Real-Time Applications with Stochastic Task Execution Times: by Sorin Manolache

By Sorin Manolache

This e-book offers 3 techniques to the research of the closing date omit ratio of purposes with stochastic job execution instances. every one most closely fits a special context: a precise one successfully acceptable to monoprocessor structures; an approximate one, which permits for designer-controlled trade-off among research accuracy and research pace; and one much less exact yet sufficiently quickly as a way to be put inside of optimization loops.

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Extra resources for Real-Time Applications with Stochastic Task Execution Times: Analysis and Optimisation

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The multiset of ready tasks in si and the one in sj are the same, 3. The PMIs in the two states differ only by a multiple of LCM , and 4. zi = zj (zi is the probability density function of the times when the system takes a transition to si ). 2. Let us consider the moment x, when the last state belonging to a certain hyperperiod Hk has been eliminated from the sliding window. Rk is the set of back states stored in the sliding window at the moment x. Let the analysis proceed with the states of the hyperperiod Hk+1 and let us consider the moment y when the last state belonging to Hk+1 has been eliminated from the sliding window.

ANALYSIS ALGORITHM 33 next states of a state s equals the number of PMIs the possible execution time of the task that runs in state s is spanning over. We propose a representation in which a stochastic process state is a triplet (τ, W, pmi), where τ is the running task, W the multiset of ready tasks at the start time of task τ , and pmi is the PMI containing the start time of the running task. 1(a)) is spanning over the PMIs pmi1 — [0, 3)—and pmi2 —[3, 5). 2(b). 4 depicts a part of the stochastic process constructed for our example.

Let Bounds = {bi ∈ N+ : 1 ≤ i ≤ g} be their set. We consider two different policies for ensuring that no more than bi instantiations of task graph Γi , ∀1 ≤ i ≤ g, are active in the system at the same time. We call these policies the discarding and the rejection policy. We assume that a system applies the same policy (either discarding or rejection) to all task graphs, although our work can be easily extended in order to accommodate task graph specific late task policies. The Discarding Policy The discarding policy specifies that whenever a new instantiation of task graph Γi , ∀1 ≤ i ≤ g, arrives and bi instantiations are already active in the system at the time of the arrival of the new instantiation, the oldest active instantiation of task graph Γi is discarded.

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