EndToEnd Scheduling

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End-To-End Scheduling
Distributed Systems Seminar, Spring 2003

• Angelo Corsaro Venkita Subramonian
• Department of Computer Science
• Washington University

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Prolog
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Distributed Real-Time Systems

• The key characteristics of Distributed Real-Time
  Systems (DRTS) are
• Tasks in the system require service from several
  processors (Resource are Distributed)
• The correctness of a Task depends on its timely
  completion (Tasks are Real-Time)
• Usually a task in a DRTS can be thought as a set
  of sub-tasks, where each sub-task represent the
  work needed from a given resource
• Execution on a processor
• Transmission over a link
• etc.
• A DRTS Task is characterized by
• End-to-End deadline Time at which the last
  sub-task has to complete
• End-to-End release time Time after which the
  first sub-task can start its execution

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Narrowing the Scope

• The general case of a Distributed Real-Time
  System is too hard
• There are some sub-classes which impose some
  restriction on the general case and are easier to
  reason about
• An interesting sub-class is that of DRTS which
  can be characterized as Flow-Shop or Generalized
  Flow-Shop problems

• The Flow-Shop is one of the abstraction used to
  model Manufacturing Systems like the following

• A key characteristic of the flow-shop is that all
  task execute on all the processors on the same
  order
• Traditional Flow-Shop problems dont have to cope
  with timeliness, but simply try to minimize the
  completion time
• If a DRTS is modeled as a flow shop, each node
  and each communication link can be modeled as a
  processor

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Examples

• The flow-shop model is a good abstraction to
  represent several classes of DRTS
• Examples are
• Distributed Control System
• Multimedia Systems
• Multi-Hop real-time networks
• Interconnected Field-Buses
• etc.etc

• In a video server the sub-task of each stream
  could be modeled as
• Access and Delivery
• Transmission
• Acquisition and Display
• Further decomposition is possible

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Notice That
Also Applies to Single Processor
We can avoid to consider multiple flow-shop at
the same time

• End-to-End timing constraints are not necessarily
  limited to distributed systems
• For instance, task accessing a non-sharable
  resource can be thought as temporarily
  executing on that resource
• This type of task can be characterized as a chain
  of three sub-tasks with an end-to-end deadline

• A system may contains many classes of tasks
• Tasks in each class execute on different
  processors on the same order
• Tasks in different classes execute on different
  processors on different order
• Multiple classes can be scheduled by statically
  partitioning the resources so to create virtual
  processors
• Warning Static partitioning might lead to poor
  utilization

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PART I
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System Model
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The Flow Shop
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The Flow Shop
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Task Models General Results

• A task is preemptable if its execution can be
  interrupted and, at a later point in time,
  resumed
• A task is non-preemptable if its execution cannot
  be interrupted
• Schedulers that make use of the fact that a task
  is preemptable are called preemptive schedulers.

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The Flow Shop with Recurrence
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Visit Graph
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Periodic Flow-Shop
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Scheduling Algorithms for Flow-Shop
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Identical-Length Task Sets
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Algorithm
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Optimality
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Homogeneous Tasks Sets
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Algorithm
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Optimality
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Example
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Example
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Removing Idle Time
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Arbitrary Task Sets
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Algorithms
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Example
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Example
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Example
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PART II
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Synchronization Protocolsin End-To-End
Scheduling
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Scope

• Job-shop model
• Each task needs to execute on a set of processors
  in a certain order
• Each task may require a different order
• Problems in End-to-End scheduling
• Priority assignment
• Assign fixed priorities to tasks so that the
  system is schedulable
• Synchronization of tasks
• Control the releases of subtask instances
  (non-first subtasks)
• Schedulability analysis
• For a given priority assignment and a given
  synchronization protocol, whether every instance
  of each task meets its deadline

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The Synchronization Problem

• Given that
• Priorities are assigned to subtasks in a task
  chain using some fixed priority assignment
  algorithm
• How do we coordinate the release of subtasks in a
  task chain so that
• Precedence constraints among subtasks are
  satisfied
• subtask deadlines are met
• end-to-end deadlines are met

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Synchronization Protocols

• Direct Synchronization (DS) Protocol
• Simple and straightforward
• Phase Modification (PM) Protocol
• Proposed by Bettati
• Used by flow-shop tasks
• Extension called Modified Phase Modification
  (MPM) Protocol
• Release Guard Protocol
• Proposed by Sun

