A Compositional Framework for Real-Time Guarantees

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A Compositional Framework for Real-Time Guarantees

• Insik Shin and Insup Lee
• Real-time Systems Group
• Systems Design Research Lab
• Dept. of Computer and Information Science
• University of Pennsylvania

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Scheduling Framework Example
OS Scheduler
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Motivating Example
VM Scheduler
OS Scheduler
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VM Schedulers Viewpoint
VM Scheduler
OS Scheduler
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Problems Approach I

• Resource supply modeling
• Characterize temporal property of resource
  allocations
• we propose a periodic resource model
• Analyze schedulability
• with the new resource model

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OS Schedulers Viewpoint
VM Scheduler
OS Scheduler
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Problem II

• Real-Time Composition
• Combine multiple real-time requirements into a
  single real-time requirement guaranteeing
  schedulability
• Example periodic task model T(p,e)

Real-Time Constraint
Real-Time Constraint
Real-Time Constraint
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Approach II

• Simple approach T(p,e)
• p LCM (T1, T2) LCM (T1, T2)
  T1xN1 T2xN2
• e p x (U1 U2), Ui ei/pi

Deadline Miss !
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Approach II

• Our approach periodic task model T(p,e)

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Outline

• Scheduling component modeling
• Periodic resource model
• Scheduling component schedulability analysis
• Scheduling component composition
• Combine the real-time guarantees of multiple
  components into the real-time guarantee of a
  single component

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Scheduling Component Modeling

• Scheduling
• assigns resources to workloads by algorithms
• Scheduling Component Model M(W,R,A)
• W workload model
• R resource model
• A scheduling algorithm

Scheduler
EDF / RM
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Resource Modeling

• Dedicated resource
• Available all the time at its full capacity

0
time
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Resource Modeling

• Dedicated resource
• Available all the time at its full capacity
• Fractional resource (slow resource)
• Available all the time at its fractional capacity

0
time
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Resource Modeling

• Dedicated resource
• Available all the time at its full capacity
• Fractional resource (slow resource)
• Available all the time at its fractional capacity
• Partitioned resource
  FeMo 02
• Available all some times at its full capacity

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time
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Resource Modeling

• Dedicated resource
• Available all the time at its full capacity
• Fractional resource (slow resource)
• Available all the time at its fractional capacity
• Partitioned resource
• Available all some times at its full capacity
• Periodic resource R(period, allocation time) (ex.
  R(3,2))
• Available periodically at its full capacity

0
time
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Scheduling Component Analysis

• Schedulability conditions
• Exact conditions for EDF/RM
• Schedulability bounds
• Utilization bounds for periodic workload under
  EDF/RM
• Capacity bounds for periodic resource under EDF/RM

Scheduler
EDF / RM
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Schedulability Conditions (EDF)

• Scheduling component M(W,R,EDF) is schedulable
  iff for all interval length t,
• demandw(EDF,t) supplyR(t) RTSS03
• demandw(EDF,t) the maximum resource demand of
  workload W for an interval length t
• supplyR(t) the minimum resource supply by
  resource R for an interval length t

demand(EDF,t)
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• supply
• supply
• supplyR(3) 1

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R(3,2)
0
time
1
R(3,2)
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Schedulability Conditions (RM)

• Scheduling component M(W,R,RM) is schedulable iff
  
• for all task Ti(pi,ei),
• ri(R) pi RTSS03
• ri(R) the maximum response time of task Ti over
  R.
• the smallest time t s.t.
• demand(RM,i,t) supplyR(t)

demand(RM,i,t)
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Schedulability Conditions (RM)

• Scheduling component M(W,R,RM) is schedulable iff
  
• for all task Ti(pi,ei),
• ri(R) pi RTSS03
• Example of finding the maximum response time
  ri(R)

resource demand
supplyR(t)
demand(RM,i,t)
time
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Motivating Example for Capacity Bound

• Given a task group G such that
• Scheduling algorithm EDF
• A set of periodic tasks T1(3,1), T2(7,1) ,
• model the timing requirements of the task
  group with a periodic task model
• G (3, 1.43) based on utilization does not work !!

Deadline miss for T2
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Motivating Example (2)

• Given a task group G such that
• Scheduling algorithm EDF
• A set of periodic tasks T1(3,1), T2(7,1) ,
• model the timing requirements of the task
  group with a periodic task model
• G (3, 2.01) works !!

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Capacity Bounds

• Resource capacity
• For a periodic resource R(p,e), its capacity is
  e/p.
• Capacity bound of a component C(W, R(p,e), A)
  CB(C)
• C is schedulable if CB(C) e/p
• How to get the capacity bounds of C(W,R(p,e),A)
• assumption the period p of R is given.
• using the exact schedulability conditions, we can
  get the minimum capacity of R satisfying the
  condition.

CB(C) 3.1/10
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Compositional Real-Time Guarantees
EDF
RM
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Compositional Real-Time Guarantees
RM
EDF
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Conclusion

• Summary
• Periodic resource model
• Scheduling component modeling and anaylsis
• Scheduling component composition
• Future work
• To evaluate the composition overhead in current
  framework
• To extend our framework with other resource
  models for
• Efficient composition w.r.t utilization and
  complexity
• Ensure composition properties, i.e.,
• C1 (C2 C3) (C1 C2 ) C3
• (C1, C2, C3) ((C1, C2), C3)

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Schedulability Conditions (EDF)

• Scheduling component M(W,R,EDF) is schedulable
  iff for all interval length t,
• demandw(t) t BHR90
• demandw(t) supplyR(t)
• demandw(t) the maximum resource demand of
  workload W over all intervals of length t
• supplyR(t) the minimum resource supply by
  resource R over all intervals of length t

Resource supply during the interval (from a
dedicated resource)
Resource demand in an interval
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Schedulability Conditions (RM)

• Scheduling component M(W,R,RM) is schedulable iff
  
• for all task Ti(pi,ei),
• ri pi AB93
• durationR(ri) pi
• ri the maximum response time of task Ti
• the maximum resource demand of W to
  finish Ti
• durationR(t) the maximum time that resource R
  takes to supply a t-time-unit resource

Duration to receive ri-time-unit resource
allocation
Deadline to receive ri-time-unit resource
allocation
Deadline to receive ri-time-unit resource
allocation
Max. Duration to receive ri-time-unit resource
allocation