The Earliest Smooth Release Time for a New Task Based on EDF Algorithm

Although EDF (Earliest Deadline First) algorithm has received extensive study during the past more than 40 years, only a few researchers have published their efforts on the bandwidth transfer between tasks. If current running tasks are compressed to free part of their occupied bandwidth to accommodate new requirements, such as a new task's insertion, then a basic requirement of this operation is smoothness, that is, no deadline should be missed. Suppose current tasks are immediately compressed at the request time of the new task, in order to guarantee the smoothness, the new task may have to be released later than the request time. An interesting and challenging problem is to find the earliest smooth release time. In this paper, an algorithm to evaluate the earliest release time for single task's insertion is presented and formally proved. To finish the algorithm, only the deadlines during the transition should be checked, and each of them needs to be checked at most once. A novel experimental approach is adopted and more than 4549320 different tests are implemented to verify the theorems in simulation.