Period Selection for Minimal Hyper-period in Real-Time Systems

Task period and deadline selection are often used to adjust the workload to the available computational resources. This paper presents a method for adjusting the periods of the tasks which obtains the minimal hyper-period. Task periods are modelled as a range of possible periods. The selected periods are not constrained to be natural numbers, but can also be rational numbers. Without this limitation, the resulting hyper-period is much smaller than that of previous works. Hyper-period for natural periods grows exponentially; with rational periods the worst case is quadratic with the largest period. Our finding has practical applications in several fields of real-time scheduling: lowering complexity in table driven schedulers, reducing search space in model checking analysis, generating synthetic workload for statistical analysis of real-time scheduling algorithms, etc.