Real-Time Scheduling Analysis for Multiprocessor Platforms Marko Bertogna PhD dissertation Scuola...

Real-Time Scheduling Analysisfor

Multiprocessor Platforms

Marko Bertogna

PhD dissertation

Scuola Superiore S.Anna, Pisa, Italy

19/05/2008 Marko Bertogna - PhD

dissertation 2

Overview The Multicore Revolution Real-Time Multiprocessor Systems:

existing results Schedulability Analysis for global

schedulers Experimental evaluation Conclusions Other research activities


dissertation 3

Main Contributions Systematization of existing results for

RT scheduling and schedulability analysis on MP

Polynomial and pseudo-polynomial schedulability tests for

Work-conserving schedulers FP EDF EDZL

Experimental comparison of existing techniques


dissertation 4

Real-Time Systems Solid theory of single processor systems

Optimal schedulers, tight schedulability tests, shared resource protocols, bandwidth reservation schemes, hierarchical schedulers, OS, etc.

Much less results for multiprocessors Many NP-hard problems, few optimal results,

heuristic approaches, simplified task models, only sufficient schedulability tests, etc.

Do we really need to investigate Multi-Processors Real-Time Systems?


dissertation 5

As Moore’s law goes on… Number of transistor/chip doubles every 18 to

24 mm months


dissertation 6

…heating becomes a problem

0,1

1

10

100

1000

71 74 78 85 92 00 04 08

Power

40048008

80808085

8086286

386486

PentiumP1

P2

P4

Pentium Tejascancelled!

P3

Hot-plate

NuclearReactor

STOP

Year

Power (W)

P V f: Clock speed limited to less than 4 GHz


dissertation 7

Solution

Denser chips with transistor operating at lower frequencies

MULTICORE SYSTEMS

Use a higher number of slower logic gates


dissertation 8

The Multicore invasion Intel’s Core2, Itanium, Xeon: 2, 4 cores AMD’s Opteron, Athlon 64 X2, Phenom: 2, 4 cores IBM-Toshiba-Sony Cell processor: 8 cores (PSX3) Microsoft’s Xenon: 3 cores (Xbox 360) ARM’s MPCore: 4 cores Sun’s Niagara UltraSPARC: 8 cores Tilera’s TILE64: 64-core Nios II: x soft Cores TI, Freescale, Atmel, Broadcom,Picochip

(picoArray up to 300 DSP cores), ...


dissertation 9

Identical vs heterogenous coresARM’s MPCore STI’s Cell Processor

• 4 identical ARMv6 cores • One Power Processor Element (PPE)• 8 Synergistic Processing Element (SPE)


dissertation 10

System model Platform with m identical processors Task set with n periodic or sporadic

tasks i

Period or minimum inter-arrival time Ti

Worst-case execution time Ci

Deadline Di

Utilization Ui=Ci/Ti, density i=Ci/min(Di,Ti)


dissertation 11

CPU1

CPU2

Problems addressed Run-time scheduling problem Schedulability problem

1

2

3

4

5

?

CPU3


dissertation 12

Assumptions Independent tasks Job-level parallelism prohibited

the same job cannot be contemporarily executed on more than one processor

Preemption and Migration support a preempted task can resume its execution

on a different processor Cost of preemption/migration integrated

into task WCET


dissertation 13

Single system-wide queue or multiple per-processor queues:

CPU1

CPU2

CPU3

Global vs partitioned scheduling

CPU1

CPU2

CPU3

Global scheduler Partitioned scheduler


dissertation 14

Partitioned Scheduling The scheduling problem reduces to:

Global (work-conserving) and partitioned approaches are incomparable

Bin-packingproblem

Uniprocessorschedulingproblem

+NP-hard in thestrong sense

Various heuristics used: FF, NF, BF, FFDU, BFDD, etc.

Well known

EDFUtot ≤ 1

RM(RTA)

...


dissertation 15

Global scheduling The m highest priority ready jobs are

always the one executing Work-conserving scheduler

No processor is ever idled when a task is ready to execute.

