compositional real-time scheduling frameworklee/05cis700/slides_pdf/lec08... · 2005. 10. 5. ·...

October 3, 2005 CIS 700 1

Compositional Real-Time Scheduling Framework

Insik Shin


Outline• Compositional scheduling framework

– Scheduling component model

– Periodic resource model • Schedulability analysis• Utilization bound• Component timing abstraction


Traditional Scheduling Framework• Single real-time task in a single application

CPU

OS Scheduler

Task Task Task

Application Application Application

Hierarchical Scheduling Framework (HFS)


• Multiple real-time tasks with a scheduler in a single application, forming a hierarchy of scheduling

CPU

OS Scheduler

ApplicationScheduler

Task Task


Task Task


Task Task


Compositional Scheduling Framework

CPU

OS Scheduler

Java Virtual Machine

J1(50,3) J2(75,5)

VM Scheduler

Multimedia

T2(33,10)

Digital Controller

T1(25,5)


VM Scheduler’s Viewpoint

CPU

OS Scheduler

Multimedia

T2(33,10)

Digital Controller

T1(25,5)


J1(50,3) J2(75,5)

VM Scheduler

CPU Share

Real-Time Guarantee on CPU Supply


Problems & Approach I

• Resource supply modeling– Characterize temporal property of resource allocations

• we propose a periodic resource model

– Analyze schedulability with a new resource model


OS Scheduler’s Viewpoint

CPU

OS Scheduler


J1(50,3) J2(75,5)

VM Scheduler

Multimedia

T2(33,10)

Digital Controller

T1(25,5) Real-Time Task

Real-Time Demand


Problems & Approach II

• Real-time demand composition– Combine multiple real-time requirements into a single

real-time requirement

Real-Time Constraint



EDF / RM

T1 (p1, e1) T2 (p2, e2) T (p, e)

Compositional Real-time Scheduling Framework

October 3, 2005 CIS 700 10

• Goal – to support compositionality

for timeliness aspect– to achieve system-level

schedulability analysis usingthe results of component-levelschedulability analysis

• Scheduling component modeling

October 3, 2005 CIS 700 11

Scheduling Component Modeling• Scheduling

– assigns resources to workloads by scheduling algorithms

• Scheduling Component Model : C(W,R,A)– W : workload model– R : resource model– A : scheduling algorithm

Resource

Scheduler

WorkloadPeriodic Task WorkloadPeriodic Task

EDF / RM

???

October 3, 2005 CIS 700 12

Resource Modeling• Dedicated resource : always available at full capacity

• Shared resource : not a dedicated resource– Time-sharing : available at some times

– Non-time-sharing : available at fractional capacity

0 time

0 time

0 time

October 3, 2005 CIS 700 13

Resource Modeling• Time-sharing resources

– Bounded-delay resource model [Mok et al., ’01]characterizes a time-sharing resource w.r.t. a non-time-sharing resource

– Periodic resource model Γ(Π,Θ) [Shin & Lee, RTSS ’03]characterizes periodic resource allocations

0 1 2 3 4 5 6 7 8 9 time

October 3, 2005 CIS 700 14

Schedulability Analysis• A workload set is schedulable under a scheduling algorithm

with available resources if its real-time requirements are satisfiable

• Schedulability analysis determines whether

resource demand,which a workload set

requires under a scheduling algorithm

resource supply,which available

resources provide≤

scheduler

resourceworkload workload

October 3, 2005 CIS 700 15

Resource Demand Bound• Resource demand bound during an interval of length t

– dbf(W,A,t) computes the maximum possibleresource demand that W requires under algorithm A during a time interval of length t

• Periodic task model T(p,e) [Liu & Layland, ’73]– i.e., T(3,2)

0 1 2 3 4 5 6 7 8 9 10

tdem

and

October 3, 2005 CIS 700 16

Demand Bound Function - EDF• For a periodic workload set W = {Ti(pi,ei)},

– dbf (W,A,t) for EDF algorithm [Baruah et al.,‘90]