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Synchronization Protocol - Example
P1
P2
(4,2)
T1
(6,2)
T2,2
(6,2)
T2,1
(6,3)
T3
Ti,j jth subtask of task Ti
Task T3 has a phase of 4 time units
(period,execution time)
Period relative deadline of parent task
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Direct Synchronization Protocol

• Greedy strategy
• On completion of subtask
• A synchronization signal sent to the next
  processor
• Successor subtask competes with other
  tasks/subtasks on the next processor

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Direct Synchronization Illustrated
T1
T2,1
On P1
On P2
T2,2
T3 misses deadline
Phase of T3
T3
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Phase Modification Protocol

• Proposed by Bettati
• Release subtasks periodically
• According to the periods of their parent tasks
• Each subtask given its own phase
• Phase determined by subtask precedence constraints

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Phase Modification Protocol Illustrated (1/2)
T1,1
T1,2
T1,3
T1,1
p1
T1,2
p1
T1,3
p1
Phase of T1,2
Phase of T1,3
Actual response time
Estimated worst case response time
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Phase Modification Protocol Illustrated (2/2)
T1
T2,1
On P1
On P2
Phase of T2,2
T2,2
Phase of T3
T3
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Phase Modification Protocol - Analysis

• Periodic Timer interrupt to release subtasks
• Centralized clock or strict clock synchronization
• Task overruns could cause Precedence constraint
  violations

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Modified PM Protocol Illustrated (1/2)
T1,1
T1,2
T1,3
T1,1
p1
Overrun ?
T1,2
p1 ?
Actual response time
Estimated worst case response time
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Modified PM Protocol Illustrated (2/2)
T1
Synch signal delayed
T2,1
On P1
On P2
T2,2
Phase of T3
T3
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Modified PM Protocol - Analysis

• MPM protocol behavior the same as PM under ideal
  conditions
• Ideal conditions Clocks synchronized, no
  overrun
• MPM protocol does not need clock synchronization
• Precedence constraints preserved even in the case
  of overruns
• Upper bound on End-to-End Response time of task Ti

Ri,k is the response time of the kth subtask of
Ti ni is the number of subtasks for the task Ti

• Lower bound on End-to-End Response time of task
  Ti

Actual Response time of nith subtask

• Lower bound high, hence high average EER time

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Release Guard Protocol

• Proposed by Sun
• A guard variable release guard - associated
  with each subtask
• Release guard used to control release of each
  subtask
• Contains next release time of subtask
• Synchronization signals just like MPM
• Release guard updated
• On getting synchronization signal
• During idle time

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Release Guard Protocol Illustrated
T1
T2,1
On P1
On P2
g1,2 4610
g1,2 9
T2,2
Idle time detected
Phase of T3
T3
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Release Guard Protocol - Analysis

• Shares the same advantages as MPM
• Upper bound on EER still the same as MPM
• Since upper bound on release time enforced by
  release guard

Ri,k is the response time of the kth subtask of
Ti ni is the number of subtasks for the task Ti

• Lower bound on EER less than that of MPM
• If there are idle times
• Results in lower average EER

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Comparison of Protocols
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Classification of Protocols
Synchronization Protocols
Without execution control
With execution control
DS
PM
MPM
RG
Task release controlled by predecessor
processor by delaying the synch signal
Task release controlled by same processor by
using guard variables
Phase modification
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Epilogue
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Concluding Remarks

• Flow-Shop can be used to model a series of
  real-world systems
• The Flow-Shop approach assumes that the task set
  is fully characterized i.e. it is amenable to
  off-line analysis, but its not ideal for on-line
  analysis
• Optimal algorithms exists for some easy cases,
  yet some classes of real systems (e.g. some
  control systems, real-time networks) usually fits
  these cases

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References

• End-To-End Scheduling to meet deadlines in
  Distributed Systems, Riccardo Bettati, Jane
  Liu
• Synchronization Protocols in Distributed
  Real-Time Systems,
• Jun Sun and Jane Liu, ICDCS 96
• Fixed Priority End-to-End Scheduling in
  Distributed Real-Time Systems,
• Jun Sun, PhD Thesis