Accurate Analysis And Calculation Of The Real-time Tasks' Best Response Time

With wide application of real-time systems in various fields,task scheduling technologies play an increasingly critical role in real-time systems.As for the characters of multitask,multip-rocessor and complex precedence constraints in real-time systems,the real-time tasks schedulability analysis methods need to be expanded and supplemented.The analysis of the real-time tasks' response time is one of the core questions of the classic real-time scheduling theory research.But now,the research of the tasks' worst response time becomes more mature,comparatively,the studies of the best response time are still fewer.In the end-to-end tasks of the multi-processor environment,the worst response time of the subsequent subtasks are influenced by its release jitter,and the release jitter of a task is determined by the worst case and best case response times of its preceding subtask.If the release jitter is overestimated,the task would have been completed within the deadline,which were judged as can not completed within the deadline.Therefore,the accurate analysis and calculation of the real-time tasks' best response time is particularly important.First,this paper uses the fixed-priority preemptive scheduling,simulate the run of the tasks with arbitrary phasing,on the basis of accurate analysis of the tasks' best response time with the deadline equal or less than the period,and introduces the level-i busy period,gains the optimal completion instant of the extendable jobs by constructing the level-i busy period,thereby proposes the method of iterative computing best case response time of the tasks with deadline more than its period.The correctness of the algorithm was proved.And then,this paper extends the analysis of the best response time.According to the existing methods ignored the influence of release jitter to the best response time, presents the iterative calculation method of the periodic tasks' best response time in the case of the release jitter.This method compensates the shortcomings of current approaches,which is because the assumption of the subtask's best case response time is arbitrary small or much smaller than the actual one in the multi-processor system,and then overestimates the worst case response time of the subsequent subtask,making the schedulibility of the tasks that would have been able to complete before the deadline be judged as unschedulable.This paper proposes optB-WCRT algorithm can calculate preceding subtask's of the end-to-end subtask best response time more precise,and then be able to reduce the constraints of the end-to-end tasks' worst response time,which can precisely judge the schedulability.Finally,this paper simulates the experiment.Through comparing the performances of the proposed optB-WCRT algorithm with the traditional setting method,Trivial method,the results proved that optB-WCRT algorithm is more accurate and efficient,which is of great significance for the real-time tasks' schedulability analysis of multi-processor system.