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 � Conclusion 2

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. 3

Background: Interconnection Network Topology 4

Background: Interconnection Network Topology � Hypercube 5

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. 6

Background: Interconnection Network – Routing Algorithm (e-Cube) (1,1,0) (1,1,1) (0,1,0) (0,1,1) (1,0,0) (0,1,1) (0,0,0) (0,0,1)

Background: Interconnection Network – Routing Algorithm (e-Cube) (1,1,0) (1,1,1) (0,1,0) (0,1,1) (1,0,0) (0,1,1) (0,0,0) (1,1,1) (0,0,1)

Background: Interconnection Network – Routing Algorithm (e-Cube) (1,1,0) (1,1,1) (0,1,0) (0,1,1) (1,0,0) (0,1,1) (0,0,0) (0,0,1) (1,1,1)

Background: Interconnection Network – Routing Algorithm (e-Cube) (1,1,0) (1,1,1) (0,1,0) (0,1,1) (1,0,0) (0,1,1) (1,1,1) (0,0,0) (0,0,1)

Background: Interconnection Network – Routing Algorithm (e-Cube) (1,1,0) (1,1,1) (1,1,1) (0,1,0) (0,1,1) (1,0,0) (0,1,1) (0,0,0) (0,0,1)

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. 12

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 13

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 14

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. 15

Design and Model (One Dimensional – System) 16

Design and Model (Node) 17

Design and Model (Two Dimensional – System) 18

Design and Model (Two Dimensional Node) 19

Design and Model (Three Dimensional – System) 20

Design and Model (Three Dimensional Node) 21

Results: One Dimensional One Dimensional 400 350 Message latency 300 Average Total Latency Queue Delay 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate 22

Results: One Dimensional Two Dimensional 400 Message latency 350 Queue Delay 300 Average Total Latency 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate 23

Results: Three Dimensional Three Dimensional 400 Message latency 350 Queue Delay 300 Average Total Latency 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate 24

Numerical Results: 400 350 One Dimension Average Message Total Latency Two Dimension 300 Three Dimension 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate

Numerical Results: 400 350 One Dimension Two Dimension Average Sending Queue Delay 300 Three Dimension 250 200 150 100 50 0 0 0.2 0.4 0.6 0.8 1 1.2 Message Generation Rate

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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