Simple and General Methods for Fixed-Priority Schedulability in Optimization Problems

This paper presents a set of sufficient-only, but accurate schedulability tests for fixed-priority scheduling. The tests apply to the general case of scheduling with constrained deadline where tasks can incur in blocking times, be subject to release jitters, activated with fixed offsets, or involved in transactions with other tasks. The proposed tests come in a linear closed-form with a number of conditions polynomial in the number of tasks. All tests are targeted for use when encoding schedulability constraints within Mixed-Integer Linear Programming for the purpose of optimizing real-time systems (e.g., to address task partitioning in a multicore system). The tests are evaluated with a large-scale experimental study based on synthetic workload, revealing a failure rate (with respect to the state-of-the-art reference tests) of less than 1% in average, and at most of 2% in a very small number of limit-case configurations.