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Extra info for Analysis and optimisation of real-time systems with stochastic behaviour
If, however, the cause of the state transition is a task completion, the time Zji is equal to to Zj + Exτ , where task τ is the task that runs in state sj and whose completion triggers the state transition. Because Zji is a sum involving the random variable Exτ , Zji too is a random variable. Its probability density function, is ∞ computed as the convolution zj ∗ τ = 0 zj (t − x) · τ (x)dx of the probability density functions of the terms. 4. z2 , z3 , z4 , z5 , and z6 are the probability density functions of Z2 , Z3 , Z4 , Z5 , and Z6 respectively.
E. ) are freed. • The ready-to-run and blocked-on-I/O jobs belonging to the task graph to be discarded are immediately removed from the ready-to-run and waiting-on-I/O queues of the scheduler. They are also eliminated from the system. The Rejection Policy The rejection policy specifies that whenever a new instantiation of task graph Γi , ∀1 ≤ i ≤ g, arrives and bi instantiations are active in the system at the time of the arrival of the new instantiation, the new instantiation is not accepted in the system.
3. SYSTEM MODELLING that task ti is a predecessor of task tj (ti ∈ ◦ tj ) and tasks ti and tj are mapped on the same processing element (M apP (ti ) = M apP (tj )). In this case, the time of the communication between task ti and tj is considered to be part of the execution time of task ti . Thus, the execution time probability density ti accounts for this intra-processor communication time. Next, we discuss the modelling of the communication time between two processing tasks that are mapped on different processing elements.