Performance Estimation for
Embedded Systems with
Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
Department of Computer and Information Science
Linköpings universitet
Sweden
1 of 12
May 3, 2000
Motivation and Characteristics
Performance estimation.
n Worst case delay on the system execution time.
Characteristics:
n Distributed hard real-time applications.
n Heterogeneous system architectures.
n Fixed priority preemptive scheduling.
n Systems with data and control dependencies.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Schedulability Analysis
Schedulability test:
n The worst case response time of each process is
compared to its deadline.
Process models:
n Independent processes;
n Data dependencies: release jitter, offsets, phases;
n Control dependencies: modes, periods, recurring tasks.
Message:
n The pessimism of the analysis can be significantly reduced
by considering the conditions during the analysis.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
3 of 12
May 3, 2000
Conditional Process Graph
Subgraph corresponding
to D∧C∧K
P
P00
P
PP111
P
PP222
C
C
PP44
D
P
PP12
12
K 12
K
P
PP666
PP55
P
PP888
P
PP999
P
PP14
14
14
PP15
15
PP13
13
P
PP16
16
16
P
PP17
17
17
P
PP10
10
10
n First processor
n Second processor
n ASIC
D
P
PP333
C
PP77
P
PP11
11
11
P
P18
18
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Problem Formulation
Input
n An application modelled using conditional process graphs (CPG).
n Each CPG in the application has its own independent period.
n Each process has a worst case execution time, a deadline, and a priority.
n The system architecture and mapping of processes are given.
Output
n Worst case response times for each process.
Performance estimation for systems modelled using
conditional process graphs.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Example
P
P00
27 P
P11
C
C
30 P
P22
P
P99
30 P
P66
25 P
P33
CPG
25 P
P10
10
24 P
P44
22 P
P77
19 P
P55
Worst Case Delays
No conditions Conditions
32 P
P11
11
P
P12
12
Γ1
120
100
Γ2
82
82
Γ2: 150
P
P88
Γ1: 200
Deadline: 110
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
6 of 12
May 3, 2000
Task Graphs with Data Dependencies
n K. Tindell: Adding Time-Offsets to Schedulabilty Analysis, Research Report
Offset: fixed interval in time between the arrival of sets of tasks.
Can reduce the pessimism of the schedulability analysis.
Drawback: how to derive the offsets?
n T. Yen, W. Wolf: Performance Estimation for Real-Time Distributed Embedded
Systems, IEEE Transactions On Parallel and Distributed Systems
Phase (similar concept to offsets).
Advantage: gives a framework to derive the phases.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Schedulability Analysis for Task Graphs
DelayEstimate(task graph G, system S)
for each pair (Pi, Pj) in G
maxsep[Pi, Pj]=∞
end for
worst case response times and
step = 0
upper bounds for the offsets
repeat
LatestTimes(G)
EarliestTimes(G)
lower bounds for the offsets
for each Pi ∈ G
MaxSeparations(Pi)
end for
until maxsep is not changed or step < limit
return the worst case delay dG of the graph G
end DelayEstimate
maximum separation:
maxsep[Pi, Pj]=0 if the execution of
the two processes never overlaps
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
8 of 12
May 3, 2000
Schedulability Analysis for CPGs, 1
Two extreme solutions:
n Ignoring Conditions (IC)
Ignore control dependencies and apply the schedulability
analysis for the (unconditional) task graphs.
n Brute Force Algorithm (BF)
Apply the schedulability analysis after each of the CPGs in the
application have been decomposed in their constituent
unconditional subgraphs.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Schedulability Analysis for CPGs, 2
In between solutions:
n Conditions Separation (CS)
Similar to Ignoring Conditions but uses the knowledge about
the conditions in order to update the maxsep table:
maxsep[Pi, Pj] = 0 if Pi and Pj are on different conditional paths.
n Relaxed Tightness Analysis (two variants: RT1, RT2)
Similar to the Brute Force Algorithm, but tries to reduce the execution
time by removing the iterative tightening loop (relaxed tightness)
in the DelayEstimation function.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
10 of 12
May 3, 2000
Average Percentage Deviation [%]
Experimental Results
100
80
Ignoring Conditions
60
Conditions Separation
40
Relaxed Tightness 1
20
Relaxed Tightness 2
Brute Force
0
80
160
240
320
400
Number of processes
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
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May 3, 2000
Conclusions
n Performance estimation for hard real-time systems with
control and data dependencies.
n Modelling using conditional process graphs that capture
both the flow of data and that of control.
n Heterogeneous architectures, fixed priority scheduling.
n Five approaches to the schedulability analysis of such systems.
n Extensive experiments and a real-life example show that:
The pessimism of the analysis can be significantly reduced
by considering the conditions during the analysis.
Performance Estimation for Embedded Systems with Data and Control Dependencies
Paul Pop, Petru Eles, Zebo Peng
12 of 12
May 3, 2000