CPU1

CPU2

CPU3


dissertation 16

Global scheduling: advantagesLoad automatically balancedEasier re-scheduling (dynamic loads, selective shutdown, etc.)Lower average response time (see queueing theory)More efficient reclaiming and overload managementNumber of preemptions

Migration cost: can be mitigated by proper HW (e.g., MPCore’s Direct Data Intervention)Few schedulability tests Further research needed


dissertation 17

Uniprocessor scheduling EDF optimal for arbitrary job collections Exact schedulability conditions

linear test for implicit deadlines: Utot ≤ 1 Pseudo-polynomial test for constrained and arbitrary

deadlines [Baruah et al. 90] Optimal priority assignments for sporadic and

synchronous periodic task systems RM for implicit deadlines DM for constrained deadlines

Exact pseudo-polynomial schedulability test for FP

Response Time Analysis (RTA)


dissertation 18

Global Scheduling No optimal scheduler known for general task

models Pfair optimal for implicit deadlines: Utot ≤ m

preemption and synchronization issues Classic schedulers are not optimal (Dhall’s effect):

Hybrid schedulers: EDF-US, RM-US, DM-DS, AdaptiveTkC, fpEDF, EDF(k), EDZL, …

m light tasks1 heavy task

Utot1


dissertation 19

Global scheduling: main results

Only sufficient schedulability tests Utilization-based tests (implicit deadlines)

EDF Goossens et al.: Utot ≤ m(1-Umax)+Umax fpEDF Baruah: Utot ≤ (m+1)/2 RM-US Andersson et al.: Utot ≤ m2/(3m-2)

Polynomial tests EDF, FP Baker: O(n2) and O(n3) tests EDZL Cirinei,Baker: O(n2) test

Pseudo-polynomial tests EDF, FP Fisher,Baruah: load-based tests


dissertation 20

Density-based tests EDF: tot ≤ m(1-max)+max

EDF-DS[1/2]: tot ≤ (m+1)/2

DM: tot ≤ m(1–max)/2+max DM-DS[1/3]: tot ≤ (m+1)/3

[ECRTS’05]

[OPODIS’05]

Gives highest priority to (at most m-1) tasks having t ≥ 1/2, and schedules the remaining ones with EDF

Gives highest priority to (at most m-1) tasks having t ≥ 1/3, and schedules the remaining ones with DM (only constrained deadlines)


dissertation 21

Critical instant A particular configuration of releases that leads

to the largest possible response time of a task. Possible to derive exact schedulability tests

analyzing just the critical instant situation. Uniprocessor FP and EDF: a critical instant is

when all tasks arrive synchronously all jobs are released as soon as permitted

Response Time Analysis for uniprocessors FP the response time of task k is given by the fixed

point of Rk in the iteration

ihp i

kkk C

T

RCR

i


dissertation 22

Multiprocessor anomaly Synchronous periodic arrival of jobs is

not a critical instant for multiprocessors:

1 = (1,1,2)2 = (1,1,3)3 = (5,6,6)

Synchronous periodic situation

Second job of 2 delayed by one unit

from [Bar07]

Need to find pessimistic situations to derive sufficient schedulability

tests


dissertation 23

Introducing the interferenceIk = Total interference suffered by task k

Iki = Interference of task i on task k

kik

ikkkkkk RI

mCRICR )(

1)(

m

RIRI k

ik

kk

)()(

k

k

kCPU1CPU2CPU3

rkrk+Rk

Ik2Ik1

Ik2

Ik3Ik4Ik5

Ik6

Ik8Ik5

Ik3

Ik7

Ik3


dissertation 24

Limiting the interference

k

k

kCPU1CPU2CPU3

rkrk+Rk

Ik2Ik1

Ik2

Ik3Ik4Ik5

Ik6

Ik8Ik5

Ik3

Ik7

Ik3

It is sufficient to consider at most the portion (Rk-Ck+1) of each term Iik in the sum

1)()( kkkkkik CRRIRI

kikkk

ikkk CRRI

mCR )1),(min(

1It can be proved that WCRTk is given by the fixed point of:


dissertation 25

Bounding the interference

Exactly computing the interference is complex

Pessimistic assumptions:1. Bound the interference of a task with

the workload:

2. Use an upper bound on the workload.

)()( kikik RWRI


dissertation 26

Bounding the workloadConsider a situation in which:

The first job executes as close as possible to its deadline

Successive jobs execute as soon as possible

)()()()( LCLNLwLW iiiii

i

iii T

CDLLN )(

))(,min()( iiiiiii TLNCDLCL where:

CiiL

Di

Ci Ci Ci

Tiεi

(# jobs excluded the last one)

(last job)


dissertation 27

RTA for generic global schedulers

An upper bound on the WCRT of task k is given by the fixed point of Rk in the iteration:

