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An Integrative Principled Approach to Network Science for Autonomic Networks John S. Baras Institute for Systems Research University of Maryland 301-405-6606 baras@isr.umd.edu Network Science Workshop August 31-September 1, 2006 Athens, Greece. Autonomous Swarms. Networks

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slide1

An Integrative Principled Approach

to Network Science

for Autonomic Networks

John S. Baras

Institute for Systems Research

University of Maryland

301-405-6606

baras@isr.umd.edu

Network Science Workshop

August 31-September 1, 2006

Athens, Greece

outline
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust-Reputation-Profiling

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
what is a network
A collection of nodes, agents, …

that collaborate to accomplish actions, gains, …

that cannot be accomplished with out such collaboration

Most significant concept for autonomous, or autonomic networks

What is a Network?
the fundamental trade off
The nodes gain from collaborating

To collaborate they need to communicate, and this represents cost

Trade-off: gain from collaboration vs cost

Multiple metrics involved typically

Many problems in communication networks, sensor networks, economic networks, social networks, biological networks, can be traced to this key trade off

The Fundamental Trade-off
modeling communication patterns
What form communications take?

How are they represented?

How are costs generated?

How connectivity is controlled?

Does agent behavior influence connectivity?

Communication patterns for learning.

Connectivity can be physical, or logical (relational)

Links-graphs, neighborhoods, MRF, etc

Modeling Communication Patterns
example cooperation in manet
Almost all functionalities

Emergent properties based on local interactions and information

Cooperative comms – process overheard info – spatial diversity

Cooperation – games - dimensioning

Example: Cooperation in MANET
outline1
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
cooperative games
Cooperative Game in characteristic function formG= {N, v}, N= {1, 2, …, N}, v :2NR , on all subsets S (coalitions) of N

S a coalition, v(S ) is “interpreted ” as the maximum utilityS can get without the cooperation of players in N\S

S a coalition, v|S is the restriction of v to the player setS

v|S (T ) = v(S ) for each T  S

{S , v|S } a subgame of the game {N, v}

Gsuperadditive: S, T  N, ST= , v(S T )  v(S ) + v(T )

Gmonotone: S  T implies v(S )  v(T )

Cooperative Games
cooperative games and payoffs
Feasible payoff vectors

Efficient payoff vectors

Individually rational payoff vectors

Imputation set:Set of all individually rational and efficient payoffs

Solutions associates with each game G a subset of I*(N, v) Can be characterized either by math relations or axioms Helps capture different notions of “desirable” properties of solutions

xdominatesythrough coalitionS (x Sy)if xi > yi, iS, x(S)  v(S)

xdominatesy (x y)if x Sy for some coalition S

Cooperative Games and Payoffs
cooperative games1
Gconvex: for each iN, S T, implies di(S )  di(T )

increasingmarginal

returns contribution of I

Grational: v(N )  iv({i})

Cooperative Games
cooperative games solution concepts
Core (stable, reasonable payoffs): gives each coalition at least as much as could get by itself

Convex and average convex games have nonempty cores

For a set of games the core is the unique solution that is individually rational, superadditive, nonempty and satisfies the reduced game property

Cooperative Games: Solution Concepts
  • Two interpretations of the core C(N, v)
  • All imputations such that no group of players has an inventive to split off from the grand coalition N and form a smaller coalition S
  • No group of players gets more than what they collectively add to the value obtainable by the grand coalition N
  • C(N, v) is nonempty iff {N, v} is balanced
cooperative games solution concepts1
Cooperative Games: Solution Concepts
  • Stable sets: V I , there is no x, y V s.t. xy, and if yV, there is xV s.t. xy
  • Nucleolus: excesse(S, x) = v(S ) – x(S ) measure of dissatisfaction of coalition S for payoffx Set (x) = (e(S, x))S N ; solution obtained by min {((x)) | x  I(N, v)}. Minimize maximal complaint.
  • The Nucleolus is always in the core
cooperative games solution concepts2
Nucleolus is the individually rational payoff that lexicographically minimizes the excess vector

Leads to iterative procedure for getting there

Use a small set of linear programs that iteratively minimize the highest excess, then the second highest excess, etc.

A solution concept is the Nucleolus if and only if it is anonymous (ind. of payer labeling), covariant (ind. of scale expressing preferences), satisfies the reduced game property

Cooperative Games: Solution Concepts
  • Shapley Value: solution  with components the expected marginal contribution made by i when entering coalition N
    • T is a carrier, if v(S ) = v(S T), v(S ) = iSi (v). Shapley Value is the unique solution that has this property, is anonymous and additive
    • For convex games Shapley Value is in the core
  • Kernel, Bargaining Set: consider coalition structures, their stability, objections and counterobjections
networks and constraints
Networks and Constraints

All coalitions cannot be formed

To coordinate (collaborate) agents need to communicate

Network (N, L)

Edges – links between payers

i and jdirectly connected

i and jpath connected

Cooperation components

Links between players in S , L(S )

