The worst-case execution time of a task is
Answer: A
It is the task's own demand with the processor entirely to itself, and it is the input to every schedulability test. The time from release to completion in the presence of other tasks is the response time, which is what the analysis computes.
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The response time of a task is the interval from
Answer: B
It includes every interval in which the task was ready but displaced by something of higher priority, which is exactly what makes it larger than the execution time. Comparing it with the deadline is the test the whole analysis exists to perform.
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The processor utilisation of a task set is
Answer: C
Correct answer: the sum of each task's execution time divided by its period
\[ U = \sum \frac{C_i}{T_i}. \] Each term is the fraction of the processor that task requires on average, and the sum is what the whole set demands. It is the first figure computed in any schedulability analysis, because a set demanding more than the processor has cannot be scheduled by any means whatever.
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A task set with a utilisation above 1.0 is
Answer: D
Correct answer: infeasible under any scheduling algorithm
Utilisation above unity means the set requires more processor time than exists, so no ordering of the work can make the deadlines. This is the one absolutely necessary condition, and no clever algorithm evades it - the remedy is faster hardware, less work, or longer deadlines.
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The laxity or slack of a task at an instant is
Answer: A
Zero laxity means it must run continuously from now to meet its deadline, and negative laxity means the deadline is already lost. Scheduling by least laxity first is optimal in the same sense as earliest deadline first.
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Rate monotonic priority assignment gives the highest priority to the task with
Answer: B
Frequency alone decides, and the assignment is fixed for the life of the system. It is optimal among fixed priority schemes for tasks whose deadlines equal their periods, which is what makes it the standard starting point.
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Deadline monotonic assignment differs from rate monotonic in ordering by
Answer: C
Correct answer: the relative deadline rather than the period
Where a deadline equals its period the two schemes coincide. They differ when a deadline is shorter, and deadline monotonic is then the optimal fixed priority assignment while rate monotonic is not - a task needing its answer quickly should be prioritised on that need rather than on how often it runs.
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The Liu and Layland utilisation bound for \( n \) tasks under rate monotonic scheduling is
Answer: D
It falls from 1.0 for one task through 0.828 for two and 0.780 for three toward 0.693 as the number grows. A set below the bound is certainly schedulable; a set above it may still be, and response time analysis must then be used.
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The rate monotonic utilisation bound as the number of tasks grows without limit tends to
Answer: A
The limit of \( n(2^{1/n}-1) \) is the natural logarithm of two, about 0.693. It is the figure usually quoted as the rate monotonic bound, and it means a fixed priority system may have to leave nearly a third of the processor idle to be provably safe.
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A task set whose utilisation lies above the rate monotonic bound but below 1.0 is
Answer: B
The bound guarantees schedulability below it and says nothing above it, so a set at 0.85 with three tasks needs the exact test. Harmonic periods are a special case in which utilisation up to 1.0 is schedulable under rate monotonic.
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