Stable Phase Theorem - Provided that PRkN-1

. TN , k N, the pipeline system assumes a periodic behavior after a finite initial phase.The complete behavior is characterized the unique trace:

ρ = tinit (inc(i) fqN-1? eqN? cN eqN-1! tL fqN ! d(i *TN)) ω.

tinit – trace recording the initial phase of the system execution.

tstable– stable phase: (inc(i) fqN-1? eqN? cN eqN-1! tL fqN ! d(i *TN)) ω

tL – subtrace recording the interleaved execution of C1..CN-1.

Analysis of a Time-driven Chain of Dependent Components

M.A. Weffers-Albu 1 , J.J. Lukkien 1 , P.D.V. v.d. Stok 1,2

The approach we took was to provide a characterization of streaming applications execution to determine performance attributes and provide insight into best design practices for optimising these attributes. Performance attributes: Number of Context Switches (NCS), Response Time of tasks and chain (RT), Resources utilization (RU) for CPU and memory.

1. Introduction The goal of our work is the prediction and optimization of performance attributes to provide guaranteed and optimized Quality of Service (QoS) for real-time streaming applications.

2. TriMedia Streaming Software Architecture

A TSSA media processing application - graph:

• Nodes: - software components

• Edges: - finite buffers (queues) that transport the data stream from one component to the next component in the graph.

eqi

fqi-1 fqi

eqi-1

Component

Processing function(ci)

Get Full Packet Put Full Packet

Put Empty Packet Get Empty Packet

Affiliation1) Eindhoven University of Technology

Department of Mathematics and Computer Science

HG 6.57, P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands2) Philips Research NatLab

Prof. Holstlaan 4, 5656AA Eindhoven, The Netherlands

3. Modeling chain execution

About the AuthorAlina Weffers-Albu received her P.D.Eng. in Software Technology from the Department of Mathematics and Computer Science of the Eindhoven University of Technology (TU/e) in 2003. In July 2003 Alina started a Ph.D. project within the SAN group of the same department, in collaboration with Philips Research Laboratories Eindhoven.

Corollaries

• Given the computation times of components actions, ρ and eager can be calculated at design time.

• Hence NCS, task and chain RT, RU for CPU and memory can also be calculated.

• Minimum Queue Capacity: 1

• Minimum NCS at Stable Phase: P(C1)<…<P(CN-1) and Cap(fqi)=2, i < N-1.

The systems we analyse are streaming applications using the TriMedia Streaming Software Architecture (TSSA) and executing on a TriMedia device.

4. ConclusionsResults

•Characterization of streaming applications execution

•Prediction and optimisation of performance quality attributes.

Impose

predicates

until

obtain

trace and schedule

which specify

the system behavior.

Unique trace ρ, eager schedule eager

eq2 eqN-1

fq1

eq1

fqN-1

C1C2 CN

fq2

…

Typical program of component Ci :

j=0;

while (true) do

{ inc(j);

receive( fqi-1, p);

receive( eqi, q);

process_func_ci(p, q);

send( eqi-1, p);

send( fqi, q);

delay( j*TN ); }

Express behavior as traces:

Tr(Ci): { (fqi-1?, eqi?, ci, eqi-1!, fqi!) },

Tr(CN): {j = 0 (inc(j) fqN-1? eqN? cN eqN-1! fqN! d(j *TN)) .}.

QoS Requirement – CN executes always strictly at rate TN.

First step solution - rate of production higher than rate of consumption for packets in fqN-1:

PRkN-1

. TN, k N

schedule consistent traces

arbitrary interleavings

channel consistent traces

priority consistent traces

• Chain RT cannot be optimized

•CN drives execution in the same way as a minimum priority data-driven component in a chain composed of only data-driven components.

Time-driven component

Data-driven components

enc.hwscaler

enc.

disk : non-scalable

dmux

audiodec.

dec.sharpenh.

main: scalabale

DVD

mixer

mixer : non-scalable

scaler

digitizer: non-scalable

digit

audiorend

read

writer

dec

enc.

scalable task

task

hierarchical task

connection to HW IO

buffer

data transfer

pip: scalable

Courtesy of E.F.M. Steffens

tinitidle time idle time idle time

TN

…