In this paper, a mathematical model is presented to identify the impacts of events with dynamic and interactive nature on the functionality of resource discovery. This mathematical model can recognize those events with the dynamic and interactive nature having an impact on the functionality of resource discovery and thus failure of resource discovery. To extract the mathematical model by which to recognize the failure of resource discovery due to the occurrence of events with the dynamic and interactive nature, a mathematical function that describes the functionality of resource discovery should be determined. To this end, in addition to the description of this function in traditional computing systems, a function describing the functionality of resource discovery is redefined based on the events with dynamic and interactive nature. The functionality of resource discovery during the occurrence of events with the dynamic and interactive nature as well as different ways for the failure of resource discovery due to the impacts of the dynamic and interactive events in distributed exascale computing systems are examined. Determining the type of failure and describing the cause of failure, as well as recognizing an event with the dynamic and interactive nature that leads to failure of resource discovery helps the resource management to prevent failure of resource discovery by changing those features that may cause the failure of resource discovery. The obtained mathematical model is analyzed in two frameworks named PMamut and Cactus. The capability of each framework to recognize events with dynamic and interactive nature based on the usage of the mathematical model are examined. Overall, the model can recognize 52 to 75% of the events that cause a failure of resource discovery.

在本文中，提出了一个数学模型来识别具有动态和交互性质的事件对资源发现功能的影响。该数学模型可以识别具有动态和交互性质的事件，这些事件会影响资源发现的功能，从而影响资源发现的失败。为了提取数学模型以识别由于具有动态和交互性质的事件的发生而导致的资源发现失败，应该确定描述资源发现功能的数学函数。为此，除了在传统计算系统中对该功能的描述之外，还基于具有动态和交互性质的事件来重新定义描述资源发现的功能的功能。研究了事件发生期间具有动态和交互性质的资源发现的功能，以及由于分布式百亿亿次计算系统中的动态和交互事件的影响而导致资源发现失败的不同方式。确定故障的类型并描述故障的原因，以及识别导致资源发现失败的具有动态和交互性质的事件，有助于资源管理通过更改可能导致故障的那些特征来防止资源发现失败资源发现。在名为PMamut和Cactus的两个框架中分析获得的数学模型。检验了每个框架基于数学模型的使用来识别具有动态和交互性质的事件的能力。