– Example: W = {T1(3,2), T2(4,1)}

iWT i

ept

i

⋅⎥⎦

⎥⎢⎣

⎢= ∑

∈

t)EDF,(W, dbf

0 1 2 3 4 5 6 7 8 9 10

tdem

and

October 3, 2005 CIS 700 17

Resource Supply Bound• Resource supply during an interval of length t

– sbfR(t) : the minimum possible resource supply by resource R over all intervals of length t

• For a single periodic resource model, i.e., Γ(3,2)– we can identify the worst-case resource allocation

October 3, 2005 CIS 700 18

Resource Supply Bound• supply =

• supply =

• sbfR(i) = 1

3

0 time

0 time

1

R(3,2)

i

R(3,2)

October 3, 2005 CIS 700 19

Resource Supply Bound• Resource supply during an interval of length t

– sbfR(t) : the minimum possible resource supply by resource R over all intervals of length t

• For a single periodic resource model, i.e., Γ(3,2)– we can identify the worst-case resource allocation

0 1 2 3 4 5 6 7 8 9 10

tsup

ply

October 3, 2005 CIS 700 20

Supply Bound Function• Resource supply during an interval of length t

– sbfΓ(t) : the minimum possible resource supply by resource R over all intervals of length t

• For a single periodic resource model Γ(Π,Θ)

[ ]otherwise

)1(,2)1( if)1(

))(1()t(sbf

Θ−Π+Θ−Π+∈

⎩⎨⎧

Θ−Θ−Π+−

=Γkkt

kkt

0 1 2 3 4 5 6 7 8 9 10

tsup

ply

October 3, 2005 CIS 700 21

Schedulability Conditions (EDF)• A workload set W is schedulable over a resource

model R under EDF if and only if for all interval i of length t

dbfw(i) ≤ t [BHR90]

dbfw(i) ≤ sbfR(i)

– sbfR(i) : the minimum resource supply by resource Rduring an interval i

– dbfw(i) : the resource demand of workload W during an interval i

Resource demandin an interval

Resource supply during the interval

(from a dedicated resource)

October 3, 2005 CIS 700 22

Schedulability Condition - EDF

024

68

101214

161820

1 4 7 10 13 16 19 22 25 28

supplydemand

• A periodic workload set W is schedulable under EDF over a periodic resource model Γ(Π,Θ)if and only if

)t(sbf t)EDF,dbf(W, 0t Γ≤>∀

time

October 3, 2005 CIS 700 23

Schedulability Condition - RM• A periodic workload set W is schedulable under

EDF over a periodic resource model Γ(Π,Θ)if and only if

• For a periodic workload set W = {Ti(pi,ei)}, – dbf (W,A,t,i) for RM algorithm [Lehoczky et al., ‘89]

)t(sbf i) t,RM,dbf(W,W T 0t i Γ≤∈∀>∀

kTHPT k

i epte

ik

⋅⎥⎥

⎤⎢⎢

⎡+= ∑

∈ )( i) t,RM,(W, dbf

October 3, 2005 CIS 700 24

Utilization Bounds

• Utilization bound (UB) of a resource model R– given a scheduling algorithm A and a resource

model R, UBR,A is a number s. t. a workload set W is schedulable if

A,RW UB U ≤

∑∈WT i

i

i pe

• For a periodic workload T(p,e), utilization UT = e/p• For a periodic workload set W, utilization UW is

scheduler

workload

resource

workload

October 3, 2005 CIS 700 25

Utilization Bounds

• Example: – Consider a periodic resource Γ(Π,Θ), where Π =

10 and Θ = 4, and suppose UB Γ,EDF = 0.4. – Then, a set of periodic task W is schedulable if

– W = {T1(20,3), T2(50,5)} s.t. UW = 0.25, is schedulable

0.4 UW ≤

EDF

workload

Γ(Π=10,Θ=4)

workload

October 3, 2005 CIS 700 26

Utilization Bound - EDF

• For a scheduling component C(W, Γ(Π,Θ),A), where A = EDF, its utilization bound is

• Pmin is the minimum task period (deadline) in W.• k represents the relationship between resource period Π

and the minimum task period Pmin, k ≈ Pmin /Π

)1(2)P(UB minEDF,

Γ

ΓΓ

−+×

=Uk

Uk

October 3, 2005 CIS 700 27

EDF Utilization Bound - Intuition• Observation for a component C(W, Γ(Π,Θ),EDF)

