Real-Time Syst (2007) 35:135–151 DOI 10.1007/s11241-006-9005-y Guaranteeing response times for aperiodic tasks in global multiprocessor scheduling Lars Lundberg · H˚ akan Lennerstad Published online: 3 November 2006 C  Springer Science + Business Media, LLC 2007 Abstract We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall’s effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U threshold = 3 − √ 7 ≈ 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy. The bound U threshold = 3 − √ 7 ≈ 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U threshold (m), which converges to U threshold from above as m →∞. The results are based on a utilization function u (x ) = 2(1 − x )/(2 + √ 2 + 2x ). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U threshold (m) by paying the extra overhead of monitoring the individual utilization of the current tasks. Keywords Multiprocessor . Scheduling . Aperiodic . Dhalls effect . Optimal threshold . Synthetic utilization 1 Introduction Many real-time services are implemented as multiprocessors that handle a number of incoming aperiodic requests (tasks). One would clearly like to guarantee certain L. Lundberg () . H. Lennerstad Department of Systems and Software, School of Engineering, Blekinge Institute of Technology, 372 25 Ronneby, Sweden e-mail: Lars.Lundberg@bth.se H. Lennerstad e-mail: Hakan.Lennerstad@bth.se Springer