Optimization of Real-Time Systems
with Deadline Miss Ratio
Constraints
Sorin Manolache, Petru Eles, Zebo Peng
{sorma, petel, zebpe}@ida.liu.se
Linköping University, Sweden
Introduction
 Task
execution times are not fixed
 stochastic task execution times
 Probabilistic
behaviour and implicitly probabilistic guarantees
 Ratio of missed deadlines is an important indicator of system
performance, obviously of stochastic nature
 soft real-time systems
 Optimizing
this indicator by means of mapping of tasks to processors
and assignment of priorities to tasks
 multiprocessor applications
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Contribution
 Task
mapping and priority assignment heuristic for deadline miss
ratio minimization
driven by
 Performance
analysis algorithm that obtains the deadline miss ratio
per task for a given task mapping alternative
 The
heuristic is iterative and transformational

 The analysis algorithm is fast and sufficiently accurate
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Outline
 Stochastic
task execution times
 Problem formulation
 Mapping heuristic
 Deadline miss ratio analysis
 Experimental results
 Conclusions
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Probability
Stochastic execution times
Expensive hardware
0% missed deadlines
Probability
Task execution time
Affordable hardware
<5% missed deadlines
Task execution time
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Problem formulation, input
 Task
graphs
 Task
periods
2s
 Task
execution time probability
density functions
transmission time
probability density functions
2s
4s
 Message
 Task
6s
and task graph deadlines
10s
 Processors, buses, interconnection
Probability
 Deadline
miss 4%
miss ratio thresholds
10s
miss 10%
Task execution time
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
miss 2%
critical
6
Problem formulation, output
1
1
 Task
mapping
 Task
priority assignment
1
2
2
1
such that
devi is minimized, where
2
3
mi  Ti
0
3

devi  mi  Ti mi  Ti , ti not critical
1

mi  Ti , ti critical

mi is the deadline miss ratio of
task ti and Ti is its deadline
miss ratio threshold
4
1
3
2
2
3
2
4
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Mapping heuristic
on Tabu search [Glover, 1989]
 At each iteration, an improvement of the cost function is sought by
modifying the problem parameters (task mapping and/or task
priority)—a move
 The reversed modification is kept tabu for a small number of
iterations
 Thus, the heuristic is forced to exit local minima
Cost function
 Based
Problem parameters
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Mapping heuristic
Initial solution
Determine
candidate moves
No
Satisfied?
Yes
Final solution
Candidate
moves
Current solution
Evaluate
candidate move
No
All candidates
evaluated?
Yes
Select best
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Moves
 One
move is performed every iteration
 A move changes the mapping and/or the priority of exactly one task
 The “best” move is selected and leads to the next temporary
solution
 At
each step, there are N(N+P-2) move outcomes to evaluate
(Exhaustive Neighbourhood search, ENS)
 N—number of tasks
 P—number of processors
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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RNS
 By
intelligently selecting a subset of promising candidate moves, the
search could be significantly sped up
 Restricted Neighbourhood Search (RNS)
 Tasks
are ranked and only the moves operating on the top [N/2]
tasks are considered
 For each selected task, the candidate processors are ranked and
only the top 2 processors are considered
 RNS
reduces the set of candidate moves at each iteration P times
compared to ENS
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Task ranking
A
A
A
A
B
C
B
E
B
C
B
C
C
F
…
B
D
A
D
D
…
E
F
E
F
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
E
F
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Deadline miss ratio analysis
 Exact
DMR analysis for monoprocessor systems [ECRTS 2001]
 Theoretically applicable to multiprocessor systems, however it
becomes prohibitively expensive
 Faster and approximate analysis for multiprocessor systems [ICCAD
2002]
 However it is still too slow to be plugged into an optimization loop

 Analysis
complexity is reduced by two means:
 Task start and finish times are approximated with discrete values
 Two types of dependencies between some random variables are
neglected
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Deadline miss ratio analysis
A
Z
Y
X
Z
Y
X
Z
Y
X
P(X>max(Y, Z)) = P(X>Y)  P(X>Z)
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Deadline miss ratio analysis
A
C
B
A
B
C
Time
P(LC(t)) = P(LC(t)|AC<t)
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Deadline miss ratio analysis
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Experimental setup
 396
randomly generated benchmarks
 # of tasks ranging from 20 to 40
 # of processors ranging from 3 to 8
 Mapping
and priority assignment with
Exhaustive neighborhood search (ENS)
Restricted neighborhood search (RNS)
 Comparison of cost function values and run times
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Experimental results
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Experimental results
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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LO-AET
Laxity optimization based on average execution times of tasks
 Why
not
Use average task execution times instead of task execution
time probability density functions
Optimize a performance indicator based on average task
execution times, e.g. average laxity
 And hope that it will lead also to an optimal deadline miss ratio
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Experimental results
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Experimental results
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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Conclusions
 Task
mapping and priority assignment heuristic for soft real-time
applications with stochastic task execution times
 Fast analysis for approximation of task and task graph deadline
miss ratios
 Average execution time based heuristics fall short of providing
quality results
Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng
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