Talk Mario Günzel, MPI, "The Shape of Time: Analyzing End-to-End Latency Curves in Cyber-Physical Systems"

In safety-critical cyber-physical systems (such as autonomous driving pipelines) functionalities are often organized into so-called cause-effect chains.
That is, a sequence of periodically activated tasks pass data from sensing to actuation.
One fundamental question is: Given an external stimulus at time $t$, then how long does it take to react to that stimulus?
In the literature, this timing behavior is formalized as Reaction Time $RT(t)$.

In this talk, the mathematical structure of this function under the well-established Logical Execution Time (LET) communication model is studied.
One main observation is that $RT$ is piece-wise linear decreasing with jumps up in-between, giving the function a sawtooth-like shape.
We demonstrate that it is possible to fully characterize $RT$ by an often times very small set of anchor points (i.e., the local maxima).
Afterwards, we study how to derive these anchor points efficiently using partitioned job chains, which are built traversing the task graph from an intermediate task in both a forward and a backward manner.

The payoff of having the full shape is that this allows analyzing a rich portfolio of timing metrics directly from the anchor points:
minimum, maximum, and average reaction time, throughput, weakly-hard constraints and longest consecutive exceedance intervals.
For most of these metrics, this is the first analysis in the context of the LET communication model.