The slack of task k is at least:

kikkkikk CRRw

mCR )1),(min(

1

kkk RDS

Rk Sk


dissertation 28

Improvement using slack values

Consider a situation in which: The first job executes as close as possible to its

deadline Successive jobs execute as soon as possible

)()()()( LCLNLwLW iiiii

i

iii T

CDLLN )(

))(,min()( iiiiiii TLNCDLCL where:

CiiL

Di

Ci Ci Ci

Tiεi

(# jobs excluded the last one)

(last job)


dissertation 29

Improvement using slack values

Consider a situation in which: The first job executes as close as possible to its

deadline Successive jobs execute as soon as possible

where:

i

iiiii T

SCDLSLN ),(

)),(,min(),( iiiiiiiiii TSLNSCDLCSL

CiiL

Di

Ci Ci Ci

TiSi

),(),(),()( iiiiiiii SLCSLNSLwLW


dissertation 30

RTA for generic global schedulers


kikkikikk CRSRw

mCR )1),,(min(

1

kkk RDS

1.

2.

If a fixed point Rk ≤ Dk is reached for every task k in the system, the task set is schedulable with any work-conserving global scheduler.


dissertation 31

Iterative schedulability test

1. All slacks initialized to zero2. Compute slack lower bound for tasks 1,

…,n if higher than old value update slack bound If lower, do nothing

3. If all tasks have a positive slack lower bound return success

4. If no slack has been updated for tasks 1,…,n return fail

5. Otherwise, return to point 2


dissertation 32

RTA refinement for Fixed Priority

The interference on higher priority tasks is always null:

An upper bound on the WCRT of task k can be given by the fixed point of Rk in the iteration:

kiRI kik ,0)(

kikkikikk CRSRw

mCR )1),,(min(

1

kkk RDS 2.

1.


dissertation 33

RTA refinement for EDF A different bound can be derived analyzing the

worst-case workload in a situation in which: The interfering and interfered tasks have a common deadline All jobs execute as late as possible

),()( ikikik SRwRI


kkk RDS 2.

1.

kikkikiikikk CRSDwSRw

mCR )1),,(),,(min(

1


dissertation 34

Complexity Pseudo-polynomial complexity Fast average behavior

We verified the schedulability of millions of task sets in a few minutes on a normal device.

Lower complexity for Fixed Priority systems at most one slack update per task, if slacks are

updated in decreasing priority order. Possible to reduce complexity limiting the

number of rounds


dissertation 35

Polynomial complexity test

A simpler test can be derived avoiding the iterations on the response times

A lower bound on the slack of k is given by:

The iteration on the slack values is the same

Performances comparable to RTA-based test

Complexity down to O(n2)


dissertation 36

Experimental results for EDF• 2 processors

• Constrained deadlines

• 1.000.000 task sets generated

• Our test is constantly superior at all utilizations

generatedtask sets

our test

Improvement over existing solutions

Task set utilization

task sets

Bertogna et al.’05Baker et al.’07Goossens et al.’03I-BCL EDFTotal task sets


dissertation 37

Experimental results for FP

• 2 processors



• Our test is constantly superior at all utilizations

generatedtask sets

our test

task sets

Density boundBaker et al.’07Bertogna et al.’05I-BCL FPTotal task sets



dissertation 38

FP vs EDF• 4 processors



• our FP test is constantly superior to all tests at every utilization

generatedtask sets

our FP test

task sets

our EDF test

Goossens et al.’03I-BCL EDFBaker et al.’07I-BCL FPTotal task sets



dissertation 39

Conclusions Multiprocessor Real-Time systems are a

promising field to explore. Still few existing results far from tight

conditions. We contributed filling this gap. Future work:

Find tighter schedulability tests. Use our techniques to analyze the efficiency of other

scheduling algorithms (EDZL, EDF-US, FP-DS, etc). Take into account exclusive resources access. Integrate into Resource Reservation framework.


dissertation 40

The end


dissertation 41

Other research activities

Limited-preemption EDF Reducing Resource Holding Times Shared resources and open

environments


dissertation 42

ARM’s MPcore


dissertation 43

Frequency and power f = operating frequency V = supply voltage (V~=0.3+0.7 f)

Reducing the voltage causes a higher frequency reduction

Ileak = leakage current (becomes non-negligible) P = Pdynamic + Pstatic = power consumed

