Dependability of Distributed Programs: Algorithms and Performance

Summary

In this paper, we use task graph models to represent the behaviour of parallel programs. These models are characterized by execution times of the tasks, and by the precedence relation between the tasks. The latter can be represented by a probabilistic ordering, or can be provided with a specific known ordering for a given application. When failures occur in the processing system, we consider a recovery mechanism based on failure detection, and subsequent task restart. Both of these operations take additional processing times which are explicitly represented in the task graph characterization. Failures themselves are represented in the model by variable failure rates. We report on the design, analysis and simulation of novel algorithms which will ensure that application software runs correctly on an MIMD system in which processing units (PU) may fail. These algorithms are based on certain existing tasks which are selected within the program, which we call agents. Their role is to carry out failure detection and if necessary restart of other tasks, as soon as they have completed their own specific assigned work. The effect of these algorithms is evaluated using analytical approximations and simulation as a function of failure rates, and other system parameters. The comparison of the simulation results with the approximate analytical results, shows a very good level of accuracy for this degree of complexity, which indicates that simple analytical formulae can be used to obtain robust first-order estimates of program execution times with and without failures. We also provide specific examples of task graphs for two well known computations (matrix multiplication and the Fast Fourier Transform) and their parallel implementation. Finally we provide simulation results which evaluate the proposed failure detection and recovery algorithms for the specific case of the FFT algorithm.