# by Sorin Manolache.'s Analysis and optimisation of real-time systems with PDF

By by Sorin Manolache.

ISBN-10: 9185457604

ISBN-13: 9789185457601

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Extra resources for Analysis and optimisation of real-time systems with stochastic behaviour

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We mean by “oldest” instantiation the instantiation whose arrival time is the minimum among the arrival times of the active instantiations of the same task graph. “Discarding” a task graph implies: • The running jobs belonging to the task graph to be discarded are immediately removed from the processors they run onto. 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.

E. no task can be both the ancestor and the descendant of another task. 2, (t2 , χ1 , t3 , χ2 , t5 ) is an example of a computation path of length 5, and task χ1 is an ancestor of tasks t3 , t4 , t5 , and χ2 . We define the relation γ ⊂ T × T as follows: • (τ, τ ) ∈ γ, ∀τ ∈ T , • (τi , τj ) ∈ γ, ∀τi , τj ∈ T, τi = τj iff – they have at least one common ancestor, or – they have at least one common successor, or – they are in a predecessor-successor relationship. As γ is a reflexive, symmetric, and transitive relation, it is an equivalence relation.

Therefore, in the case when bi = 1, 1 ≤ i ≤ g, it is sufficient to analyse the system solely over the time interval [0, LCM ). One could choose the following state space definition: S = {(τ, W, t) : τ ∈ T, W ∈ set of all multisets of T, t ∈ R}, where τ represents the currently running task, W stands for the multiset1 of ready tasks at the start time of the running task, and t represents the start time of the currently running task. A state change occurs at the time moments when the scheduler has to decide on the next task to run.