# Using semantic properties for real time scheduling

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4 T 1 sends a message M from T 2 after its 4 th execution Figure 7. System S 1 is not feasible T 2 receives a message M from T 1 after its 2 nd execution T 2 sends a message M to T 1 after its 3 rd execution This system is not feasible for two reasons: it doesn t respect the necessary condition (property 1): U = = 10 9 > 1, deadlock cannot be avoided. Now, let us assume that this sequential model comes from the pseudo code described in Figure 10. Furthermore, Figure 8. Code and execution tree of task T 1 In fact, either T 1 uses R 1 and then T 2 can be processed at time 10 even if R 2 is still locked, or T 1 uses R 2, then T 2 can be processed at time 8 before T 1 locks R 2. We present in Figure 9 a valid scheduling tree of the application. The system is thus feasible, despite the negative conclusion when using the classical sequential model. Figure 10. System S 2 since x is an input parameter of both tasks, and, since they are always released at the same time, they always consider the same value for x. We can notice that, according to the semantic of tests, either T 2 executes its THEN branch and T 2 its ELSE branch, or conversely. Thus either message M is send and received or message M. The deadlock thus doesn t take place. Moreover, the case corresponding to U greater than 1 is impossible, because of the semantic. And the system is feasible in practise. Figure 11 presents a valid scheduling tree. Here again, only the semantically correct branches have been kept. Figure 9. A scheduling tree of S Considering semantic We consider a system S 2 composed of two communicating tasks T 1 <0, 5, 9, 9> and T 2 <0, 5, 9, 9>. We assume that: T 1 receives a message M to T 2 after its 1 st execution Figure 11. A scheduling tree of S 2 - Missing branches are semantically inconsistent 4

5 5 Conclusion and future work We have laid the basis for future works. We intend to develop a complete model based methodology for scheduling analysis. For that purpose, we will extend the Petri nets based methodology proposed in [CGGC96, GCG00]. The former examples prove that the classical sequential model of tasks as well as the notion of schedule must be refined. They also prove that it is mandatory to take semantic into account in the feasibility analysis. The general frame of our future investigations is given in Figure 12. [Gro99] E. Grolleau. Ordonnancement temps réel hors-ligne optimal à l aide de réseaux de Petri en environnement monoprocesseur et multiprocesseur. PhD thesis, ENSMA: Ecole Nationale Supérieure de Mécanique et d Aérotechnique Ecole Doctorale Sciences Pour l Ingénieur, Novembre [LL73] C.L. Liu and J.W. Layland. Scheduling algorithms for multiprogramming in real-time environnement. Journal of the ACM, 20(1), pages 46, 61. [Nie91] E. Niehaus. Program representation and translation for predictable real-time systems. In Proceedings og the 12 th IEEE Real-Time Systems Symposium, pages 53 63, San Antonio, Texas, [Pua05] I. Puaut. Obtention de pires temps d exécution (wcet, worst case execution times). Technical report, Université de RENNES 1, IRISA, Septembre Figure 12. Our methodology References [Bab96] J.P. Babau. Etude du comportement temporel des applications temps réel à contraintes strictes basée sur une analyse d ordonnançabilité. PhD thesis, University of Poitiers, France, [But97] G.C. Buttazo. Hard real Time computing systems: predictable scheduling algorithms and applications. Kluwer Academic, [CGGC96] A. Choquet-Geniet, D. Geniet, and F. Cottet. Exhaustive computation of the scheduled task execution sequences of a real-time application. In Proc. of FTRTFT 96, October [CPRS03] [GCG00] A. Colin, I. Puaut, C. Rochange, and P. Sainrat. Calcul de majorants des pires temps d exécution : état de l art. Techniques et Sciences Informatiques (TSI), 22(5): , E. Grolleau and A. Choquet-Geniet. Off line computation of real time schedules by means of petri nets. In R. Boel and G. Stremersch, editors, Discrete events systems, pages Kluwer Academic Publishers,

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