In time-triggered systems, where the schedule table is predefined and
statically configured at design time, sporadic event-triggered (ET) tasks can
only be handled within specially dedicated slots or when time-triggered (TT)
tasks finish their execution early. We introduce a new paradigm for
synthesizing TT schedules that guarantee the correct temporal behavior of TT
tasks and the schedulability of sporadic ET tasks with arbitrary deadlines. The
approach first expresses a constraint for the TT task schedule in the form of a
maximal affine envelope that guarantees that as long as the schedule generation
respects this envelope, all sporadic ET tasks meet their deadline. The second
step consists of modeling this envelope as a burst limiting constraint and
building the TT schedule via simulating a modified Least-Laxity-First (LLF)
scheduler. Using this novel technique, we show that we achieve equal or better
schedulability and a faster schedule generation for most use-cases compared to
other approaches inspired by, e.g., hierarchical scheduling. Moreover, we
present an extension to our method that finds the most favourable schedule for
TT tasks with respect to ET schedulability, thus increasing the probability of
the computed TT schedule remaining feasible when ET tasks are later added or
changed