Network (S , L(S )) induces a partition of S

Cycle Free and Cycle Complete networks

Wheels

constrained coalitions
Constrained Coalitions
  • Network-restricted cooperation game or constrained coalition {N, vL}
  • {N, v, L} communication situation
  • Characteristic function
  • Myerson value : Shapley value of {N, vL}
  • Component decomposability, component efficiency, fairness
network formation
Network Formation
  • Form links pairwise
  • Iterative game
  • Better understanding of topologies – dynamics – topology control
  • Network formation with costs for establishing links
  • {N, v, L, c} {N, vL,c}
  • Stability vs efficiency of the resulting network
  • Small world graphs
outline2
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
example trust management system
Example: Trust Management System

Prior trust relations

Trust

Decision

Trust

Credential

Credential

Distribution

Evaluation

Policy

Local observations

Local key exchanges

Applications

trust evaluation in autonomic networks
The network is modeled as a directed graph G(V,E)

G is the trust graph

A directed link from node i to node j corresponds to the trust relation i has on j

The weight cij represents the opinion of i on j,

Trust evaluation is to estimate the trustworthiness of nodes

ti represents node i being either GOOD or BAD, denoted as ti=1 or -1

si is the estimated trust value of node i

si is a subjective concept, while ti is an existing but unknown fact

Objective: to drive si as close to ti as possible based on available Jij

Trust Evaluation in Autonomic Networks
local voting rule
In homogenous networks, the trustworthiness of an agent is based on other peers’ opinion

The most straightforward scheme is to ask neighbors to “vote” for it

Values of the votes are equal to cij

Iterative voting rule:

Evaluation starts from a small set of trusted nodes

Our interest is to study evolution of the estimated trust value si and its property at the equilibrium

Local Voting Rule
trust dynamics
Trust revocation:

Changes in topology, membership, secure paths

Referees of a node may change, trust evidence for a node may change

Votes timeout or negative votes

Trust spreads

Trust-connected network

Trust Dynamics
  • Trust spreading

Initial “islands” of trusts

deterministic voting rule
We use the weighted average as the voting rule, where weights are ‘vote values’ (all quantities nonnegative)

is the degree of node i

n represents discrete time

Assume is a constant, i.e. it doesn’t change with time, which is true when considering the steady state

The voting rule can be written in system equation

Deterministic Voting Rule
voting with headers
We introduce the notion of headers

Headers are pre-trusted agents and only vote for nodes that they fully trust.

If node i is trusted with bi headers, it gets bi more votes with value 1. Let B = diag[b1 , b2 ,…, bN ].

The system equation changes to

Convergence

Theorem: Given a virtuous network, in order to have a trust connected graph, the number of headers of each node must satisfy

This theorem proves, as well as provides, a network design method to establish a fully trusted network by introducing headers

Voting with Headers
stochastic threshold rule
Stochastic threshold rule with uncertainty parameter b:

Where

Update sequence – random asynchronous updates

Difficult to achieve synchronicity in autonomic networks

The probability that node i is chosen as the target at each iteration is fixed as qi

Stochastic Threshold Rule

Zi(k) is the normalization factor

convergence
The steady state can be derived using the Markov chain

If and , the voting rule converges to the steady state with a unique stationary distribution

The unique stationary distribution is

where

and Z is the normalization function

Criterion: probability of correct estimation

Convergence
trust in virtuous networks
Trust in Virtuous Networks

All nodes are good and have full confidence in their neighbors. We study Pcorrect at steady state.

Left figure: The threshold should be less or equal to 0, otherwise the trust estimate of each node converges to -1.

Right figure: When threshold is equal to 0 -- phase transition. Small change on the parameter results in opposite performance of the voting rule.

virtuous networks with uncertainty
All nodes are good, but because of uncertainty and incompleteness, Jij’s are random variables

Assume

Assume that the probability of a good node having an incorrect opinion on its neighbors is pe

Virtuous Networks with Uncertainty
  • Simulation results
    • When peis larger, the system more probably stays in the random phase.
    • When pe is large enough (pe > 0.15), the system always stays in the random phase.
  • Theoretical analysis: replica method in spin glasses
network topology
Random Graph (Erdös and Rényi, 1960)

Nodes link to each other randomly

Small-world model (Watts & Strogatz,1998)

Short average distance (six degree of separation)

Large clustering coefficient

Scale-free model (Barabási & Albert, 1999)

The distribution of degrees follows the power law

Existence of hubs

Rich get richer

Recent research discovered lots of complex networks being scale-free

Network Topology
spreading speed and topology
The time for updating rule to reach steady state, i.e., how fast the trust values converge.

Perron-Frobenius Theorem in algebraic graph theory: For a stochastic matrix A

isthe largest eigenvalue of A, which is 1 and isthe second largest eigenvalue of A.

The convergence rate of An is of order

Normalized adjacency matrices are stochastic matrices, therefore those with smaller converge faster.