Pdynamic ACV2f (main contributor until hundreds nm) Pstatic VIleak (always present, due to subthreshold

and gate-oxide leakage) Reducing V allows a quadratic reduction of

Pdynamic


dissertation 44

Power density

40048008

80808085

8086

286386

486Pentium® proc

P6

1

10

100

1000

10000

1970 1980 1990 2000 2010

Year

Po

wer

Den

sity

(W

/cm

2)

Hot Plate

NuclearReactor

RocketNozzle


dissertation 45

How many cores in the future? Intel’s 80 core prototype already

available Able to transfers a TB of data/s (Core 2 Duo

reaches 1.66GB data/s) To be released in 5 years


dissertation 46

Beyond 2 billion transistors/chip

Intel’s Tukwila Itanium based 2.046 B FET Quad-core 65 nm technology 2 GHz on 170W 30 MB cache 2 SMT 8 threads/ck


dissertation 47

Intel’s timeline Year Processor

ManufacturingTechnology

FrequencyNumber of transistors

1971 4004 10 m 108 kHz 23001972 8008 10 m 800 kHz 35001974 8080 6 m 2 MHz 45001978 8086 3 m 5 MHz 290001979 8088 3 m 5 MHz 290001982 286 1,5 m 6 MHz 1340001985 386 1,5 m 16 MHz 2750001989 486 1 m 25 MHz 12000001993 Pentium 0,8 m 66 MHz 31000001995 Pentium Pro 0,6 m 200 MHz 55000001997 Pentium II 0,25 m 300 MHz 75000001999 Pentium III 0,18 m 500 MHz 95000002000 Pentium 4 0,18 m 1,5 GHz 420000002002 Pentium M 90 nm 1,7 GHz 550000002005 Pentium D 65 nm 3,2 GHz 2910000002006 Core 2 Duo 65 nm 2,93 GHz 2910000002007 Core 2 Quad 65 nm 2,66 GHz 5820000002008 Core 2 Quad X 45 nm >3 GHz 820000000


dissertation 48

From 4004 (1971) to Pentium D (2005): Tech: 10 um 65 nm : 150 x f: 100kHz 3 GHz: 25000 x # MOS: 2.300291.000.000: 125.000 x P: 0.2W100W: 500 x

Vdd reduced (from 5V to ~1V) Not all MOS change state

Great part of chip occupied by cache

f Vdd-Vtt Ileak Vdd, 1/Vtt


dissertation 49

Intel 4004 (1971) Intel Pentium IV (2000)


dissertation 50

Itanium temperature plot


dissertation 51

CPU1

CPU2

CPU3

Problems addressed Run-time scheduling problem Schedulability problem

1

2

3

4

5

?


dissertation 52

Incandescent light bulb: 25-100 W

Compact fluorescent lights: 5-30 W

Typical car: 25 kW Human climbing stairs: 200 W 1 kWh = 1 kW constantly

supplied for 1 h ENEL: 0.13-0.18 €/kWh

Device Power Lavastoviglie 2000 W Asciuga Biancheria 2000 W Forno Elettrico 2000 W Friggitrice Elettrica 1800 W

Lavatrice 1600 W Asciugacapelli 1300 W

Ferro da stiro 1200 W

Aspirapolvere 1100 W Forno a microonde 800 W

Tostapane 800 W Robot da cucina 500 W

Frigorifero 160 W

Televisore 50 W


dissertation 53

Density and utilization bounds


dissertation 54

Uniprocessor feasibility

Deadline modelTask model

Implicit Constrained or Arbitrary

Sporadic or Synchronous

Periodic

Linear test:Utot ≤ 1

Unknown complexity;Pseudo-polynomial test if Utot< 1:

EDF until Utot/(1- Utot) · max(Ti-Di)

Asynchronous Periodic

Linear test:Utot ≤ 1

Strong NP-hard;Exponential test: EDF until 2H+Dmax+rmax


dissertation 55

Uniprocessor static priority run-time scheduling


Implicit Constrained

Arbitrary


Periodic

RM optimality

DM optimality

Unknown complexity; Audsley’s bottom-up

algorithm (exponential complexity)


Unknown complexity;Audsley’s bottom-up algorithm (exponential

complexity)


dissertation 56

Uniprocessor static priority feasibility

Deadline model

Task model

Implicit Constrained Arbitrary


Periodic

Pseudo-polynomial test: RM until Tmax or

RTA

Pseudo-polynomial test: DM until Dmax or

RTA

Unknown complexity;Audsley’s bottom-up

algorithm (exponential)


