october 3, 2005cis 7001 compositional real-time scheduling framework insik shin
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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
CPU
OS Scheduler
Task Task Task
• Single real-time task in a single application
Application Application Application
October 3, 2005 CIS 700 4
Hierarchical Scheduling Framework (HFS)
CPU
OS Scheduler
Application Scheduler
Task Task
Application Scheduler
Task Task
Application Scheduler
Task Task
• Multiple real-time tasks with a scheduler in a single application, forming a hierarchy of scheduling
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)
October 3, 2005 CIS 700 10
Compositional Real-time Scheduling Framework
• Goal – to support compositionality for timeliness aspect– to achieve system-level schedulability analysis using the results of component-level schedulability 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
scheduler
resourceworkload workload
resource demand,which a workload set
requires under a scheduling algorithm
resource supply,which available
resources provide≤
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 possible
resource 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
t dem
and
October 3, 2005 CIS 700 16
• 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)}
Demand Bound Function - EDF
i
WT ie
p
t
i
t)EDF,(W, dbf
0 1 2 3 4 5 6 7 8 9 10
t dem
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
0 time
0 time
3
1
R(3,2)
R(3,2)
i
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
t sup
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)
0 1 2 3 4 5 6 7 8 9 10
t sup
ply
otherwise
)1(,2)1( if
)1(
))(1()t(sbf
kkt
k
kt
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 R during 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
0
2
4
6
8
10
12
14
16
18
20
1 4 7 10 13 16 19 22 25 28
supply
demand
Schedulability Condition - EDF
• 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
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
k
THPT ki e
p
te
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 p
e• 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,
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)
Pmin
t
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
Pmin
t
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))
Pmin
t
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))
Pmin
t
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))
Pmin
t
October 3, 2005 CIS 700 32
• 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.
Utilization Bound - RM
1
23
3)(UB
n
1
RM,U
Unn
1
)1(2
)1(22)P,(UB
n
1
minRM,Uk
UknUn
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
periodicresourceΓ(Π,Θ)
periodic interfaceΓ(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-U
U
W
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
Uk
U
2
)1(2O EDF,
1
12122
log
1O RM,
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
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