  In time-triggered systems, where the schedule table is predefined and
statically configured at design time, sporadic event-triggered (ET) tasks are
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
simple polling approaches. 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.