What kind of networks or which network topology has smaller second largest eigenvalue

Spreading Speed and Topology
network topology and deterministic voting rule
Adding just 1% more edges, spreading finishes in 10 times less rounds.Network Topology and Deterministic Voting Rule
  • We consider the Φsmall-world model proposed by Watts and Strogatz
    • High clustering coefficient and small average graphical distance between any pair.
    • We use Φ-model, which is modeled by adding small number of new edges into a regular lattice.
network topology and stochastic voting rule
B Small-world model:

Prw represents “short cuts fraction” on a regular lattice

Regular lattice: Prw=0; Random graph: Prw=1

Prw in [0.1,0.01] is the area for the small world model

Network Topology and Stochastic Voting Rule
  • The performance of the voting rule increases as Prw increases.
    • A more random graph has shorter average distance
    • Accuracy of trust information degenerates over the path length, so a short spreading path has more accurate information and leads to good result
outline3
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
ising and spin glass models
Statistical Physics models for magnetizationIsing and Spin Glass Models
    • Orientation of each particle’s spin depends on its neighbors
    • Ising Model: behavior of simple magnets
    • Spin Glass Model: complex materials
  • Math interpretation:
    • s = {s1, s2,…, sn} is a configurationof n particle spins, where sj = 1 or -1 , spin j is up or down
    • Energy for configuration s
  • Ising Model: Jij = J for all i, j
  • Spin Glass Model: Jij depend on i,j and can be random
ising sg models and games
Ising/SG Models and Games
  • Ising/SG models can be interpreted as dynamic (repeated) games:
    • The value of si represents whether node i is willing to cooperate or not
    • each particle selects spin to maximize its own payoff
    • Ising model (Jij = J>0) : align its spin with the majority of neighbors spin
      • High T, conservative agents, not willing to change, small payoffs
      • Low T, aggressive agents, larger payoffs
    • Collection of local decisions reduces the total energy of the interacting particles
  • Inspires an approach where trust is an incentive for cooperation
    • Jij can be interpreted as the worth of player j to player i
    • decide to cooperate or not based on benefit from cooperation and trust values of neighbors
statistical mechanics of spin glasses
Statistical Mechanics of Spin Glasses
  • Statistical Mechanics primary object of interest
    • Recent excitement: computation of ground state, partition functionZ, NP - complete, Replica Method
    • Application and extensions to several well known problems: turbocodes, image restoration, neural networks, learning, associative memory, SAT, knapsack, SA, number parttioning, graph partitioning, CDMA, MIMO, …
spin glass cooperative game

2

6

J21

J12

3

Subset S={1,2,3,4}

v(S)=J12+J21+J14+J41+J43+J34 -J36 -J15

1

5

J34

J14

J41

4

J43

Spin Glass Cooperative Game
  • Spin glass model as a cooperative game (spin glass game)
    • SN= {1, 2, …, n} is a coalition, in which all nodes cooperate
    • Interaction topology (Jij’s) moderates effects pos. and neg. feedback
    • v(S) : value of the characteristic function of the game , v: 2NR, which is the maximum payoff S can get without cooperation from other nodes N/S.
    • The cooperative game is denoted as Γ =(N, v)
  • Object: to find what form or policy for Jij can induce all (or most) nodes to cooperate: maximize the coalition
cooperation and games
In autonomic networks

Cooperation is restricted to only local interactions

Decision is made by each node individually

Nodes are self-interested

Explain and analyze emergent properties

Game theoretic methods

Provide a framework for modeling individual interactions

Understand complex global structures and dynamics of a system composed of a large number of agents with simple local interactions

Guide for analytical approach

Examples: Ising – spin glass models, prisoner’s dilemma

Goal: how to encourage nodes to collaborate in games?

Incentive: trust systems to promote cooperation and circumvent misbehaving nodes.

Cooperation and Games
trust as mechanism to induce collaboration profiling reputation
Trust is an incentive for collaboration

Nodes who refrain from cooperation get lower trust values

They will be eventually penalized because other nodes tend to only cooperate with highly trusted ones.

Assume, for node i, that the loss for not cooperating with node j is a nondecreasing function of Jji as f (Jji), and the new characteristic function is

Theorem : if , the core is nonempty and

is a feasible payoff allocation in the core.

By introducing a trust mechanism, all nodes are induced to collaborate without any negotiation

Trust as Mechanism to Induce Collaboration – Profiling--Reputation
dynamic coalition formation
Dynamic Coalition Formation
  • System model
  • Two linked dynamics
  • Trust propagation
  • Game evolution
  • Stability of dynamic coalition
    • Nash equilibrium: no node will gain if it changes its current strategy, while others keep unchanged.
results of game evolution
Theorem: , there exists τ0, such that for a reestablishing period τ > τ0

The iterated game converges to Nash equilibrium;

In the Nash equilibrium, all nodes cooperate with all their neighbors.

Comparison of games with (without) trust mechanism, strategy update:

Results of Game Evolution

Percentage of cooperating pairs vs negative links

Average payoffs vs negative links

outline4
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
example direct network trust

1

C

C

2

D

C

n

D

C

n+1

??

??

Example: Direct Network Trust
  • Direct trust is based on past interactions between User A and User B.
  • It is A’s belief about B’s future behavior.
  • Helps A decide for himself and based on local information what to do next.

