Determination of an optimal retry time in multiple-module computing systems

The optimal amount of time used for retrying an instruction on detection of an error in a computing system is usually determined under the assumption that the system is composed of a single module, within which all fault activities are confined until some module-replacement action is taken. The authors consider fault activities in multiple-module systems. They first relax the single-module assumption and model the fault activities in a multiple-module system as a Markov process. The randomization approach is applied to decompose the Markov process into a discrete-time Markov chain subordinated to a Poisson process. Using this decomposition, several interesting measures can be derived such as the conditional probability of successful retry given a retry period and the fact that a non-permanent fault has occurred, and the mean time until which all modules in the system enter a fault-free state. All the measures derived are used to determine, along with the parameters characterizing fault activities and costs of recovery techniques, whether or not retry should be used as a first-step recovery means on detection of an error; and the best retry period subject to a specific probability of successful retry