On the correctness, optimality and precision of Static Probabilistic Timing Analysis

In this paper, we investigate Static Probabilistic Timing Analysis (SPTA) for single processor systems that use a cache with an evict-on-miss random replacement policy. We show that previously published formulae for the probability of a cache hit can produce results that are optimistic and unsound when used to compute probabilistic Worst-Case Execution Time (pWCET) distributions. We investigate the correctness, optimality, and precision of different approaches to SPTA. We prove that one of the previously published formulae for the probability of a cache hit is optimal with respect to the limited information that it uses. We improve upon this formulation by using extra information about cache contention. To investigate the precision of various approaches to SPTA, we introduce a simple exhaustive method that computes a precise pWCET distribution, albeit at the cost of exponential complexity. Further, we integrate this precise approach, applied to small numbers of frequently accessed memory blocks, with imprecise analysis of other memory blocks, to form a combined approach that improves precision, without significantly increasing its complexity. The performance of the various approaches are compared on benchmark programs.