A

B

example indirect network trust
Example: Indirect Network Trust

User 8 asks for access to User 1’s files.User 1 and User 8 have no previous interaction

What should User 1 do?

2

1

7

Use transitivity

of trust

(i.e. use

references)

4

6

3

5

8

direct trust
User i

is of type ti{Good, Bad}

chooses action ai{C,D}, i=1…N

receives payoff Ri=R(ai,a(i),ti)

wants to maximize his own payoff (local behavior)

Direct Trust
direct trust1
Questions we are investigating

How can collaboration of Good nodes be achieved?

Maximization of the Good node payoff

How quickly can it be achieved?

Repeated interactions

How many bad nodes can destroy it?

Within our framework, the following parameters affect the answers to the above questions.

Payoffs

Strategies

Topology

Direct Trust
direct trust2
Prior probability (reputation, profiling) for user types

Bayes-Nash equilibrium

Strategy for User i :

Direct Trust

evolving reputation

direct trust3
Two sequences evolving with time:

Vector of actions (strategies), time 1:n

Set of vectors of neighbor probabilities (reputations), time 1:n

Direct Trust
example direct trust learning
Where is trust in all this?

Remember:“Direct trust is based on past interactions between User A and User B.It is A’s belief about B’s future behavior.Helps A decide what to do next.”

Trust is how users use the history of past actions to decide what to do next.

Quantified with updated probabilities (reputations) pi.

Example: Direct Trust -- Learning
semirings definitions
 is used to combine edge weights along a path:

 is used to combine path weights:

ab

a

b

Semirings-Definitions

a

ab

b

semirings examples
Shortest Path Problem

Semiring:

 is + and computes total path delay

 is and picks shortest path

Bottleneck Problem

Semiring:

 is and computes path bandwidth

 is and picks highest bandwidth

Semirings-Examples
computing indirect trust1
Path interpretation

Linear system interpretation

Computing Indirect Trust

Indicator vector of pre-trusted nodes

computing indirect trust2
Treat as a linear system

We are looking for its steady state.

Benefits

Result of computation linked explicitly to properties of matrix W

Easier to see effect of attacks, of pre-trusted nodes, of changes in the topology (manipulation of W).

Speed of convergence linked to circuits of W.

Computing Indirect Trust
attacker
The Attacker wants to change the opinion of a node s for a node d as much as possible.

Similar to: The Attacker wants to change the distance (path length) from a node s to a node d as much as possible.

Similar to: The Attacker wants to change the capacity (throughput) from a node s to a node d as much as possible.

Attacker
most vital edge
In all cases, the Attacker attacks a single edge, called the “Most Vital Edge”.

All that changes is the semiring and the interpretation of the weights.

Ramaswamy, Orlin, and Chakravarti found two different characterizations of the Most Vital Edge for the (min,+) and the (max,min) semiring.

Is there a unified characterization?

Most Vital Edge
edge tolerances
Upper (Lower) edge tolerance of an edge e, w.r.t. an optimal path p*, is the highest (lowest) weight of e that would preserve the optimality of p*.

In a shortest path problem (min, +), the most vital edge is the path edge whose weight has the largest difference with the upper tolerance.

In a maximum capacity problem (max, min), the most vital edge is the path edge whose weight has the largest difference with the lower tolerance.

Edge Tolerances
upper tolerance example
Upper Tolerances for the Shortest Path Problem

10

12

Most Vital Edge

Upper Tolerance Example

2

4

Upper Tolerances

5

5

6

6

Shortest Path

1

3

5

1

10

lower tolerance example
Lower Tolerances for the Shortest Path Problem

“Smallest” required changes

4

-4

-4

4

-∞

-∞

Lower Tolerance Example

2

4

Lower Tolerances

5

5

6

6

Shortest Path

1

3

5

1

10

attacked edge on the path
Attacked Edge on the Path

Trust Edge Attack

2

1

7

New Optimal Path p’, trust value: t’

4

RESULT: Decrease Trust!

6

3

5

8

Optimal Path p*, trust value: t*

attacked edge not on the path
Attacked Edge not on the Path

Trust Edge Attack

2

1

7

New Optimal Path p’, trust value: t’

RESULT:Increase Trust!Change Path!

4

6

3

5

8

Optimal Path p*, trust value: t*

tolerances for any optimization semiring
Optimization semirings:  is min or max

-minimal (maximal) tolerance αe (βe) of edge e instead of lower (upper) tolerance.

 is the inverse of  defined by: a  x = b  x = b  a

w(e) is the weight of edge e. w(p) is the weight of path p.

Tolerances for any Optimization Semiring
  • If e  p*
  • If e  p*
outline5
Networks

Constrained Coalitional Games

Iterative Dynamics on Graphs

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
component based networking cbn
MANETs are complex engineering systems composed of many heterogeneous hardware and software components

It is our fundamental view that MANET must be viewed as distributed, asynchronous and hybrid dynamic systems

They should be regarded as systems of subsystems that sense, make decisions and executeactions ---- as closed-loop systems

The subsystems that perform this sensing or decision making or action execution (be they single nodes or collections of nodes) are not co-located

As a result communications occur between sensing blocks, decision making blocks and action execution blocks that are subject to greatly varying constraints on communication bandwidth and delay

This distributed asynchronous dynamic systems view of MANETs has not been promoted to date

It is essential, in our view, for understanding fundamental architectural issues and issues such as stability and robustness, and performance vs complexity trade-offs, and it leads to new fundamental rethinking of the analytical foundations for dynamic collaboration (between nodes and/or subsets of nodes) subject to the constraints of distributed operation, asynchronous operation, bandwidth, delay.

