Thinking Architecturally An information theory and complex system viewpoint

Architecture in computer science view Computer science is based on three main principles Reduction A problem can be re-expressed as another problem or a set of other problems Recursion State machine concept You need a fix point to leverage on it Entropic representation of information You can represent all information through bits

Software architecture Algebraic view A software architecture Define the set of software component that can calculate all defined specification Any specification should be reducible to a recursive (state machine based) combination of the software architecture components Can eventually be checked through an algebraic specification tester Ensure that all information needed for answering the specifications are available at the time they are needed. A good architecture is one that have the largest expressive power with the slightest component NP is the set of languages definable by existential, second-order formulas (Fagin's theorem, 1974) John Day’s approach in “Patterns in Network Architecture” “ Architecture is maximizing the invariances and minimizing the discontinuities”

Internet architecture a la ANA Abstractions permit to "hide" heterogeneity. Functional Block (FB) Information Dispatch Point (IDP) Information Channel (IC) Compartment. space where FBs, IDPs and ICs live FB1 IC FB2 c ba Node compartment Network compartment

Scenario with overlays

Information theoretic view on architecture A network is a set of distributed components Local in a node or distributed Sitting in one layer or crossing layers Tightly or lightly coupled Cooperating to transmit information from point to point. Architecture defines type of collaboration Collaborating through protocols

Cooperation ? Full Cooperation  Do the best possible behavior to reach a goal  Assuming full collaboration Is the goal achievable ? How to achieve the goal ? Multi-user information Theory Non–cooperative Selfish behavior Different rational goal How to mitigate conflicting rational goal ? Game theory Malicious behavior Harmful goal How to contain irrational objectives ? Behavioral inference

Cooperation framework Each Node implement a forwarding function The forwarding function implement the cooperation

Forwarding function Examples Flooding Routing Distributed computation Network coding Any other ?

General case: Multi Sender-Receiver Multi-Relay Sender Receiver L1L2L3Lm Broadcasting

Classical forwarding ?

Extension ?

Why to forward ? Let’s define for each packet a set of attributes A i Destination address D(P i ) Some Attributes are extracted from packet, some are coming from local context Let’s define a utility function U(A i, D(P i ), ID, A) The utility of forwarding message i destinated to D(P i ) to node ID with context A The utility function capture the selfishness of the node Forwarding scheme : Calculate for each packet in buffer its utility Forward the largest utility A1A1 A2A2 AnAn ID, A

Utility functions Classical routing : Assign the utility function 1 if the node ID is on the path to destination D(P i ) null otherwise PROPHET: The delivery likelihood is the utility Self Limiting Epidemic forwarding: The utility is scaled down everytime a packet is received or forwarded. Community or content networking :Give a higher utility to some contents or community. What if the utility doesn’t depend on destination adress ? Results in epidemic forwarding Might construct utility function changing over time and adapting to information increase Spray and focus Move from opportunistic to infrastructure mode

Complex system view to architecture A complex system consists of several component interacting with each other Local dynamic Interaction with environment Environment changing local state Local state changing environment Architecture in this case is about coupling Form of f and g functions How a global structure emerges from microscopic coupling dynamic

Mean Field theoretical approaches