– C is schedulable iff dbf (W,EDF,t) ≤ sbfΓ (t)

Pmint

sbfΓ (t)

dbf (W,EDF,t)

October 3, 2005 CIS 700 28


– C is schedulable iff dbf (W,EDF,t) ≤ sbfΓ (t) – dbf (W,EDF,t) ≤ UW· t

UW· t

Pmint

sbfΓ (t)

dbf (W,EDF,t)

October 3, 2005 CIS 700 29


– C is schedulable iff dbf (W,EDF,t) ≤ sbfΓ (t) – dbf (W,EDF,t) ≤ UW· t– UΓ(t-2(Π-Θ)) ≤ sbfΓ (t)

UW· t

UΓ(t-2(Π-Θ))

Pmint

sbfΓ (t)

dbf (W,EDF,t)

October 3, 2005 CIS 700 30


– C is schedulable iff dbf (W,EDF,t) ≤ sbfΓ (t) – dbf (W,EDF,t) ≤ UW· t– UΓ(t-2(Π-Θ)) ≤ sbfΓ (t) – Therefore, C is schedulable if UW· t ≤ UΓ(t-2(Π-Θ))

UW· t

UΓ(t-2(Π-Θ))

Pmint

October 3, 2005 CIS 700 31

EDF Utilization Bound - Intuition• For a component C(W, Γ(Π,Θ),EDF)

– for all t > Pmin, if UW· t ≤ UΓ(t-2(Π-Θ))then C is schedulable.

UW ≤ UΓ(t-2(Π-Θ)) / t

UW· t

UΓ(t-2(Π-Θ))

Pmint

October 3, 2005 CIS 700 32

Utilization Bound - RM

• For a scheduling component C(W, Γ(Π,Θ),A), where A = RM, its utilization bound is – [Saewong, Rajkumar, Lehoczky, Klein, ’02]

– We generalize this earlier result, where k ≈ Pmin/ Π.

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−⎟

⎠⎞

⎜⎝⎛

×−−

=Γ

ΓΓ 1

233)(UB

n1

RM,U

Unn

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−+−+

×=Γ

ΓΓΓ 1

)1(2)1(22)P,(UB

n1

minRM,UkUknUn

October 3, 2005 CIS 700 33

Component Abstraction• Component timing abstraction

– To specify the collective real-time demands of a component as a timing interface

Periodic (50,7)

EDF

Periodic (70,9) timing

interfacevirtual

real-time task

October 3, 2005 CIS 700 34

Component Abstraction• Component timing abstraction

– To specify the collective real-time demands of a component as a timing interface

Periodic (50,7)

EDF

Periodic (70,9) timing

interface

periodic interfaceΓ(Π,Θ)

periodicresourceΓ(Π,Θ)

October 3, 2005 CIS 700 35

Component Abstraction (Example)• In this example, a solution space of a periodic

resource Γ(Π,Θ) that makes C(W, Γ(Π,Θ),EDF) schedulable is

(a) Solution Space under EDF

0

0.2

0.4

0.6

0.8

1

1 10 19 28 37 46 55 64 73

resource period

reso

urce

cap

acity

Periodic (50,7)

EDF

Periodic (70,9)

Γ(Π,Θ)Γ(Π,Θ)

October 3, 2005 CIS 700 36

Component Abstraction (Example)• An approach to pick one solution out of the solution space

– Given a range of Π, we can pick Γ(Π,Θ) such that UΓ is minimized. (for example, 28 ≤ Π ≤ 46)

(a) Solution Space under EDF

0

0.2

0.4

0.6

0.8

1

1 10 19 28 37 46 55 64 73

resource period

reso

urce

cap

acity

Periodic (50,7)

EDF

Periodic (70,9)

Γ(29,9.86)Γ(Π,Θ)

October 3, 2005 CIS 700 37

Component Timing Abstraction• Component timing abstraction

– To abstract the collective real-time demands of a component as a timing interface

Periodic (50,7)

EDF

Periodic (70,9) periodic

interfaceΓ(29, 9.86)

October 3, 2005 CIS 700 38

Compositional Real-Time Guarantees

T21(25,4)

T22(40,5)

R(?, ?)

