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Outline
Background
Interconnection Networks Colored Petri Net
Using Coloured Petri Nets with Time (CPN Tools) to Model - - PowerPoint PPT Presentation
Using Coloured Petri Nets with Time (CPN Tools) to Model - - PowerPoint PPT Presentation
Using Coloured Petri Nets with Time (CPN Tools) to Model Interconnection Network Amin Ranjbar December 2008 Outline Background Interconnection Networks Colored Petri Net Motivation Model and Design Numerical Results
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Background: What is Interconnection Network?
A set of processors with local memories
which communicate through a network.
Terminology
Topology: The way nodes are interconnected. Routing Algorithm: Determines the path from
source to destination.
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Background: Interconnection Network Topology
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Background: Interconnection Network Topology
Hypercube
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Background: Interconnection Network – Routing Algorithm
Topologies are simple and regular Very low delay and extra high bandwidth are
needed
Simple routing algorithms are developed for
interconnection networks (deadlock is an important concern)
Example: e-cube routing in hypercube
networks
Messages are routed along first dimension, then
routing continues in other dimensions.
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Background: Interconnection Network – Routing Algorithm (e-Cube)
(0,0,0) (0,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,1,1)
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Background: Interconnection Network – Routing Algorithm (e-Cube)
(0,0,0) (0,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,1,1) (1,1,1)
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Background: Interconnection Network – Routing Algorithm (e-Cube)
(0,0,0) (0,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,1,1) (1,1,1)
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Background: Interconnection Network – Routing Algorithm (e-Cube)
(0,0,0) (0,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,1,1) (1,1,1)
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Background: Interconnection Network – Routing Algorithm (e-Cube)
(0,0,0) (0,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) (0,1,1) (1,1,1)
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Background: What is CPN?
Modelling language for systems where
synchronisation, communication, and resource sharing are important.
Combination of Petri Nets and Programming
Language.
Control structures, synchronisation, communication,
and resource sharing are described by Petri Nets.
Data and data manipulations are described by
functional programming language.
CPN models are validated by means of
simulation and verified by means of state spaces and place invariants.
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Background: What is CPN?
Places describe the state of the system. Places carry markers, called tokens. Transitions describe the actions of the system Arcs tell how actions modify the state and when
they occur
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Background: CPN Advantages
The relationship between CP-nets and ordinary
Petri nets (PT-nets) is analogous to the relationship between high-level programming languages and assembly code.
In theory, the two levels have exactly the
same computational power.
In practice, high-level languages have much
more modelling power – because they have better structuring facilities, e.g., types and modules.
CPN has:
Color (type) Time
Hierarchy
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Motivation
The interconnection network plays a central role in
determining the overall performance of a multi- computer system.
If
the network cannot provide adequate performance, for a particular application, nodes will frequently be forced to wait for data to arrive.
The best approach for performance evaluation of
interconnection networks is a simulator which can provide an extensible framework for evaluating different interconnection networks.
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Design and Model (One Dimensional – System)
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Design and Model (Node)
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Design and Model (Two Dimensional – System)
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Design and Model (Two Dimensional Node)
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Design and Model (Three Dimensional – System)
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Design and Model (Three Dimensional Node)
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Results: One Dimensional
One Dimensional
50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate Average Total Latency
Message latency Queue Delay
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Results: One Dimensional
Two Dimensional
50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate Average Total Latency
Message latency Queue Delay
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Results: Three Dimensional
Three Dimensional
50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate Average Total Latency
Message latency Queue Delay
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Numerical Results:
50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2
Message Generation Rate Average Message Total Latency
One Dimension Two Dimension Three Dimension
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Numerical Results:
50 100 150 200 250 300 350 400 0.2 0.4 0.6 0.8 1 1.2
Message Generation Rate Average Sending Queue Delay
One Dimension Two Dimension Three Dimension
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Conclusion
Average Message latency in three
dimensional hypercube is always more than two or one dimensional.
Average Message Latency increases by
increasing message generation rate.
Average Queue length in one dimensional
hypercube is always more than two or three dimensional.
Average Queue length increases by
increasing message generation rate.
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