introductory seminar on research cis5935 fall 2009

Introductory Seminar on Research

CIS5935 Fall 2009

Ted Baker

Outline

• Introduction to myself– My past & current research areas

• Technical background for the remainder• A recent paper, on Sustainable MP Scheduling

– What is it?– Why do I want it?– How do I get it?– Sustainability of specific algorithms & tests

My past research

• Relative computability– Relativizations of the P=NP? question (1975-1979)

• Algorithms– N-dim pattern matching (1978)– extended LR parsing (1981)

• Compilers & PL implementation– Ada compiler and runtime systems (1979-1998)

• Real-time runtime systems, multi-threading– FSU Pthreads & other RT OS projects (1985-1998)

• Real-time scheduling & synch.– Stack Resource Protocol (1991)– Deadline Sporadic Server (1995)

• RT Software standards– POSIX, Ada (1987-1999)

Recent/current research

• Multiprocessor real-time scheduling (1998-…)

– how to guarantee deadlines for task systems scheduled on multiprocessors?

with M. Cirinei & M. Bertogna (Pisa), N. Fisher & S. Baruah (UNC)

• Real-time device drivers (2006-…)

– how to support schedulability analysis with an operating system?

– how to get predictable I/O response times?with A. Wang & Mark Stanovich (FSU)

Background

• Real-time scheduling goals & problems• Workload models• Scheduling algorithms & tests

Real-time scheduling

Context = embedded systems, controllersProblems =• How to schedule a computational workload to

meet timing constraints? (deadlines)• How to do this while meeting other constraints

and goals? (energy, fault tolerance, etc.)• How to guarantee constraints will always be met,

in the face of workload variations

Typical quality questions

• Is a given system schedulable to meet deadlines?

• Is a given system schedulable by a given algorithm?

• If deadlines are missed, by how much?• How good is a given algorithm at finding a

feasible schedule?• How sensitive is a schedulability

guarantee to variations in parameters?

Workload models

• job = schedulable unit of computation, with– arrival time– worst-case execution time (WCET)– deadline

• task = sequence of jobs• task system = set of tasks• independent tasks:

can be scheduled without consideration of interactions, precedence, coordination, etc.

Example: sporadic task i• Ti = minimum inter-arrival time

• Ci = worst-case execution time

• Di = relative deadline

job released job completes deadline next release

iC

?iDiD

iT

scheduling window

Multiprocessor scheduling

• m identical processors (vs. uniform/hetero.)

• shared memory (vs. distributed)• Kinds of algorithms:

– preemptive vs. non-preemptive– on-line vs. off-line– global vs. partitioned

Optimality

• There is no optimal on-line global scheduling algorithm for sporadic tasks [Fisher, 2007]

• But there are some good algorithms

Some good scheduling algorithms

• Fixed task-priority– global, or partitioned, hybrids, …

• EDF– global or partitioned, hybrids, …

• EDZL…

Example: Global EDF

• m identical processors• global =

– jobs can run on any processor– can be preempted, and migrated

• EDF = “earliest deadline first”– earlier deadline implies higher priority– the top m jobs will execute– no processor is idle unless there are

fewer than m jobs ready to run

Schedulability testing

Global-EDF schedulability for sporadic task systems can be decided by brute-force state-space enumeration (in exponential time) [Baker, OPODIS 2007]

but we don’t have any practical algorithm.

We do have several practical sufficient conditions.

Sufficient Conditions for Global EDF

• Varying degrees of complexity and accuracy

• Examples: • Goossens, Funk, Baruah: density test (2003)• Baker: analysis of -busy interval (2003)• Bertogna, Cirinei: iterative slack time

estimation (2007)

• Difficult to compare quality, except by experimentation

• All tests are very conservative

Example: Density Test

)()1()( max mmsum

n

iisum

1

i

n

i

1max max

),min( ii

ii TD

C

where

Sporadic task system is schedulable on m unit-capacity processors if

My recent researchon Sustainable Schedulabilty

done with Sanjoy Baruah (UNC)presented by T. Baker at ECRTS

July 2009Dublin

7/3/2009 ECRTS 2009 (Dublin) - Ted Baker 18

General schedulability testing

Will a will workload W meet all deadlines ifscheduled by algorithm A on platform P?

exact test : “yes” ⇔ schedulablesufficient test : “yes” ⇒schedulable

Goal: validate timing propertieson which correctness, reliability, safety depend.

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Potential weakness• Real systems differ from models

– clock and timer inaccuracies– blocking/non-preemption– execution time variation

• Differences must not invalidate test• Solution:

– pessimistic assumptions

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What is pessimistic?

