By by Sorin Manolache.

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2. ANALYSIS ALGORITHM 33 In this section, we first sketch the stochastic process construction and analysis procedure based on a simplified example. Then the memory efficient construction of the stochastic process underlying the application is detailed. Third, the algorithm is refined in order to handle multiple concurrently active instantiations of the same task graph. Finally, the complete algorithm is presented. 1 The Underlying Stochastic Process Let us define LCM as the least common multiple of the task periods.

ANALYSIS ALGORITHM 33 In this section, we first sketch the stochastic process construction and analysis procedure based on a simplified example. Then the memory efficient construction of the stochastic process underlying the application is detailed. Third, the algorithm is refined in order to handle multiple concurrently active instantiations of the same task graph. Finally, the complete algorithm is presented. 1 The Underlying Stochastic Process Let us define LCM as the least common multiple of the task periods.

Task t10 has a period of 3. For all tasks and task graphs of this example, their deadline is equal to their period (δi = πi , 1 ≤ i ≤ 14 and δΓi = πΓi , 1 ≤ i ≤ 3). The late task policy for this example is the discarding policy. The set of bounds on the number of simultaneously active instantiations of the same task graph is Bounds = {1, 1, 2}. The deployed scheduling policy is fixed priority for this example. As the task priorities do not change, this policy obviously satisfies the restriction that the sorting of tasks according to their priorities must be invariable during the intervals in which the queue of ready tasks does not change.