October 3, 2005 CIS 700 1 Compositional Real-Time Scheduling Framework Insik Shin
October 3, 2005 CIS 700 1
Compositional Real-Time Scheduling Framework
Insik Shin
October 3, 2005 CIS 700 2
Outline• Compositional scheduling framework
– Scheduling component model
– Periodic resource model • Schedulability analysis• Utilization bound• Component timing abstraction
October 3, 2005 CIS 700 3
Traditional Scheduling Framework• Single real-time task in a single application
CPU
OS Scheduler
Task Task Task
Application Application Application
Hierarchical Scheduling Framework (HFS)
October 3, 2005 CIS 700 4
• Multiple real-time tasks with a scheduler in a single application, forming a hierarchy of scheduling
CPU
OS Scheduler
ApplicationScheduler
Task Task
ApplicationScheduler
Task Task
ApplicationScheduler
Task Task
October 3, 2005 CIS 700 5
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)
October 3, 2005 CIS 700 6
VM Scheduler’s Viewpoint
CPU
OS Scheduler
Multimedia
T2(33,10)
Digital Controller
T1(25,5)
Java Virtual Machine
J1(50,3) J2(75,5)
VM Scheduler
CPU Share
Real-Time Guarantee on CPU Supply
October 3, 2005 CIS 700 7
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
October 3, 2005 CIS 700 8
OS Scheduler’s Viewpoint
CPU
OS Scheduler
Java Virtual Machine
J1(50,3) J2(75,5)
VM Scheduler
Multimedia
T2(33,10)
Digital Controller
T1(25,5) Real-Time Task
Real-Time Demand
October 3, 2005 CIS 700 9
Problems & Approach II
• Real-time demand composition– Combine multiple real-time requirements into a single
real-time requirement
Real-Time Constraint
Real-Time Constraint
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
EDF Utilization Bound - Intuition• Observation for a component C(W, Γ(Π,Θ),EDF)
– 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
EDF Utilization Bound - Intuition• Observation for a component C(W, Γ(Π,Θ),EDF)
– 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
EDF Utilization Bound - Intuition• Observation for a component C(W, Γ(Π,Θ),EDF)
– 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