• Should cover full range of possibilities.• How to validate over such a range?• People tend to assume system behavior is

monotonic, and rely on boundary testing.• This can be dangerous.• For example, does WCET of individual jobs

give worst-case behavior of the entire system?

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Goals

• Our notions of “pessimistic” should be consistent with the analysis that underlies the schedulability test.

• The test should be monotonic with respect to any workload parameters that are considered to be bounds on actual values.

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Predictability(Ha & Liu 1994)

• For arbitrary job sets on multiprocessors, if scheduling algorithm is work-preserving, preemptive, global (migration), with fixed job priorities:– Job completions times are monotonically

related to job execution times.– It is safe to consider only upper bounds

for job execution times in schedulability tests.

• Not true for non-preemptive scheduling

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Sustainabilty(Baruah & Burns 2006)

• Extends idea to a wider range of relaxations of workload parameters:– shorter execution times– longer periods– less release-time jitter– later deadlines

• Relaxation should preserve schedulability• They considered single-processor systems• We consider multiprocessors

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Why to relax?

• Safety– Run-time behavior may fall short of

pessimistic model parameters.• Modular design

– Start with pessimistic parameters, relax as design evolves.

• Efficiency– Revise estimates at job arrival, schedule

more precisely.

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How?

• Actual/nominal?

– actual max. job exec. time < Ci, or

– value Ci used by scheduler is reduced

• Per job/task?

– Ci reduced differently for each job, or

– Ci reduced for all jobs of task

• Use in scheduling decisions, or not?These may or may not make a difference in

sustainability, depending on context.

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Getting specific

• Sustainability depends on the platform and workload model as well as the scheduling algorithm.

• Platform : SMP• Workload model : sporadic task set• Scheduling algorithms : global FTP, EDF,

EDZL

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SMP Platform

• m identical processors• bounded cost for migration, context switch

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Sporadic task workload

• fixed set of tasks• each generates a sequence of jobs• each job of a task has parameters:

– exec. time• Ci is an upper bound

– inter-arrival time• Ti is a lower bound

– deadline, relative to arrival time, Di

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Where is pessimism?

• Ti : lower bound

• Ci : upper bound

• Di : lower bound?

So sustainability means allowing for the following relaxations:

• Longer inter-arrival times• Shorter execution times• Longer deadlines

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Global Scheduling

• Fixed Task Priority (FTP): m tasks with highest task priority allowed to execute

• EDF: m jobs with earliest deadlines allowed to execute

• EDZL: same, except jobs with zero laxity preemptlaxity = remaining-time-to-deadline – remaining-WCET

Common property: Limit of one (or 2, for EDZL) preemption per job allows us to bundle worst-case preemption/migration overhead into WCET of jobs

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Longer inter-arrival times

• Sustainability is built into the sporadic workload model– per-job or per-task– actual, nominal too for algorithms that

do not make use of Ti in scheduling decisions

• So global FTP, EDF, EDZL are sustainable w.r.t. longer inter-arrival times

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Shorter execution times

• Depends on scheduling algorithm• Studied by Ha & Liu (1994) • Non-preemptive scheduling not sustainable• Preemptive work-conserving fixed-job-

priority SMP scheduling with migration is sustainable– FTP and EDF are sustainable

• Proved for job sets, covers sporadic tasks– actual/nominal, per job/task

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EDZL & shorter exec. time

• Difference from FTP & EDF: job priority can change (breaks Ha & Liu assumption)

• EDZL is sustainable

– per-job/task– nominal and actual, or just actual

(Piao, Han, Kim et al. 2006; new proof here)

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Longer deadlines?

• FTP is sustainable, for sporadic tasks• EDF & EDZL sustainability open for

sporadic tasks(not sustainable for job sets*)– exact test (if one exists) might be risky– or scheduler should ignore deadline

changes– sustainable tests are of interest*Apparently also not sustainable for sporadic task sets,

with respect to relaxation of a single job deadline (see appendix).However, it might be sustainable w.r.t. uniform relaxation of deadlineover all jobs of a task.

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Sustainable schedulability test

• If the test says a task set is schedulable, then it remains schedulable if we reduce pessimism in our assumptions, e.g., – decrease task execution times– increase task periods– reduce release-time jitter– lengthen job deadlines

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Relationships

• Algorithm sustainable ⇒ test sustainable• Algorithm not sustainable ⇒

exact test not sustainable

So an inexact test might be better, if it is sustainable and the algorithm is not.

This might be true for global EDF.Do we know any sustainable tests?

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Self-sustainable test(new)

• If the test says a task set is schedulable, then the test still says it is schedulable if we reduce pessimism in our assumptions, e.g.– decrease task execution times– increase task periods– reduce release-time jitter– lengthen job deadlinesDo we know any self-sustainable tests for global EDF?

