多台并行随机CIMS可靠性的扩散估计界

DIFFUSION ESTIMATION BOUNDARY OF RELIABILITY OF STOCHASTIC CIMS WITH PARALLEL MULTI SERVER

ＣＩＭＳ可靠性模型随机研究的突出特点是工作站的并行结构使系统的状态个数呈现指数级增大，同时，并行结构与有限的缓冲库相互交织在一起，这使系统状态呈爆炸趋势．显然，对系统作精确的分析与系统呈现的状态爆炸趋势构成了难以解决的矛盾，如何解决这一矛盾正是ＣＩＭＳ随机理论有待开发的重要课题．我们把扩散近似方法引入到多台并行的ＣＩＭＳ可靠性模型中，以简单的连续过程描述了具有状态爆炸趋势的复杂离散过程．给出了ＣＩＭＳ的稳态可用度，稳态停工频度和稳态生产率的上下估计界．

An obvious character of mathematical model for studying reliability of stochastic CIMS is that the parallel structure of working stations makes the number of system states increase with exponential growth,and the parallel structure contains limited buffers. This makes system state have a tendency of explosion.Therefore,the exact analysis of the system is in contradiction with the tendency of explosion of the system,which is difficult to be solved.How to solve the problem is just the main topic that CIMS stochastic theory investigates. In the paper, we introduce a diffusion approximation method into the mathematical model of reliability of CIMS with parallel multi server,and describe complicated process with state explosive tendency of the system by employing a simple continuous process. We give some clear expressions of up estimation boundaries and down estimation boundaries for availability, downwork frequency and production rate of the repairable CIMS under steady state. Finally we give a numerical example to show that the estimation of boundaries is realized easily.