CS452 - Real-Time Programming - Spring 2008

Lecture 31 - Practical Control and Calibration

Questions & Comments

1. Anything else that would be useful

Real-time Scheduling

Much real-time computing operates in an environment like the following

1. Groups of sensors that provide polling with fixed periodicity
2. Sensor input triggers tasks which also run with fixed periodicity

Typical example, a group of sensors that returns

• the rotational speed of the wheels, and
• the exhaust mixture, and
• the torque, and ...

and a set of tasks that

• updates the engine parameters, and
• updates the transmission parameters, and
• passes the speed on to the instrument controller, and ...

Each time a sensor returns a new datum a scheduler runs

1. makes ready any task that the data makes ready to run
2. decides which of the ready tasks to schedule, and
3. starts it running.

This is a hard real-time appoication.

Academic research on real-time programming divided the universe of programs into three categories.

1. Hard real-time: the controlled system self-destructs if a deadline is ever missed.
2. Soft real-time: the controlled system is incorrect is a deadline is missed.
3. Not real-time: it doesn't matter when the results are ready.

(By this classification pretty well all real applications are soft real-time.)

The deadlines of the example discussed above are the next scheduling of the task.

• That is, a task completes successfully if and only if it completes before it is next scheduled.

Why are we discussing this particular case?

• Because one of the few hard results standing the test of time applies to this case, and
• because it is believed that this result applies to many neighbouring, practical, cases.
• It is believed often to apply to bottleneck cases, where everything happens together by accident.

The theorem applies to the important question,

• `Which task should be scheduled next in order to maximize use of the processor with no deadlines ever being missed?'

And the answer is,

• `Rate monotone scheduling.'

which is

• Always schedule that ready task that runs most often.

How it's proved.

Consider all possible collections of tasks,

• each task having a periodicity Ti, and an execution time Ci. (C is for cost.)

Show that, if the set of tasks can be scheduled successfully by any scheduling algorithm, then

• it will be scheduled successfully by rate-monotone scheduling.

Proof

Definitions

Overflow at t. A task cannot be scheduled at t because its previous execution is not complete.

Feasible. A set of tasks that can be successfully scheduled.

Response time. The time between the the readying of a task and its completion. If a set of tasks is feasible then for every execution of every task RT < Ti.

Critical instant for a task. The scheduling time at which it has the longest response time.

Results

1. The critical instant for a task occurs when it is readied at the same time as all other tasks.
   • Think about it.
2. When there are exactly two tasks, then rate monotone works.
   • Let the higher priority task be task 0. It meets its deadlines if C0 < T0
   • Lower priority task can be scheduled at exactly the same time as the higher priority one.
   • Then as long as RT = C0 + C1 < T1 the set is feasible. This is true regardless of the relative values of T0 and T1.
   • If it is true for T0 > T1, then it is clearly true for T0

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