Timing analysis of First-Come First-Served scheduled interval-timed Directed Acyclic Graphs

Abstract

Abstract-Analyzing worst-case application timing for systems with shared resources is difficult, especially when non-monotonic arbitration policies like First-Come-First-Served (FCFS) scheduling are used in combination with varying task execution times. Analysis methods that conservatively analyze these systems are often based on state-space exploration, which is not scalable due to its inherent susceptibility to combinatorial explosion.We propose a scalable timing analysis method on periodically restarted Directed Acyclic Task Graphs, that can provide conservative bounds on task timing properties when shared resources with FCFS scheduling are used. By expressing task enabling and completion times in intervals, denoting best-case and worst-case timing properties, contention on the shared resources can be estimated using conservative approximations.With an industrial case study we show that our approach can easily analyze models with thousands of tasks in less than 10 seconds, and the worst-case bounds obtained show an average improvement of 46% compared to bounds obtained by static worst-case analysis.

Temporal analysis flow based on an enabling rate characterization for multi-rate applications executed on mpsocs with non-starvation-free schedulers

“…The approach from [6] combines systems with First-Come First-Served (FCFS) schedulers with HSDF models. This approach considers a subclass of the systems we consider.…”

“…FCFS schedulers belong to the class of non-starvation-free which is supported by our method. Next to that, only acyclic graphs are considered while we also support cyclic graphs and, furthermore, pipelined schedules are not considered in [6] which means that the source can only be triggered when the previous result is produced.…”

“…The average rate at which tasks consume data should also be equal to the rate at which the source produces data. The average period of a task is equal to the period of its corresponding SDF actor and can be calculated with (6).…”

“…Furthermore, we use VH as the set of HSDF actors and EH as the set of edges in the HSDF graph. Each SDF actor va has an average period Pa as defined in Equation (6). Because the SDF actor is split in qa actors in the HSDF graph, on average, each of these actors have to fire once per qa • Pa, which is equal to qs • Ps (see Equation ( 6)).…”