EDF

RM

R2(?, ?)R2(10, 4.4)

T11(25,4)

T12(40,5)EDF

R1(?, ?)R1(10, 3.1)

October 3, 2005 CIS 700 39

Compositional Real-Time Guarantees

T21(25,4)

T22(40,5)

R(?, ?)

EDF

RM

R(5, 4.4)

R2(10, 4.4)

T2(10, 4.4)

T11(25,4)

T12(40,5)EDF

R1(10, 3.1)

T1(10, 3.1)

October 3, 2005 CIS 700 40

Abstraction Overhead

• For a scheduling component C(W, Γ(Π,Θ), A), its abstraction overhead (OΓ) is 1-

UU

W

Γ

Periodic (50,7)

EDF

Periodic (70,9) periodic

interfaceΓ(29, 9.86)

UW=0.27 UΓ=0.34

October 3, 2005 CIS 700 41

Abstraction Overhead Bound

• For a scheduling component C(W, Γ(Π,Θ), A), its abstraction overhead (OΓ) is

– A = EDF

– A = RM

W

W

UkU×+−×

≤Γ2

)1(2O EDF,

( )( )

1

12122log

1O RM, −

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−+

≤Γ

W

W

UkUk

October 3, 2005 CIS 700 42

Abstraction Overhead• Simulation Results

– with periodic workloads and periodic resource under EDF/RM

– the number of tasks n : 2, 4, 8, 16, 32, 64– the workload utilization U(W) : 0.2~0.7– the resource period : represented by k

October 3, 2005 CIS 700 43

Abstraction Overhead

00.05

0.10.15

0.20.25

0.30.35

2 4 8 16 32 64

The Number of Tasks

Analytical Bound - EDF Simulation Result - EDF

• k= 2, U(W) = 0.4

October 3, 2005 CIS 700 44

Summary• Compositional real-time scheduling framework

- with the periodic model [Shin & Lee, RTSS ‘03]

1. resource modeling– utilization bounds (EDF/RM)

2. schedulability analysis• exact schedulability conditions (EDF/RM)

3. component timing abstraction and composition• overhead evaluation

– upper-bounds and simulation results

October 3, 2005 CIS 700 45

Future Work• Extending our framework for handling

– Soft real-time workload models– non-periodic workload models– task dependency

October 3, 2005 CIS 700 46

References

• Insik Shin & Insup Lee,“Periodic Resource Model for Compositional Real-Time Gaurantees”, the Best Paper of RTSS 2003.

• Insik Shin & Insup Lee,“Compositional Real-time Scheduling Framework”, RTSS 2004.

October 3, 2005 CIS 700 47

THE

THE END

END

ENDTHE

THANK YOU

Compositional Real-Time Scheduling FrameworkOutlineTraditional Scheduling FrameworkHierarchical Scheduling Framework (HFS)Compositional Scheduling FrameworkVM Scheduler’s ViewpointProblems & Approach IOS Scheduler’s ViewpointProblems & Approach IICompositional Real-time Scheduling FrameworkScheduling Component ModelingResource ModelingResource ModelingSchedulability AnalysisResource Demand BoundDemand Bound Function - EDFResource Supply BoundResource Supply BoundResource Supply BoundSupply Bound FunctionSchedulability Conditions (EDF)Schedulability Condition - EDFSchedulability Condition - RMUtilization BoundsUtilization BoundsUtilization Bound - EDFEDF Utilization Bound - IntuitionEDF Utilization Bound - IntuitionEDF Utilization Bound - IntuitionEDF Utilization Bound - IntuitionEDF Utilization Bound - IntuitionUtilization Bound - RMComponent AbstractionComponent AbstractionComponent Abstraction (Example)Component Abstraction (Example)Component Timing AbstractionCompositional Real-Time GuaranteesCompositional Real-Time GuaranteesAbstraction OverheadAbstraction Overhead BoundAbstraction OverheadAbstraction OverheadSummaryFuture WorkReferences

compositional real-time scheduling frameworklee/05cis700/slides_pdf/lec08... · 2005. 10. 5. ·...

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