Component Based Networking (CBN)
manet as distributed hybrid systems
Our long term approach will utilize a mixture of methods from computer science (distributed communicating processes, formal models, formal verification-validation) and from control-communication systems (hybrid systems, multi-agent systems, feedback, system dynamics and stability).

We are developing formal dynamic models for MANET that respect the constraints, while at the same time formally specifying the structure (what the network consists of?) and behavior (what the network does?) of a MANET as a system from a systems engineering perspective.

It is within this framework that distributed and asynchronous operation will be built in as constraints (logical or numerical), and where bandwidth and delay constraints between sensing, decision making and action execution blocks will also be modeled.

To completely model and understand properties of MANET we need a framework that combines logical and numerical models, thus hybrid systems.

MANET as Distributed Hybrid Systems
component based system synthesis process

Iterate to Find a Feasible Solution / Change as needed

Change structure/behavior model as needed

Define

Requirements

Effectiveness

Measures

Map behavior

onto structure

Allocate

Requirements

Create

Sequential

build &

Test Plan

Specifications

Perform

Trade-Off

Analysis

Assess

Available

Information

Create

Behavior

Model

Create

Structure

Model

Component-Based System Synthesis Process

Model-based

Beyond UML

Rapsody

UPPAAL

Artist Tools

MATLAB, MAPLE

Modelica

DOORS, etc

OPCAD

CPLEX, SOLVER,

ILOG

Integrated System Synthesis Tools - Environments

missing …

Generate

derivative

requirements

metrics

Model-Based

Information-Centric

Abstractions

Integrated Multiple Views is Hard !

system synthesis and integration is the next frontier
From a Reductionist Approach to an Integrative Approach

The challenge is to generate system predictable behavior by integrating behaviors of the components

It is not all in the software environments

Need a combination of

Model-Based system and software design and integration (software tools environments)

and

Deeper analysis of underlying abstractions and models and their properties

System Synthesis and Integration is the Next Frontier
model based integration software environments needs
Domain Specific Modeling Languages (DSML) with semantics that can be composed and manipulated

Composition platforms correct by construction systems platforms and models of computations; substantial reduction in V&V

System and component behavioral abstractions that can support Incremental System Integration  while preserving testability and predictability

Fully integrated semantically control, software and systems design tools and platforms

Model-Based Integration Software Environments Needs
deeper analysis of system models and properties needs
Principles for system integration System Science  Network Science

Fundamental performance limitations of networked systems  implementation technology free

Fundamental performance limitations of distributed asynchronous systems, with concurrency constraints, with non-collocated sensors, decision making and actuation nodes, with multiple feedback loops, with delay and bandwidth constraints

Distributed control of and inference in the same

Theories of compositionality

Much better integration of logic and optimization for trade-off analysis in dynamical systems

Deeper Analysis of System Models and Properties Needs
overhead oh vs performance
Overhead (OH) vs Performance

From Ananthram Swami

cross linked models
Executablesystem models (ESM) utilize modern software engineering methodologies to develop object-oriented and component-based models of sensor networks, utilizing UML2 and other advanced software systems.

From these models automatic generation of executable code for all elements of a MANET is possible for either simulation or field tests. Embedded in these models are semantics of the operation and composition of the various components.

Formal system models (FSM) of MANET protocols are based on communicating extended finite state machines (deterministic or stochastic) (CEFSM) or on colored timed Petri nets (deterministic or stochastic) (CTPN). They are linked with the executable models via bisimulation relationships, and typically correspond to approximations of the executable models by emphasizing timing behavior of the modeled system in a timed automata sense.

Performance system models (PSM) of MANET and MANET protocols are based on various approximate dynamic system model frameworks (queuing systems, differential equations and fluid flow, difference equations, discrete event systems) together with performance metrics (or utilities) that can be evaluated using the models either analytically or by efficient numerical schemes.

Performance models are linked to executable models via bisimulation relationships, and typically correspond to approximations of the executable models emphasizing performance and quality of service metrics computation or bounds.

Performance models are also linked to Formal models via bisimulation relationships and critical event correspondence.

Cross-Linked Models
cross linked models1
This is already a substantial extension from the software engineering work.

A further and substantial extension is that we will develop a formal compositional (or component based) version of this approach.

This includes development of semantics for linking components of MANET protocols and of MANET, including the associated theories of components and compositionality. This, methodology and framework is in itself an important contribution to network science.

It is this specific framework and underlying mathematical methodologies that we utilize to describe, model and evaluate the structure of MANET (including network structure and network architecture) versus multi-criteria (multiple metrics) performance.

