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Task Scheduling Questions and Answers

41.

Match the algorithm with its utilisation bound for a large task set.

1. Rate monotonic   2. Earliest deadline first   3. Rate monotonic with harmonic periods

P. 1.000   Q. 0.693   R. 1.000 also

Answer: A

The three figures are the ones to carry: fixed priorities cost about thirty per cent of the processor in the general case, dynamic priorities cost nothing, and choosing harmonic periods recovers the loss without abandoning fixed priorities.

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42.

Match the protocol with what it does.

1. Priority inheritance   2. Priority ceiling   3. Sporadic server

P. Bounds the load aperiodic work may impose   Q. Raises the holder to the waiter's priority   R. Raises the holder to the resource's assigned priority

Answer: B

The first two bound blocking on a shared resource and differ in whose priority is borrowed; the third bounds interference from work that arrives unpredictably. All three exist to turn an unbounded quantity into a bounded one so the analysis can proceed.

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43.

Put the steps of a schedulability analysis in order.

1. Apply the utilisation bound test   2. Measure or bound each task's worst-case execution time   3. Compute response times by iteration if the bound test is inconclusive   4. Assign priorities by deadline monotonic order

Answer: C

Correct answer: 2, 4, 1, 3

Execution times must be known before anything can be computed. Priorities are then assigned, since the analysis depends on the ordering. The utilisation bound test is tried first because it is cheap, and response time analysis is used only where the bound test proves inconclusive - which is whenever the utilisation lies between the bound and unity.

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44.

Consider the following statements about scheduling.

1. A utilisation above unity is always infeasible   2. The rate monotonic bound is necessary and sufficient   3. Earliest deadline first is optimal on one processor

Answer: D

Correct answer: 1 and 3 only are correct

Statements 1 and 3 are correct: utilisation above unity is infeasible for any algorithm, and earliest deadline first is optimal on one processor. Statement 2 overstates the rate monotonic bound, which is sufficient but not necessary - a set exceeding it may still meet every deadline, which is why response time analysis exists.

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45.

Consider the following statements about priority inversion.

1. It arises from a shared resource   2. Inheritance bounds it   3. It cannot occur under earliest deadline first

Answer: A

The first two are correct. Dynamic priorities give no immunity: a task with a near deadline can just as well be blocked by one with a distant deadline holding a lock, and the deadline inheritance protocol is the corresponding remedy.

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Answer: B

Correct answer: the average execution time of each task

Real-time analysis is about guarantees, so it works from the worst-case execution time; an average tells you what usually happens and nothing about the case that misses the deadline. Periods and relative deadlines are the other two inputs, and all three must be bounds rather than typical values.

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Answer: C

Correct answer: the set demands more processor than exists and cannot be scheduled

A utilisation of 1.4 means the work requires forty per cent more processor time than the hardware provides, and no algorithm can create it. Earliest deadline first is optimal, but optimality means it succeeds whenever success is possible - and here it is not.

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48.

A task consistently completes in 2 ms but its worst case is measured at 9 ms on one rare path. The analysis must use

Answer: D

The whole point of a hard real time guarantee is that it holds on the day the rare path is taken at the worst moment. If nine milliseconds makes the set unschedulable, the remedy is to shorten that path rather than to discount it.

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49.

A system misses a deadline only when a particular combination of events coincides. This is characteristic of

Answer: A

Correct answer: the critical instant having been reached at last

The worst case for a task occurs when it is released simultaneously with every higher priority task, and that coincidence may take a very long time to occur in practice. A system that runs correctly for months and then misses a deadline has probably just reached its critical instant - which is exactly what analysis, rather than testing, is for.

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Answer: B

The number of possible phasings is enormous and the worst one may occur once a year, so testing establishes only that the system has not yet failed. Analysis proves the bound and testing validates the inputs to it, which is why both are used.

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