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BCL Test

min (Dk Ck ),Ii,k ik

m(Dk Ck )

or

Sporadic task system is global EDF schedulable on m unit-capacity processors if for each

min (Dk Ck ),Ii,k ik

m(Dk Ck )

(Bertogna, Cirinei, Lipari ECRTS 2003)

and there is some i≠k for which

k

Ii,k Dk Ck

N i,k (Dk Di) /Ti 1

Ii,k N i,kCi min(Ci,max(0,Dk N i,kTi))

7/3/2009 ECRTS 2009 (Dublin) - Ted Baker 39

• We don’t know.• We have proven BCL test is not self-

sustainable with respect to nominal deadline relaxation.

Is it Sustainable?

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A load-based test

Sporadic task system is global-EDF schedulable on m unit-capacity processors if

where

)()1()( max LOAD

)()1( max mm

(Baruah & Baker, ECRTS 2008)

DBF( i, t)max(0,(t DiTi

1)Ci)

LOAD()maxt0

DBF( i,t) / ti1

n

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Is it sustainable?

• We don’t know, but it is not self-sustainable.

• Is there a better test, that is sustainable?• Yes, this is self-sustainable:

)()2(1

)()1(max)(

max

max

LOAD

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Why one is sustainable and the other not

() ( ( ) 1)max ( )

Load

( ) 1 ( ( ) 2)max ( )

not schedulable

schedulable

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Summary

• Sustainability depends on workload modelas well as platform and scheduling algorithm

• For sporadic tasks and SMP:– Global FTP is fully sustainable– Global EDF & EDZL are (only?) exec. time and inter-

arrival time sustainable

• Self-sustainability is a strong form of sustainability for tests– Not all tests are deadline self-sustainable– But at least one is

7/3/2009 ECRTS 2009 (Dublin) - Ted Baker 44

Suggestion

• Papers on scheduling algorithms, and schedulability tests, should routinely address sustainability.

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The End

questions?

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Appendix 1

A tentative proof that global EDF is not sustainable for sporadic task

systems w.r.t. relaxation of individual job deadlines

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Example

Task WCET (Ci) Deadline (Di) Period (Ti)

A 2 4 8B 2 4 8C 4 8 8D 8 13 13

B

D

A

C

0 62 4 148 10

m = 2 processors

1816 2012

A

B

C

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Claim

• This task appears to be global EDF schedulable.

• This checks out for integer time values up to a scale factor of 3, using brute-force test.

• But it still needs a careful proof.• If this task set is schedulable, it shows that

global EDF is not sustainable for sporadic task systems w.r.t. single-job deadline relaxation.

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If B’s first deadline is relaxed?

B

D

A

0 62 4 148 10 1816 2012

A

BC

D can be blocked for 6 time units, missing its deadline.This does not happen

if both of B’s deadlines are relaxed equally.

D

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If B is just released later?

B

D

A

0 62 4 148 10 1816 2012

A B

C

D is blocked for only 4 time units,since the second B has later deadline than D.

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Appendix 2

Another self-sustainable test for global EDF on sporadic task sets.

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Density Test for Global EDF*

)()1()( max mmsum

n

iisum

1

i

n

i

1max max

),min( ii

ii TD

C

where

Sporadic task system is schedulable on m unit-capacity processors if

(Goossens, Funk, Baruah RTS 2003)

7/3/2009 52ECRTS 2009 (Dublin) - Ted Baker

This is another test for global EDF that is fully self-sustainable.

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Appendix 3

Discussion of Sustainability & Workload Models

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Job Workload models

• A job has an arrival time, deadline, and execution time.

• The execution time may depend on how the job’s execution is scheduled, but there is an upper bound.

• A workload model specifies a collection of possible sets of jobs.

• It is schedulable by an algorithm if every set of jobs that conforms to the model is scheduled to meet all deadlines.

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Kinds of sustainability

1. With respect to differences between actual run-time behavior and model.– e.g., actual execution time is less than

nominal WCET.– a property of the model

2. With respect to changes in the model.– e.g., nominal WCET is reduced– a property of the model and scheduling

algorithm

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Sustainability of Model

• Sustainability can be built into a workload model, e.g., specify for each task

– maximum job execution time, Ci

– minimum inter-arrival time, Ti

– shortest relative deadline, Di

• Otherwise, it may be imposed by the scheduling algorithm.

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Sustainable scheduling algorithm

• If all job sets satisfying a model are schedulable, then sets of jobs that falls short of the model’s assumptions are also schedulable, e.g.,– shorter execution times– longer periods– less release-time jitter– later deadlines