This represents a uniquely innovative departure from the current state of the art in MANET investigations that focus almost entirely on network behavior (i.e. the dynamics of the algorithms for network operation).

Our framework allows us to investigate the design of both structure and operation (i.e. behavior) within a well integrated framework.

Cross-Linked Models
cross linked models2
A very significant and unique feature of our approach is that we will be able to check correctness of functionality as well as performance of the MANET protocol or MANET or its components.

Furthermore and most significantly the proposed approach and framework allows the automation (to a large degree) of the validation, verificationand testing of the MANET protocol and of the MANET design and operation.

This is our vision and long term research in this area.

Among other things it represents a truly innovative and fundamental contribution to Network Science.

Cross Linked Models
current state of manet routing the need for component based routing
Formal methods and models hardly used  lack of systematic analysis of correctness and proof of properties

Evaluation predominantly done by simulations

Limited knowledge as to specific relations between parts and parameters of the protocol and performance

Ad hoc approach to cross-layer design

Very limited consideration of trade offs between performance – reliability – security

Problems from conventional layering: inflexibility, inefficiency, side-effects

Conventional layers create time, energy, OH inefficiencies – especially for MANET (Jung and Biersack 2000)

Current State of MANET Routing – the Need for Component Based Routing
cbr what is it what are the goals cbn
Not a single routing protocol, but a collection of elementary modules that can be combined to form routing protocols with various capabilities, limitations, efficiency, and a synthesis environment to meet requirements

Heterogeneous wireless communication networks  very large and complex software systems  Model and Component Based Software Engineering

Routing protocols have special needs and requirements, such as loopfreeness, etc, examples of formal model requirements

Longer term vision

new and powerful methodology for cross-layer design, that examines layers from the fundamental perspective of components / compositions

component based networking (CBN)  scientific foundation for systems of systems (networks of networks) synthesis problems

Basic research problem: develop thissystems engineering or component based analysis and synthesis subject to various formal model constraints

CBR – What is it? – What are the Goals?CBN
can components be determined formally
Explicit interfaces are fundamental for components – make explicit all the means for communication and coordination of components

Requires a much stronger notion of interface than is common in OO models or model based software

Component-based systems behavioral specifications integrated into component interfaces are important need to go beyond EFSM and CEFSM

Model-based generators of component adaptors

Semantic foundations of architectural and component-based design within UML

Compositional techniques for the analysis of embedded and real-time systems in UML

Compositional model checking of UML behavioral models Statecharts

Can Components be Determined Formally?
formal methods network protocols
Protocols: set of rules, syntax, semantics

Network Protocols: Specification, Verification, Monitoring

Reason about Network Routing Protocols

Formal methods allow to check:

if protocol is working properly;

if implementation is correct;

do devices deviate from protocol standard, etc

SPIN, UPPAAL, Esterel, etc

Bhargavan et al, 2002, formal models for DSDV-AODV

Yang and Baras 2002-2003, formal model for TORA

Yang and Baras 2005-2006, automated Vulnerability Analysis of MANET routing protocols

Formal Methods: Network Protocols
modularity of routing protocols
All MANET routing protocols studied (AODV, DSR, OLSR, TORA, …) can be modularized into four functional components:

Route Discovery Component: how to search path from source to the desired destination by RREQ, RREP message or by link state advertisement.

Route Maintenance Component: how to propagate the information of a broken link once it’s detected by Topology Database Maintenance Component, how to delete the routing paths cached which contain the broken link.

Data Packet Forwarding Component: how to relay data packets from source node to destination node by routing paths (hops) cached.

Topology Database Maintenance Component: how to detect the local connectivity when it’s up or down.

Modularity of Routing Protocols
subcomponents for aodv
AODV:

Route Discovery Component: Subcomponents

Expanding_ring: RREQ’s TTL incremented by TTL_increment in each retransmission for RREQ_timeout.

Hop_defined: Hops traversed by RREQ aren’t encapsulated into packet. Next hop is stored in Route_Cache_Table.

Cached_RREP: Intermediate node on RREQ’s path can initiate RREP.

Route Maintenance Component: Subcomponents

Local_connectivity_update: Use overheard packet to update Local_Connectivity_Table.

Local_repair: Intermediate node on data packet’s path can initiate Route Discovery Procedure.

Route_error_disseminate: notify hosts implementing unreachable nodes as routing hop to delete the entry.

Packet Forwarding Component: Subcomponents

Hop_based: Look up next routing hop in each intermediate node’s Route_Cache_Table.

Unsolicited_forwarding: Forward data packet without waiting for Ack from the receiver hop.

Topology Database Maintenance Component: Subcomponents

Hello_detection: Period beacon message to confirm the existence of the neighboring node.

Subcomponents for AODV
subcomponents for dsr
DSR:

Route Discovery Component: Subcomponents

Fixed_ring: RREQ’s TTL is a fixed value.

Path_defined: Hops traversed by RREQ are encapsulated into packet. Routing path is stored in Route_Cache_Table.

Cached_RREP: Intermediate node on RREQ’s path can initiate RREP.

