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Scheduling of Embedded RealTime Systems: CP, SA or B

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Uses lower-bound estimates to prune branches. Pros and Cons: ... Better (safe) estimations of the optimum for different objective functions. ... – PowerPoint PPT presentation

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Title: Scheduling of Embedded RealTime Systems: CP, SA or B


1
Scheduling of Embedded Real-Time Systems CP, SA
or BB?
  • presented by Cecilia Ekelin
  • Department of Computer Engineering
  • Chalmers University of Technology
  • http//www.ce.chalmers.se/cekelin

2
Embedded System Design
S
A
A
S
T5
T2
T1
P3
P2
Messages
Network bus
P1
T3
T6
Processor node
M6,7
P5
P4
A
A
S
S
T7
T4
Software tasks
Hardware architecture
3
Embedded System Characteristics
  • Application-specific Interacts with a
    well-defined environment.
  • Safety-critical Timing and execution constraints
    must be guaranteed off-line.
  • Cost-effective The design is subject to
    economical optimization.

How should the tasks be allocated and scheduled
onto the nodes?
4
Algorithm Design Problem
Specification
  • Modeling complex constraints
  • Multi-objective contradicting objectives
  • Search low average run-time complexity

HW/SW partitioning
Architecture Tasks
Allocation Scheduling
Model
Implementation
Product
5
Approaches BB
  • Branch-and-Bound
  • Generates a search-tree of all possible
    schedules.
  • Uses lower-bound estimates to prune branches.
  • Pros and Cons
  • Guaranteed to find a feasible/optimal schedule.
  • Exponential runtime in the worst-case.
  • Lower bounds have to be accurate (complicated).
  • Difficult to introduce new constraints.

6
Approaches SA
  • Simulated annealing
  • Makes random changes to an (initial) schedule.
  • Uses an energy-function containing objectives and
    constraints to measure the solution quality.
  • Pros and Cons
  • Flexible.
  • No search heuristics are needed.
  • Polynomial worst-case runtime.
  • - No solution guarantee.
  • - Requires a well-balanced energy-function.

7
Approaches CP
  • Constraint programming
  • - Formulates the problem using variables and
    constraints.
  • - Uses constraint propagation and search to find
    a valid variable assignment.
  • Pros and Cons
  • Constraints and objectives are handled
    independently.
  • Constraints are used pro-actively to reduce the
    search-space.
  • General-purpose tools and algorithms exist.
  • Solution guarantee.
  • - Exponential runtime in the worst-case.

8
Real-Time Scheduling
  • Basic system model
  • A set of processor nodes Pj
  • A set of periodic tasks Ti
  • Task properties
  • Worst-Case Execution Time (WCET)
  • Release time (R)
  • Deadline (D)

T1
T1
T1
T1
P1
T2
T2
T2
P2
0
lcp
9
Constraint Programming (Example)
  • Uses library clp(FD) in SICStus Prolog.
  • Variables
  • The processor Ni 1,2
  • The start time Si 0,lcp
  • Constraints
  • Release times Si gt Ri
  • Deadlines Si WCETi lt Di
  • Non-preemptive disjoint2(rect(Si, WCETi, Ni,
    1))

10
Modeling
11
Optimization
  • Single-objective
  • - Feasible solution x, objective function f
  • x is optimal if f(x)ltf(x) (for all x)
  • Objectives
  • Network communication
  • Load-balance
  • Maximum lateness
  • Jitter
  • Multi-objective
  • Several contradicting objective functions fi(x)
  • How should these be combined to define an optimal
    solution?

12
Multi-Objective Optimization
  • Objective based definition SA,BB,CP
  • Weighted sum f(x) ci fi(x)
  • Constraint based definition CP
  • Pareto-optimal fi(x)lt fi(x)
  • Combination CP
  • gi(x)100 (fimax(x) - fi(x))/(fimax(x) -
    fimin(x))
  • f(x) gi(x) subject to gi(x)gtmin gi(x)

13
Search Performance
  • Intelligent heuristics are essential for CP and
    BB to experience acceptable runtimes.
  • Heuristics are used to
  • Guide the search towards promising regions in the
    search space (i.e. schedule construction).
  • Avoid and discard bad or inferior regions (e.g.,
    lower bounds and symmetry exclusion).

14
Search Heuristics (CP)
  • Schedule construction
  • Assign allocation variables before scheduling
    variables.
  • - Group tasks according to interaction.
  • Lower-bounds
  • Statically solve a simpler (relaxed) problem.
  • E.g., k-cut for communication
  • Symmetry exclusion
  • Avoid mirrored schedules on identical processors.
  • Extends BB result for heterogeneous processors.

15
Experimental Results
  • CP versus SA (Di Natale Stankovic 1995)
  • Setup 86 task sets, 59 tasks/set, 2 nodes,
  • fjitter, resource and locality constraints

x-axis runtimes (secs) y-axis solved instances
16
Experimental Results
  • CP versus BB (Jonsson 1998)
  • Setup 100 task sets, 15 tasks/set, 4 nodes,
  • flateness, communication constraints

-Example Ex 1 with locality constraints, Ex 2
without
17
Conclusions
A constraint programming framework for real-time
systems scheduling provides powerful modeling
capabilities and yet manages to reduce the
average run-time complexity.
18
Future Work
  • Improving the performance
  • - Better (safe) estimations of the optimum for
    different objective functions.
  • Improving the modeling
  • Introducing more variability in the parameters.
  • Introducing energy-awareness.
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