End-To-End Latency of Cause-Effect Chains: A Tutorial

In many applications of cyber-physical systems, a sequence of tasks is necessary to perform a certain functionality. For example, from a sensor to an actuator, the first task reads the sensor value (cause), the second task processes the data, and the third task produces an output for the actuator (an effect is triggered). For such scenarios, the end-to-end timing properties (the so-called end-to-end latency) of the sequence of tasks (the so-called cause-effect chain) are of importance. This tutorial recaps different metrics for the end-to-end latency of cause-effect chains, and summarizes fundamental properties and existing analytical results in a systematic manner. To that end, this tutorial has a special focus on the reaction time (how fast can a reaction be in the worst case) and the data age (how old is the data source of an actuation in the worst case). The goal of this tutorial is to provide a systematic view of the fundamental end-to-end timing properties of cause-effect chains and offer an outlook of possible research directions in the near future. Furthermore, we extend the proof of one fundamental property in the literature to comply with the current state-of-the-art definition of end-to-end latencies.