Perform ance Estim ation for Em bedded System s w ith Data and - - PowerPoint PPT Presentation

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Perform ance Estim ation for Em bedded System s w ith Data and Control Dependencies

Paul Pop, Petru Eles, Zebo Peng

Department of Computer and I nformation Science Linköpings universitet Sweden

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 2 o f 12 May 3 , 2 0 0 0

Motivation and Characteristics

Perform ance estim ation. Worst case delay on the system execution time. Characteristics: Distributed hard real-time applications. Heterogeneous system architectures. Fixed priority preemptive scheduling. Systems with data and control dependencies.

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 3 o f 12 May 3 , 2 0 0 0

Schedulability Analysis

Message: The pessimism of the analysis can be significantly reduced by considering the conditions during the analysis. Schedulability test: The worst case response time of each process is compared to its deadline. Process m odels: Independent processes; Data dependencies: release jitter, offsets, phases; Control dependencies: modes, periods, recurring tasks.

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 4 of 12 May 3 , 2 0 0 0

Conditional Process Graph

P4 P4 P5 P5 P7 P7 P13 P13 P15 P15

First processor Second processor ASIC

C C D D P0 P18 P1 P1 P2 P2 P3 P3 P6 P6 P8 P8 P9 P9 P10 P10 P11 P11 P12 P12 P14 P14 P16 P16 P17 P17 C K K P0 P18 P1 P2 P3 P6 P8 P9 P10 P11 P12 P14 P16 P17

Subgraph corresponding to D∧C∧K

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Problem Form ulation

I nput

An application modelled using conditional process graphs (CPG).

Each CPG in the application has its own independent period. Each process has a worst case execution time, a deadline, and a priority. The system architecture and mapping of processes are given.

Output

Worst case response times for each process. Perform ance estim ation for system s m odelled using conditional process graphs.

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 6 of 12 May 3 , 2 0 0 0

Exam ple

P3 P3 P5 P5 C P0 P0 P1 P1 P6 P6 P2 P2 P7 P7 P4 P4 P8 P8 C 27 30 24 19 25 30 22

Γ1: 20 0

P11 P11 P12 P12 P9 P9 P10 P10 25 32

Γ2: 150

Worst Case Delays CPG No conditions Conditions Γ1 120 100 Γ2 82 82

Deadline: 110

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 7 o f 12 May 3 , 2 0 0 0

Task Graphs w ith Data Dependencies

• 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?

• 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.

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 8 of 12 May 3 , 2 0 0 0

DelayEstimate(task graph G, system S) for each pair (Pi, Pj) in G maxsep[Pi, Pj]=∞ end for step = 0 repeat LatestTimes(G) EarliestTimes(G) 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

Schedulability Analysis for Task Graphs

worst case response times and upper bounds for the offsets lower bounds for the offsets maximum separation: maxsep[Pi, Pj]=0 if the execution of the two processes never overlaps

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Schedulability Analysis for CPGs, 1

Tw o extrem e solutions:

Ignoring Conditions (IC) Ignore control dependencies and apply the schedulability analysis for the (unconditional) task graphs. Brute Force Algorithm (BF) Apply the schedulability analysis after each of the CPGs in the application have been decomposed in their constituent unconditional subgraphs.

Pe rfo rm an ce Estim atio n fo r Em be dde d Syste m s w ith Data an d Co n tro l De pe n de n cie s Paul Po p, Pe tru Ele s, Ze bo Pe n g 10 of 12 May 3 , 2 0 0 0

Schedulability Analysis for CPGs, 2

I n betw een solutions:

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. 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.

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Experim ental Results

20 4 0 6 0 8 0 10 0 8 0 16 0 24 0 320 4 0 0

Average Percentage Deviation [ % ] Number of processes Relaxed Tightness 2 Relaxed Tightness 1 Conditions Separation Brute Force Ignoring Conditions

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Conclusions

Perform ance estim ation for hard real-time systems with control and data dependencies. Modelling using conditional process graphs that capture both the flow of data and that of control. Heterogeneous architectures, fixed priority scheduling. Five approaches to the schedulability analysis of such systems. 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.