The Misconception of Exponential Tail Upper-Bounding in Probabilistic Real Time

Abstract

Measurement-based probabilistic timing analysis, a probabilistic real-time computing method, is based on the extreme value theory (EVT), a statistical theory applied to worstcase execution time (WCET) analysis on real-time embedded systems. The output of the EVT theory is a statistical distribution, in the form of generalized extreme value distribution or generalized Pareto distribution. Their cumulative distribution function can asymptotically assume one of the three possible forms: 1) light; 2) exponential; or 3) heavy tail. Recently, several works proposed to upper-bound the light-tail distributions with their exponential version. In this letter, we show that this assumption is valid only under certain conditions and that it is often misinterpreted. This leads to unsafe estimations of the WCET, which cannot be accepted in applications targeting safety critical embedded systems.