阈值调控的流体模型优化策略分析

Optimization strategies analysis of fluid model with threshold control

为实现阈值调控的流体排队模型中单位时间内社会收益的最优化,利用一阶常系数线性微分方程组的标准型理论,结合边界条件求解完全可视情况下该模型的稳态流体水平,并假设缓冲器在工作期和空闲期之间交替运行,进而使用指数型社会效用函数,分析了单位时间内社会收益与阈值N的关系,流出率μ对社会收益的影响,以及给定参数下单位时间内社会收益最优策略.研究结论既可以有效地避免系统拥堵和缓解服务台的工作压力,又能够给个体和决策者提供适当参考,使决策者最大限度地利用和维护系统.

To optimize the social benefits per unit time in the fluid queuing model with threshold control,the paper takes use of the standard theory for the first-order linear system of the ODEs with constant coefficients and compute the constant by the boundary conditions to solve the steady-state distribution of the fluid level in the fully observable case.Assuming that the buffer alternates between working and idle periods,using the exponential utility function to evaluate the relationship between the social benefits per unit time and the threshold N,and then the effect of the output rateμon the social optimal strategies per unit time are derived.The research conclusion can not only effectively avoid system congestion and relieve the pressure of the service,but also provide appropriate suggestions for individuals and decision makers to take full use of the system.