A mathematical model to describe resource discovery failure in distributed exascale computing systems

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.