On fixed priority scheduling, offsets and co-prime task periods

In fixed priority scheduling, offsets are used to spread out the load on the processor. If offsets remove the possibility of a common release for all tasks then the utilisation bound on feasibility (schedulability) is increased. When tasks have arbitrary offsets, it is difficult, by inspection of their timing characteristics alone, to determine if a common release of all tasks will occur during system execution. We present a simple test that will determine the existence of a common release. Moreover, we show that tasks sets that have co-prime periods must experience a common release (regardless of any imposed offsets). As such tasks are those that would appear to benefit most from the use of offsets this represents an important, though unfortunate, result. (C) 1998 Elsevier Science B.V. All rights reserved.