EnricoBini Modeling event-driven real-time application using DAGs CarloVitucci GiuseppeLipari Scuola Superiore A.Anna Ericsson Lab Italy

Our Approach Preliminar study of the application Analysis of the results Model definition Goal definition Linear Programming Algorithm

Results of the preliminar study Both tasks and external environment generate events Tasks are activated by events configurations The application is composed by tasks and events Graph structured application!!!

The task  i Condition of activation First instant of execution t i Worst case computation time C i Instant of execution end t i +C i Non-preemptive hypothesis!! Events/signals generated at the end of  i.

Activation condition Receiving a signal (Precedence constraint). Receiving all the signals in a set (AND-synchronization constraint). Receiving at least one signal in a set (OR-synchronization constraint). Receiving a signal and the condition x i is true (Conditional constraint). Waiting only W k for receiving a signal (Timeout constraint).

The precedence constraint 11 22Graphicalrepresentation t1t1 C1C1 t2t2 View in the t-space The timeline 11 22 t1t1 t2t2 C2C2 C1C1 t

The AND-synchronization constraint t1t1 C2C2 t2t2 C1C1 t3t3 View in the t-space 11 22 t1t1 t2t2 C2C2 C1C1 t 22 11 33 33 C3C3 t3t3 Graphical representation The timeline

The OR-synchronization constraint 22 11 33 Graphical representation t1t1 C2C2 t2t2 t3t3 View in the t-space 11 22 t1t1 t2t2 C2C2 C1C1 t 33 C3C3 t3t3 The timeline

The conditional constraint 11 22 t2t2 t1t1 C1C1 C2C2 t 22 11 33 33 C3C3 t3t3 xixi TRUE FALSE T F Behaviour in the t-space Where M is big enough to make meaningless the rest. The timeline Graphicalrepresentation

The timeout constraint 22 11 33 RECEIVED WkWk xx TIMEOUT The timeline 22 C1C1 C2C2 xx t1t1 tt3t3 11 33 C3C3 R CxCx t2t2 txtx WkWk Behaviour in the t-space

The number of CPU bounds the concurrency (Non-concurrency constraint). Does the hardware imply any constraint? There could be a time interval [a,b] when the CPU is not completely available (CPU bandwidth constraint). What about using a hybrid multiprocessor? (Hybrid CPUs condition)

The non-concurrency constraint The timeline 11 22 t1t1 t2t2 C2C2 C1C1 t Formal definition The non-concurrency constraint is equivalent to: “  1 precedes  2 or  2 precedes  1 ” t1t1 C1C1 t2t2 View in the t-space C2C2

CPU bandwidth constraint Formal definition In the time interval [a,b], the CPU utilization must be U < 1. t1t1 t2t2 View in the t-space Example If the precedence  1  2 holds and t 2 is close to [a,b],  2 must be delayed accordingly.

Hybrib CPUs condition x ip is 1 if  i executes on processor p 0 otherwise. Depending on the CPU, the Worst Case Computation Time is different!! C ip as the WCET of task  i on processor p So we define: The execution of  i so ends at t i +x i1 C i1 +x i2 C i2 +…+x iP C iP. An additional constraint is x i1 +x i2 +…+x iP =1.

Let’s put all togheter The constraints define an admissible region in the variable space titi tjtj After the definition of a cost function… … we can perform a Linear Programming algorithm to hunt for the optimum!!

This is the last slide So far… We are developing the model to capture the application features. We are searching LP algorithms present in the literature. Soon we will … …define a good cost function …develop a new algorithm to find such optimum!!