A New EDF Feasibility Test

We present a new algorithm for testing the feasibility of a set of nonrecurrent tasks (or jobs) with real-time constraints scheduled under the EDF policy (Earliest Deadline First). The proposed feasibility test has a lower complexity than the previously known test. The rst step of the algorithm is to construct the Hasse diagram of the set of tasks where the partial order is de ned by the inclusion relation on the tasks. Then, the algorithm constructs the shortest path in a geometrical representation at each level of the Hasse diagram. Depending on the maximal slope of each path, the set of tasks is either feasible of not. The worst-case complexity of this feasibility test depends on structural characteristics of the set of jobs since it is the sum of the levels in the Hasse diagram. Whatever the set of jobs, this is better than the worst-case complexities of existing approaches. Furthermore, we provide a probabilistic analysis of the complexity when the tasks are random. For Poisson arrivals and exponentially distributed latencies, we show that the asymptotic complexity for assessing feasibility is O(N log(N)). As an interesting by-product, the algorithm provides a new way to derive the best speeds of the processor so as to minimize the total energy consumption while meeting the deadline of each task. The exact complexity of this algorithm (sub-cubic in the number of tasks) is lower than the complexity of all the algorithms solving the same problem, known by the authors. Key-words: Real-Time Systems, Scheduling, Feasibility, Dynamic Voltage Scaling, Earliest Deadline First. ∗ ENS Lyon LIP, 46 Allée d'Italie, 69007 Lyon, France. Email: [email protected] † LORIA, Ensem, 2 avenue de la Forêt de la Haye, 54516 Vandoeuvre, France. Email: [email protected] Unité de recherche INRIA Lorraine Technopôle de Nancy-Brabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLERS LÈS NANCY (France) Téléphone : 03 83 59 30 30 International : +33 3 3 83 59 30 30 Télécopie : 03 83 27 83 19 International : +33 3 83 27 83 19 Antenne de Metz, technopôle de Metz 2000, 4 rue Marconi, 55070 METZ Téléphone : 03 87 20 35 00 International: +33 3 87 20 35 00 Télécopie : 03 87 76 39 77 International : +33 3 87 76 39 77 2 B. Gaujal, N. Navet