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Laurea Specialistica Telecommunications Engineering

19 July 2010

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

Author

Massimo Monti

Supervisors

• Prof. Marco Luise

(University of Pisa)

• Prof. Filippo Giannetti

(University of Pisa)

• Prof. Christian Tschudin (University of Basel)

Thomas Meyer

(University of Basel)

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

2

Chemically Inspired Communication System Chemical Model Communication Model

Sender 1 Sender 2 Receiver 1 Receiver 2

Loss

Ack1 Ack2

Ch

IN1 IN2 OUT

Dynamics Congestion Avoidance CNP (T.Meyer, to be published)

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

3

Chemical Metaphor......

Molecules  Packets Chemical vessel  Communication network nodes Chemical reactions  Communication links Chemical virtual machines  Computers with standard CPU Chemical model implementation: Fraglets simulator.

Concept of Chemical Networking Protocols (CNPs)

Equilibrium Self-Healing Robustness Self-Optimization Life-like properties observed in nature

Goal

Self-Protection

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

4

User Information

User information is encoded inside packets. A certain type of molecules (species) contain the same string of symbols. e.g. [node2 HELLO WORLD]

System State Information

System state information is encoded in the packet rate itself.

• Concentration of a chemical species ≡ Number of molecules of that species.
• Reactions happen according to the «Law of mass action»:

Reaction Rate Species concentration Randomize queue entries Schedule the service

CNP Information Encoding

Forwarding as fast as possible

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

5

Dynamics Forecast

• Communication protocol implementations Abstract chemical models
• Chemical model dynamics are analyzable
• Dynamics analysis

Chemical model optimization Protocol implementation optimization

CNP Properties

mapped lead to lead to

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

6

The Chemical Master Equation (CME) Standard Analysis of Network Dynamics (1/2) The chemical model as a continuous time discrete space Markov jump process

(System state equals species concentration)

Dynamics of the system probability distribution governed by the CME

Features: Exact analysis of the stochastic dynamical behavior of a model Very high computational complexity Solution not always possible

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

7

The Differential Rate Equations Approximation (DREs) Standard Analysis of Network Dynamics (2/2) Deterministic approximation of the exact stochastic behavior.

Features: Decrease of the computational complexity (still high) High concentration systems required Dependence on initial condition

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

8

The New Signal Processing Approach Concept

Chemical networks as systems of blocks and interconnections. Concentration seen as a continuos-time continuos-value signal.

Features

• Transfer function description

Generality of results

• Based on Differential Rate Equations (DREs) approximation

(DREs model description Laplace transform solution)

Low computational complexity Deterministic approximation Dependence on initial condition

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

9

Our Analysis Approach of Linear CNPs

1 Output N Output Loop Network Parallel of N-Node Series of N-Node

The Disperser CNP

Disperser Features: Elementary Reactions Connections Typology Species ≡ Vessels ≡ Nodes Impulse input ≡ Injenction of molecules Distributed average computation Molecules equally distributed over the network

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

10

Node 1 Node 2 Simulink Schematic Node 4 Node 3

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

11

Frequency Transforms Analysis Results (1/2)

The Disperser CNP

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

12

Impulse Responses Analysis Results (2/2)

The Disperser CNP

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

13

State Variable Representation Block Diagram

• State matrix
• Input matrix
• Output matrix
• Direct transmission matrix

System Control Theory (1/2) Analyzed systems must be Linear Time Invariant (LTI)

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

14

Frequency Transform Frequency characterization of species concentration Step Response Dynamical behavior of the network Analyzed systems must be Linear Time Invariant (LTI) System Control Theory (2/2)

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

15

• Traffic Generation of Tx.1
• Tx.1 Output Rate
• Tx.2 Output Rate
• Channel Limitation
• Actual Network Output Rate
• Selective Feedbacks

A Non-Linear CNP

Non-Linear Chemical Model DREs with Non-Linearities

• Species
• Molecules
• Reactions
• Chemical Homeostasis
• Species Dilution Flow
• Reaction Coefficients

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

16

System linearization around a fixed point (steady states) State Variable Representation

Non-Linear Chemical Model DREs with Non-Linearities

Metabolic Control Analysis to Non-Linear CNPs Concept:

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

17

Frequency Transform W (s)

(n)

Tx 1 Tx 2 Rx 1 Rx 2

V

• ut

Ack1 Ack2 R V

• ut

Vin ‘

Analysis Results (1/2)

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

18

Step Response Analysis Results (2/2)

Tx 1 Tx 2 Rx 1 Rx 2

V

• ut

Ack1 Ack2 R V

• ut

Vin ‘

Laurea specialistica 19 July 2010

Massimo Monti

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols

19

Discussion Protocol behavior was not easily predictable.

• Now, all linear chemical networks are analyzable, with

similar procedures to those shown.

• Non-linear networks are linearizable (MCA), with the

side effect of a high computational complexity.

• Even links with delay have been analyzed (not shown).
• Bi-stable systems.
• Fixed point near the saddle point.
• Stochasticity of CNPs briefly introduced.

Conclusion Limits & Future

!

End

Specialistic Degree 19 July 2010

Telecommunications Engineering Transmission and Communication Systems

A Signal Processing Approach to the Analysis of Chemical Networking Protocols Massimo Monti

Thank You

End