which illustrates effectiveness of the approach.