Route Maintenance Component: Subcomponents

Packet_salvage: In multipath Route_Cache_Table, another path can substitute current broken path.

Route_Error: notify hosts implementing unreachable nodes as routing hop to delete the entry.

Packet Forwarding Component: Subcomponents

SourcePath_based: Data Packet follows the sequence of hops defined by source node, and don’t look up routes at intermediate nodes.

Topology Database Maintenance Component: Subcomponents

Solicited_forwarding: Each sender of data packet (source node and intermediate node) will wait for ACK from the receiver hop, and make a copy of the data packet in Maintenance_Buffer. The data packet will be retransmitted without receiving ACK before Maintenance_timeout.

Subcomponents for DSR
description of components using uml2
Class and Object Diagrams

Describe the physical structure of the protocol

Activity and Sequence Diagrams

Represent behavior models of each component

Mapping of behavior diagrams to structure

Helps to identify interfaces needed for plug and play components

Description of Components using UML2
description of aodv components
Description of AODV Components
  • Route Discovery
  • Expanding ring search
  • Hop-based
  • Sequence numbers maintenance
  • Route Maintenance
  • Local connectivity update
  • Local repair
  • Route error disseminate
  • Sequence numbers maintenance
  • Packet Forwarding
  • Hop-based
  • Unsolicited forwarding
  • Topology Database Maintenance
  • Hello messaging
route discovery behavior model
Route Discovery Behavior Model

Description:

When the Intermediate Node receives RREQ or RREP it initiates its own Route Discovery Process

packet forwarding behavior model
Packet Forwarding Behavior Model

Description:

This component forwards data packets in a hop-by-hop manner.

Drops the packets if there is no valid route.

Performs unsolicited forwarding.

Does not wait for a reply from the next-hop in order to send the packet.

topology database maintenance
Topology Database Maintenance

Description:

This component describes the current topology of the network.

Each node knows if it is connected to it’s neighbors by sending out periodic Hello Messages.

It also knows if a link has been broken when it receives a Hello Message but nothing else happens.

component relationships
Component Relationships

Route Discovery

NODE

Topology Database

Maintenance

Route Maintenance

LINK

Packet Forwarding

Routing Protocol

routing protocol metrics vs component derivative metrics
Goal: Evaluate the components against relevant metrics that will not only differentiate the various components but will also relate the performance of the component with the routing protocol performance.

Also link to other layer metrics (e.g. MAC)

Derivative Metrics:

Route discovery latency (sec)

Route discovery overhead(packets/sec)

Number of routes found and ranking

Quality of the routes (stability, E2E rate delay loss)

Routing Protocol Metrics vs Component Derivative Metrics
performance metrics for routing components
Component selection: how to evaluate and compare different components under different environments (Network topology, Traffic scenario, Mobility profile, Link states)?

Meaningful Component Metrics are crucial for components performance evaluation, comparison, selection

Finer metrics than System Performance Metrics (Latency, Throughput, Packet Loss Ratio)

Statistics can be collected during network activities

Performance Metrics for Routing Components
performance metrics for routing components cont
Route Discovery Component: Metrics

1. Percentage of Route Discovery Failure (DPDF):

#RREQ Unreplied / #Total RREQ Initialized

2. Route Discovery Inefficiency Ratio (DOIR):

#Total Routing Discovery Traffic Rcvd / #RREQ Replied

3. Percentage of Route Cache Hit for High Layer Data Packet (DPCH):

#Cache Hit Data Packet from High Layer / #Total Data Packet from High Layer

4. Percentage of Cached RREP (DPCR):

#Cached RREP Generated/ #Total RREP Generated

5. Average Delay for Route Discovery (DDRD):

Accumulated Delay Time / # RREQ Replied

Topology Database Maintenance Component: Metrics

1. Overhead of Topology Database Maintenance (TODM):

# Total Control Packet Traffic Introduced by Topology Database Maintenance /

# Data Packet Reaching Destination

Performance Metrics for Routing Components (cont)
performance metrics for routing components cont1
Route Maintenance Component: Metrics

Percentage of Data Packet Reaching Destination Aided by Route Maintenance (MPDA):

# Data Packet Reaching Destination Aided by Route Maintenance / # Data Packet Reaching Destination

2. Average Overhead of Route Maintenance (MORM):

# Total Control Traffic Introduced by Route Maintenance / #Data Packet Reaching Destination Aided by Route Maintenance

3. Percentage of Route Maintenance Success (MPMS):

# Data Packet Reaching Destination Aided by Route Maintenance / # Data Packet Attempting Route Maintenance

Packet Forwarding Component: Metrics

Percentage of Failed Forwarding (FPFF):

# Failed Data Packet Forwarding between hops/ # Data Packet Forwarding between hops

2. Percentage of Failed Forwarding Detected by Soliciting Data Packet Forwarding (FPFD):

# Detection of Failed Data Packet Forwarding between hops / # Failed Data Packet Forwarding between hops

3. Average End to End Delay for Packet Forwarding (FDPF):

Accumulated End to End Delay / # End to End Data Packet Forwarding

Performance Metrics for Routing Components (cont)
performance of components route discovery
Four instantiations

