Multi-Path Bound for Parallel Tasks With Conditional Branches

Parallel execution and conditional execution are increasingly prevalent in modern embedded systems. In real-time scheduling, a fundamental problem is how to upper-bound the response times of a task. Recent work applied the multi-path technique to reduce the response time bound for tasks with parallel execution, but left tasks with conditional execution as an open problem. This paper focuses on upper-bounding response times for tasks with both parallel execution and conditional execution using the multi-path technique. By designing a delicate abstraction regarding the multiple paths of various conditional branches, we derive a new response time bound. We further apply this response time bound into the scheduling of multiple parallel tasks with conditional branches. Experiments demonstrate that the proposed bound significantly advances the state-of-the-art, reducing the response time bound by 9.4% and improving the schedulability by 31.2% on average.