Rate Mono Tonic

8/14/2019 Rate Mono Tonic

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A presentation for

Brian Evans

Embedded Software Class

By Nate Forman

Liaison Technology Inc.

3/30/2000For Real-Time Scheduling


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3/2000 Rate Monotonic Analysis, Nate Forman

Agenda

Introduction

Anatomy of a Task

Rate Monotonic

Principles and Tests

Extended Rate Monotonic

Analysis

Demonstration Mars Pathfinder Mission


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Introduction

Rate Monotonic refers to assigning priorities as a monotonicfunction of the rate (frequency of occurrence) of those

processes.

Rate Monotonic Scheduling (RMS) can be accomplished

based upon rate monotonic principles.

Rate Monotonic Analysis (RMA) can be performed staticallyon any hard real-time system concept to decide if the system

is schedulable.


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Anatomy of a Task

1

2

3time

Task Execution Time (C) End Of Period (T = Period Length)


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Rate Monotonic Assumptions

All tasks are periodic

Task switching is instantaneous

Tasks account for all processor execution time

Tasks become ready to execute precisely at the

beginning of their periods and relinquish the CPU only

when execution is complete


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Rate Monotonic Assumptions (2)

Task interactions are not allowed

Task deadlines are always at the end of the period

Tasks with shorter periods are assigned higher priorities;

no other criteria are considered for priority assignment

Task execution is always consistent with rate monotonic

priority: a lower priority task never executes when a

higher priority task is ready


7/223/2000 Rate Monotonic Analysis, Nate Forman

Utilization Bound (UB) Test

Processor Utilization for a task, i Ui =Ci

Ti

Utilization Bound for n tasks U(n) = n(2 - 1)1

n

Results:

If Ui

U(n) then the set of tasks is schedulable.

If Ui > 1 then the set of tasks is unschedulable.

If U(n) < Ui 1 then the test is inconclusive.



UB Test Example

Task Execution Time

(C)

Period (T)

1 40 100

2 40 150

3 100 350

U(3) = 3(21/3 1) = 0.779U1 = 40 / 100 = 0.4

U2 = 40 / 150 = 0.267

U3 = 100 / 350 = 0.286

Utotal = 0.953

Result:U1+2 = 0.667, schedulable.

However, 0.779 < 0.953 < 1

Therefore, inconclusive for 3.



Response Time (RT) Test

Theorem: If a task meets itsfirstdeadline with worst-case taskphasing, that deadline will always be met.

For the response time for task i, find the least fixed-point of the

following recurrence:

a0 = Cjj H + {i}

an+1 = Ci + Cjj H

an

Tj

where H is the set of tasks with higher priority than task i.



RT Test Example

Task Execution Time

(C)

Period (T)

1 40 100

2 40 150

3 100 350

a0 = Cj = 40 + 40 + 100 = 180j H + {i}

a1 = C3 + Cj = 100 + (2 * 40) + (2 * 40) = 260j H

180

Tj

a2 = C3 + Cj = 100 + (3 * 40) + (2 * 40) = 300j H

260

Tj

a3 = C3 + Cj = 100 + (3 * 40) + (2 * 40) = 300j H

300

Tj

a2 = a3 = 300

300 < 3 = 350

3 is schedulable.


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Extensions to RMA

Aperiodic task handling

Preperiod task deadlines (Di = deadline for task i)

Nonzero task switching times (S = task switch time)

Interrupt handling for top-priority tasks

Task blocking and interaction through shared resources

(Bi = blocking time for task i)


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Sporadic Servers

A conceptual task that uses its execution budget

handling incoming aperiodic tasks

Its execution budget is only replenished after a periodwhere it is completely consumed instead of after every

periods end.

Avoids deferred execution effect and reduces aperiodic

tasks to the same model as periodic tasks


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Priority Inversion

A high priority task is ready to execute, but a lower

priority task continues execution because it holds a lock

on a shared resource that the high priority task needs.

Unbounded priority inversion occurs when a system

allows tasks with lower priority than the blocked task to

preempt the blocking task.


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Priority Inversion (2)

To successfully share resources, a system needs two

properties: freedom from mutual deadlock, andbounded

priority inversion.

The combination of priority inheritance and the priority

ceiling protocol guarantee the above properties.

Priority Inheritance: When a task blocks the execution

of other, higher priority tasks, it executes at the highest

priority of all of the tasks it blocks.


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Priority Ceiling Protocol

Priority Ceiling: of a binary semaphore is the highest

priority of all of the tasks that may lock it.

A task attempting to a execute critical section is blockedunless its priority is higher than the priority ceilings of

all of the locked semaphores in the system.

The task holding the lock on the highest priority ceiling

semaphore inherits the priorities of tasks blocked in this

way.


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Extended UB Test

for i = Di / Ti, redefine utilization bound:

U(n, i) =

n ((2 i)1/n 1) + 1 i, 0.5 < i 1

i, i 0.5


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Extended UB Test (2)

+ ++Ci + 2S

Ti

Ti

Bifi =

j Hn

Cj + 2S

Tj

(Ck + 2S)k H1Ti

1

Updatedprocessor utilization:

where Hn is the set of higher priority tasks that can preempt task i

more than once (shorter periods) and H1 are higher priority tasks

that can preempt task i only once (longer periods)

Compare each fi to its utilization bound, U(n, i). The results can

be interpreted as before.


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Extended RT Test

Theorem: If a task meets itsfirstdeadline with worst-case taskphasing, that deadline will always be met.

The above theorem still stands although the deadline is Di instead

of Ti. For the response time find the least fixed-point of therecurrence below:

a0 = Bi + (Cj + 2S)j H + {i}

an+1 = Bi + Ci + 2S + (Cj + 2S)j H

an

Tj

where H is the set of tasks with higher priority than task i.


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What really happened on Mars?(the first time)

Two tasks were critical for controlling communication onthe landers communication bus, the scheduler task

(bc_sched) and the distribution task (bc_dist).

Each of these tasks checked each cycle to be sure that the

other had run successfully.

time = 0.125 s

bc_sched

bc_dist

bus active


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Mars Pathfinder: The Problem

bc_dist was blocked by a much lower prioritymeteorological science task (ASI/MET)

ASI/MET was preempted by several medium priority

processes such as accelerometers and radar altimeters.

bc_sched started and discovered that bc_dist had not

completed. Under these circumstances, bc_sched reacted by

reinitializing the landers hardware and software andterminating all ground command activities.


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Mars Pathfinder: Resolution

Faster, better, cheaper had NASA and JPL using shrink-wrap hardware (IBM RS6000) and software (Wind River

vxWorks RTOS).

Logging designed into vxWorks enabled NASA and WindRiver to reproduce the failure on Earth. This reproduction

made the priority inversion obvious.

NASA patched the landers software to enable priorityinheritance.


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Resources

www.sei.cmu.edu: Software Engineering Institute,

technical reports and presentations on rate monotonic

analysis

www.jpl.nasa.gov: NASA Jet Propulsion Laboratory,

information about Mars missions, pictures

Guaranteeing Real-Time Performance Using RMA, The

Embedded Systems Conference, R. Obenza & G. Mendal

research.microsoft.com: letter by Glenn Reeves of JPL

about Mars Pathfinder mission

http://www.ece.utexas.edu/~bevans/courses/ee382c/projects

/fall99/ -- The RMADriver Application

Documents

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