Chapter 6: Specialized Computing Domains

Exercise 1

Rate monotonic scheduling (RMS) is an algorithm for assigning thread priorities in preemptive, hard, real-time applications in which threads execute periodically. RMS assigns the highest priority to the thread with the shortest execution period, the next-highest priority to the thread with the next-shortest execution period, and so on. An RMS system is schedulable, meaning all tasks are guaranteed to meet their deadlines (assuming no inter-thread interactions or other activities such as interrupts, resulting in processing delays) if the following condition is met:

This formula represents the maximum fraction of available processing time that can be consumed by n threads. In this formula, C_i is the maximum execution time required for thread i, and T_i is the execution period of thread i.

Is the following system composed of three threads schedulable?

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Thread