Author's personal copy Tests for global EDF schedulability analysis Marko Bertogna a , Sanjoy Baruah b,⇑ a Scuola superiore Sant’ Anna, Pisa, Italy b University of North Carolina Chapel Hill, NC, USA article info Article history: Received 26 January 2010 Received in revised form 6 August 2010 Accepted 8 September 2010 Available online 18 September 2010 Keywords: Multiprocessor scheduling Earliest Deadline First Global scheduling Schedulability analysis abstract Several schedulability tests have been proposed for global EDF scheduling on identical multiprocessors. All these tests are sufficient, rather than exact. These different tests were, for the most part, indepen- dently developed. The relationships among such tests have not been adequately investigated, so that it is difficult to understand which test is most appropriate in a particular given scenario. This paper repre- sents an attempt to remedy this, by means of three major contributions. First, we summarize the main existing results for the schedulability analysis of multiprocessor systems scheduled with global EDF, show- ing, when possible, existing dominance relations. We compare these algorithms taking into consideration different aspects, namely, run-time complexity, average performances over randomly generated work- loads, sustainability properties and speedup factors. Second, based on this comparative evaluation we propose a recommended approach to schedulability analysis, that suggests a particular order in which to apply preexisting tests, thereby accomplishing both good provable performance and good behavior in practice. And finally, we propose a further improvement to one of these preexisting tests to improve its run-time performance by an order of magnitude, while completely retaining its ability to correctly identify schedulable systems. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Scheduling and schedulability analysis of multiprocessor sys- tems with migration support has recently been receiving increas- ing attention in the real-time research community. Recent advancements in multiprocessor and multicore technology are reducing the migration-related penalties of global scheduling algo- rithms, rendering more likely the adoption of such kind of schedul- ers in actual systems. From a real-time system design perspective, it is not only important to have a test that is able to detect the schedulability of a given task set, but also to do that in a reasonable amount of time. In this paper we compare, both theoretically and experimen- tally, the performances of the main existing schedulability tests for sporadic task systems with hard real-time requirements, sched- uled with global Earliest Deadline First (EDF) on an identical multi- processor platform. In particular, we report on an exhaustive set of simulations which analyze which test is able to detect the larger number of schedulable task sets, for different randomly generated distributions of task set parameters. We identify dominance and incomparability relationships among the different tests. (A sched- ulability test dominates another if all task systems identified as being schedulable by one are also so identified by the other; two tests are incomparable if there are task systems identified as sched- ulable by each that the other fails to identify as being so.) Based on this comparison, we present observations regarding the practical application of the considered tests. We propose a spe- cific order in which a subset of the tests – those that dominate all other considered tests – be applied, such that the likelihood of identifying schedulable systems with relatively small computa- tional effort is increased, while ensuring (i) that the entire suite of tests is together able to identify all schedulable task systems that are identified by any considered test; and (ii) the theoretical performance of the suite of tests, as quantified by its processor speedup factor, is the best possible. This recommended suite of tests has, as its final test (i.e., the one to be applied if none of the prior tests is able to determine that the system being tested is EDF schedulable), a recently-proposed test that is based on the notion of forced-forward demand bound function (FFDBF) [10]. The inclusion of this test is necessary in order to retain the optimality property (on the processor speedup factor); however, prior implementations of this test have tended to be relatively inefficient. We propose here a means of speeding up the run-time of this test by incorporating ideas from the Quick convergence Processor-demand Analysis (QPA) test, proposed by Zhang and Burns [25] in the context of uniprocessor EDF schedula- bility analysis. Organization: The remainder of this paper is organized as follows. In Section 2, we briefly describe the task and machine 1383-7621/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.sysarc.2010.09.004 ⇑ Corresponding author. E-mail address: baruah@cs.unc.edu (S. Baruah). Journal of Systems Architecture 57 (2011) 487–497 Contents lists available at ScienceDirect Journal of Systems Architecture journal homepage: www.elsevier.com/locate/sysarc