Real-time scheduling with resource sharing on uniform multiprocessors

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a uniform multiprocessor platform where each task may access at most one of |R| shared resources and at most once by each job of that task. The resources have to be accessed in a mutually exclusive manner. We propose an algorithm, GIS-vpr, which offers the guarantee that if a task set is schedulable to meet deadlines by an optimal task assignment scheme that allows a task to migrate only when it accesses or releases a resource, then our algorithm also meets the deadlines with the same restriction on the task migration, if given processors 4 + 6|R| times as fast. The proposed algorithm, by design, limits the number of migrations per job to at most two. To the best of our knowledge, this is the first result for resource sharing on uniform multiprocessors with proven performance guarantee.

Competitive analysis of partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. We propose an algorithm which can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are three times faster.

Competitive analysis of static-priority partitioned scheduling on uniform multiprocessors

Consider the problem of scheduling a set of sporadically arriving tasks on a uniform multiprocessor with the goal of meeting deadlines. A processor p has the speed Sp. Tasks can be preempted but they cannot migrate between processors. On each processor, tasks are scheduled according to rate-monotonic. We propose an algorithm that can schedule all task sets that any other possible algorithm can schedule assuming that our algorithm is given processors that are √2 / √2−1 ≈ 3.41 times faster. No such guarantees are previously known for partitioned static-priority scheduling on uniform multiprocessors.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.