### What would be the maximum computation time

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Assignment - Read the paper "Rhythmic Tasks: A New Task Model with Continually Varying Periods for Cyber-Physical Systems" by Kim, Lakshmanan, and Rajkumar and answer the following questions.

1. The paper describes a new task model for engine tasks where the time between task releases varies depending on the speed at which the engine is running. Is it possible to describe such tasks as periodic, sporadic or aperiodic? Justify your answer.

2. In §I of the paper, the authors discuss a specific example of a periodic task with period 140 ms and worst case execution time 60 ms running alongside an engine task with variable period between 10 ms and 120 ms. Show that, if the worst case execution time of the engine task is 4 ms, the system is schedulable.

3. Consider a second engine with lower maximum speed so that its minimum engine task period is 55 ms. According to the same test, what would be the maximum computation time allowed for the system to be schedulable? Show your working.

4. In §IV of the paper, a new schedulability test for rhythmic (a.k.a., engine) tasks is proposed, for the case where there is one rhythmic task and one periodic task. According to the new schedulability test, what is the maximum execution time for the engine task for the engine from question 2 in steady state? What is it for the engine from question 3? Show your working and comment on the result.

5. Plot the maximum execution time for the engine task against the period, at steady state, according to (i) the utilisation bound test and (ii) the new schedulability test. Discuss the results.

6. Consider the case that the engine from question 2 accelerates at a rate of α = 0.3 for nα = 1 job release. If the computation time of the engine task is constant, is the system schedulable during and after acceleration? Show your working.

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