Independence Thresholds: Balancing Tractability and Practicality in Soft Real-Time Stochastic Analysis

The issue of stochastic response-time analysis is considered in the context of soft real-time multiprocessor schedulers. For such analysis to yield tractable, closed-form results, it is inevitably necessary to assume that execution times are probabilistically independent. However, stochastic dependencies among tasks are often common in actual systems. To enable closed-form analysis results to be applied to such systems, the concept of an independence threshold is introduced. Such a threshold is a "tunable" per-task parameter that can be adjusted to control the extent of dependency in task execution times as assumed in analysis, such thresholds can even be applied in settings where explicit dependencies exist among tasks through resource sharing. A method is presented for setting independence thresholds in which measured task execution times are subjected to known statistical independence tests. This method is applied in a case study involving MPEG decoding. In this case study, the usage of independence thresholds enabled up to a 3.5-fold reduction in provisioned task execution times compared to a worst-case provisioning without compromising analysis assumptions.