Unknown complexity

Strong NP-hard

Audsley’s bottom-up algorithm (exponential)


dissertation 57

Uniprocessor static priority schedulability




Periodic

Pseudo-polynomial

simulation until Tmax or RTA

Pseudo-polynomial

simulation until Dmax or RTA

Unknown complexity;Lehoczky’s

test (exponential)


Strong NP-hard;Simulation until 2H+rmax or other exponential tests


dissertation 58

Multiprocessor feasibility



Sporadic

Linear test:Utot ≤ m

Unknown complexity;Synchronous periodic not a critical

instant

Synchronous Periodic

Unknown complexity; Horn’s algorithm in

(0,H]

Unknown complexity


Strong NP-hard


dissertation 59

Multiprocessor run-time scheduling



Sporadic P-fair, GPS Requires clairvoyance

Synchronous Periodic P-fair, GPS,

LLREF, EKG, BF

Unknown complexity; Clairvoyance not

needed;Horn’s algorithm in

(0,H]

Unknown complexity; Clairvoyanc

e not needed


Unknown complexity; Clairvoyance not needed


dissertation 60

Feasibility conditions

Σi Ci /min(Di,Ti) ≤ m

load > m

load* > m

Utot > m

Sufficient feasibility and schedulability tests

???

Not

fe

asib

leF

easi

ble


dissertation 61

Multiprocessor static job priority feasibility

Deadline model

Task modelImplicit Constrained Arbitrary

SporadicUnknown

complexity


instant


Unknown complexity;Simulation until hyperperiod for all N!

job priority assignments

Unknown complexity


Unknown complexity

Strong NP-hard


dissertation 62

Multiprocessor static job priority schedulability

Deadline model


SporadicUnknown

complexity


instant


Unknown complexity;Simulation until hyperperiod

Unknown complexity


Strong NP-hard


dissertation 63

Multiprocessor static priority run-time scheduling


ImplicitConstrain

edArbitrary

Periodic (synchronous or asynchronous)

Unknown complexity; Cucu’s optimal priority assignment

Sporadic Unknown complexity;


dissertation 64

Multiprocessor static priority feasibility

Deadline model


SporadicUnknown complexity;

Synchronous periodic not a critical instant


Strong NP-hard; Simulation until hyperperiod for all n! priority assignments


Strong NP-hard; Simulation on exponential feasibility interval for all n!

priority assignments


dissertation 65

Multiprocessor static priority schedulability

Deadline model


SporadicUnknown complexity;

Synchronous periodic not a critical instant


Unknown complexity; Simulation until hyperperiod


Strong NP-hard; Simulation on exponential feasibility interval


dissertation 66

RTA for Uniprocessors For FP, the worst-case response time of a

task is given by the first instance released at a critical instant

For EDF, it is given by an instance in a busy interval starting with a critical instant

With these observations it is possible to compute the WCRT of all tasks. Example: for FP, the WCRT of a task k is given by the fixed point of:

ihp i

kkk C

T

RCR

i


dissertation 67

RTA refinement for EDF Still valid the bound: A different bound can be derived analyzing

the worst-case workload in a situation in which:

The interfering and interfered tasks have a common deadline

All jobs execute as late as possible

),()( ikikik SRwRI

CiiDk

Di

Ci Ci

Ti

k

Si

),()()( ikEDFik

ikk

ik SDwDIRI

ii

ikik C

T

DDDBF

1

with:

i

i

iikki

ikiki S

C

TDBFDCDBFSDw

0

,min),(

),()( ikikik SRwRI

and:


dissertation 68

RTA refinement for EDF A different bound can be derived analyzing

the worst-case workload in a situation in which:

The interfering and interfered tasks have a common deadline

All jobs execute as late as possible

CiiDk

Di

Ci Ci

Ti

k

Si

),()()( ikEDFik

ikk

ik SDwDIRI i

i

ikik C

T

DDDBF

1

with:

i

i

iikki

ikiki S

C

TDBFDCDBFSDw

0

,min),(

),()( ikikik SRwRI

and:


dissertation 69

Polynomial complexity test

A lower bound on the slack of k is given by:

For EDF:

For FP:


dissertation 70

Limiting the number of iterations

Real-Time Scheduling Analysis for Multiprocessor Platforms Marko Bertogna PhD dissertation Scuola...

Documents

Transcript of Real-Time Scheduling Analysis for Multiprocessor Platforms Marko Bertogna PhD dissertation Scuola...