TTL based flooding + nexthop storage (AODV like)

TTL based flooding + path storage

Network flooding + nexthop storage

Network flooding + path storage (DSR like)

Metrics (key to evaluating components)

Path Discovery Failure, Path Discovery Overhead (Efficiency)

Impact of cached routes (data pkt cache hit, RREP generated by cache)

Quality of paths (avg hops, avg src-dst connectivity )

Path Discovery Latency

Performance of Components:Route Discovery
performance of components route discovery cont
Simulation setup:

- 100 nodes move in area 5x5 km

- Mobility Model: Random way point, mobility

speed varied at 0, 25, 50, 75 and 100

meters/second. Pause time is 0.

- Traffic Mode: data packet arrivals as Poisson

process, with mean interarrival time 0.5, 1, 1.5

and 2 seconds. Packet length is randomly set as

exponential (1024).

Performance of Components: Route Discovery (cont)
performance of components route discovery cont1
Performance of Components: Route Discovery (cont)

1. “Path Storage” vs “Neighbor Storage”

  • Path Discovery Overhead: Average number of routing packets received / each RREQ replied
  • Path Discovery Failure Ratio: Portion of unreplied RREQs to total RREQs generated

Path Discovery Overhead

Path Discovery Failure Ratio

Mobility speed (m/s)

Mobility speed (m/s)

  • “Path Storage” contributes to:
  • reduce Path Discovery Overhead (Inefficiency)
  • decrease Path Discovery Failure
correlation between system metrics and component metrics
How component influences system performance?

Analyze correlation between values of component metrics and system metrics.

Detach system metrics (e.x End to End Delay) to percentage of each component’s metrics(e.x Path Discovery Delay).

Figure out “bottleneck” component.

Trace Data Packet

Differentiate each component .

Record component metric’s value.

Correlation Between System Metricsand Component Metrics
packet registration table
Create registration table for each component.

Route Discovery Component: Pkt_Enroll_Route_Disc.

Route Maintenance Component: Pkt_Enroll_Route_Maint.

Data Packet Forwarding: Pkt_Enroll_Data_Forward.

Topology Database Maintenance: Pkt_Enroll_Topo_Maint.

Packet Registration Table

Route

Discovery

Component

Pkt_Enroll_Route_Disc

Register to

Route

Maintenance

Component

Pkt_Enroll_Route_Maint

Data Pkt

Topology

Database

Component

Pkt_Enroll_Data_Forward

Packet

Forwarding

Component

Pkt_Enroll_Topo_Maint

route discovery delay vs end to end delay
Simulation Scenarios:Route Discovery Delay vsEnd to End Delay
  • Network Topology: 20 nodes in 2 x 2 km.
  • Traffic Mode: Data Traffic (12,000 bytes/sec)

Voice Traffic (57,000 bytes/sec)

Video Traffic (698,000 bytes/sec)

  • Mobility: Random way point, mobility speed varied at 0, 15 and 30 meters/second. Pause time is 0.
route discovery delay vs end to end delay cont
Route Discovery Delay vsEnd to End Delay (cont.)

Video Traffic (698,000 bytes/sec)

Proportion of Route Discovery Delay to E2E Delay (percentage)

Mobility Speed (meters/sec)

0 15 30

  • As mobility speed is increased, Route Discovery Delay has higher proportion of End to End Delay.
route discovery delay vs end to end delay cont1
Route Discovery Delay vs End to End Delay (cont.)

Mobility Speed: 15 meters/sec

Proportion of Route Discovery Delay to E2E Delay (percentage)

data voice video

Traffic Type (Bit Rate)

  • As bit rate is increased, Route Discovery Delay has higher proportion of End to End Delay.
route discovery delay vs end to end delay cont2
Route Discovery Delay vs End to End Delay (cont.)

Proportion of Route Discovery Delay to E2E Delay (percentage)

0 15 30

data voice video

  • Generally, proportion of Route Discovery Delay will be increased along with increasing bit rate and mobility speed.
outline6
Networks

Constrained Coalitional Games

Iterative Dynamics on Graph

Trust and Collaboration

Direct and Indirect Trust Computation

Component Based Networking

Network Design and Trade-offs

Outline
manet network design dimensioning
Formal Hybrid Models (Component Based Networking)

Performance Models (Rates – Throughput, packet losses, delays)

Sensitivity Computation and Trade offs (Automatic Differentiation / Infinitesimal Perturbation Analysis / Cross Entropy)

and UMD CONSOL-OPTCAD, ILOG CPLEX-SOLVER

MANET Network Design-Dimensioning

Fundamental Trade-Off: BenefitsvsCost of Collaboration

Performance

Metrics and

sensitivities

AD/IPA/CE

processor

Topology-Mobility

Traffic patterns

and matrix

Network Conditions

QoS

Protocol components

Design parameters

and

architecture

Performance

Models

Multi-objective

designer/optimizer

CBN

Formal Models

Routing Protocol

MAC Protocol

Flow Control Protocol