An Integrative Principled Approach

1
An Integrative Principled Approach to Network
Science for Autonomic Networks John S.
Baras Institute for Systems Research University
of Maryland 301-405-6606 baras_at_isr.umd.edu N
etwork Science Workshop August 31-September 1,
2006 Athens, Greece
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Autonomous Swarms
3
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

4
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

5
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

6
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

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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

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Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graphs
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

9
Cooperative Games

• Cooperative Game in characteristic function form
  G 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 utility S can get without the
  cooperation of players in N \ S
• S a coalition, vS is the restriction of v to
  the player set S
• vS (T ) v(S ) for each T ? S
• S , vS a subgame of the game N, v
• G superadditive S, T ? N, S ?T ?, v(S ? T )
  ? v(S ) v(T )
• G monotone S ? T implies v(S ) ? v(T )

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Cooperative Games and Payoffs

• Feasible payoff vectors
• Efficient payoff vectors
• Individually rational payoff vectors
• Imputation set Set of all individually rational
  and efficient payoffs
• Solution s 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
• x dominates y through coalition S (x ?S y) if
  xi gt yi, i?S, x(S) ? v(S)
• x dominates y (x ? y) if x ?S y for some
  coalition S

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Cooperative Games

• G convex for each i?N, S ? T, implies di(S )
  ? di(T )
• increasing marginal
• returns contribution of I
• G rational v(N ) ? ?iv(i)

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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

• 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

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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 excess e(S, x) v(S ) x(S )
  measure of dissatisfaction
  of coalition S for payoff x 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

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Cooperative Games Solution Concepts

• 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

• 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

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Networks and Constraints
All coalitions cannot be formed To coordinate
(collaborate) agents need to communicate Network
(N, L) Edges links between payers i and j
directly connected i and j path
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
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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

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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, v L,c
• Stability vs efficiency of the resulting network
• Small world graphs

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Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graphs
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

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Example Trust Management System
Prior trust relations
Trust Decision
Trust Credential
Credential Distribution
Evaluation Policy
Local observations
Local key exchanges
Applications
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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 ti1 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

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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

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Trust Dynamics

• Trust spreading

Initial islands of trusts

• 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

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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 doesnt
  change with time, which is true when considering
  the steady state
• The voting rule can be written in system
  equation

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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 diagb1 , 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

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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

Zi(k) is the normalization factor
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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

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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.
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Virtuous Networks with Uncertainty

• All nodes are good, but because of uncertainty
  and incompleteness, Jijs are random variables
• Assume
• Assume that the probability of a good node having
  an incorrect opinion on its neighbors is pe

• Simulation results
• When pe is larger, the system more probably stays
  in the random phase.
• When pe is large enough (pe gt 0.15), the system
  always stays in the random phase.
• Theoretical analysis replica method in spin
  glasses

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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

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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
• is the largest eigenvalue of A, which is 1
  and is the 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

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Network Topology and Deterministic Voting Rule

• We consider the F small-world model proposed by
  Watts and Strogatz
• High clustering coefficient and small average
  graphical distance between any pair.
• We use F-model, which is modeled by adding small
  number of new edges into a regular lattice.

• Adding just 1 more edges, spreading finishes in
  10 times less rounds.

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Network Topology and Stochastic Voting Rule

• B Small-world model
• Prw represents short cuts fraction on a regular
  lattice
• Regular lattice Prw0 Random graph Prw1
• Prw in 0.1,0.01 is the area for the small world
  model

• 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

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Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graphs
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

34
Ising and Spin Glass Models

• Statistical Physics models for magnetization

• Orientation of each particles spin depends on
  its neighbors
• Ising Model behavior of simple magnets
• Spin Glass Model complex materials
• Math interpretation
• s s1, s2,, sn is a configuration of 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

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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 Jgt0) 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

36
Statistical Mechanics of Spin Glasses

• Statistical Mechanics primary object of interest
• Recent excitement computation of ground state,
  partition function Z, 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,

37
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 (Jijs) 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 G (N, v)
• Object to find what form or policy for Jij
  can induce all (or most) nodes to cooperate
  maximize the coalition

38
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, prisoners
  dilemma
• Goal how to encourage nodes to collaborate in
  games?
• Incentive trust systems to promote cooperation
  and circumvent misbehaving nodes.

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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

40
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.

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Results of Game Evolution

• Theorem
  , there exists t0, such that for a
  reestablishing period t gt t0
• 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

Percentage of cooperating pairs vs negative links
Average payoffs vs negative links
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Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graphs
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

43
Example Direct Network Trust

• Direct trust is based on past interactions
  between User A and User B.
• It is As belief about Bs future behavior.
• Helps A decide for himself and based on local
  information what to do next.

A
B
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Example Indirect Network Trust
User 8 asks for access to User 1s 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
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Direct Trust

• User i
• is of type ti?Good, Bad
• chooses action ai?C,D, i1N
• receives payoff RiR(ai,a?(i),ti)
• wants to maximize his own payoff (local behavior)

46
Direct Trust

• 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

47
Direct Trust

• Prior probability (reputation, profiling) for
  user types
• Bayes-Nash equilibrium
• Strategy for User i

evolving reputation
48
Direct Trust

• Two sequences evolving with time
• Vector of actions (strategies), time 1n
• Set of vectors of neighbor probabilities
  (reputations), time 1n

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Example Direct Trust -- Learning

• Where is trust in all this?
• RememberDirect trust is based on past
  interactions between User A and User B.It is As
  belief about Bs 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.

50
Semirings-Definitions

• ? is used to combine edge weights along a
  path
• ? is used to combine path weights

a
a?b
b
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Trust Semiring PropertiesPartial Order

• Combined along-a-path weight should not increase
  
• Combined across-paths weight should not decrease

a
b
2
3
1
a
b
52
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

53
Computing Indirect Trust
2
1
7
4
6
3
5
8
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Trust Path Semiring

• 0 ? trust, confidence ? 1
• ? is
• ? is

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Computing Indirect Trust

• Path interpretation
• Linear system interpretation

Indicator vector of pre-trusted nodes
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Computing Indirect Trust

• 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.

57
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.

58
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?

59
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.

60
Upper Tolerance Example

• Upper Tolerances for the Shortest Path Problem

4
2
Upper Tolerances
6
6
5
5
Shortest Path
1
3
5
1
10
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Lower Tolerance Example

• Lower Tolerances for the Shortest Path Problem

4
2
Lower Tolerances
6
6
5
5
Shortest Path
1
3
5
1
10
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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
63
Attacked Edge not on the Path
Trust Edge Attack
2
1
7
New Optimal Path p, trust value t
RESULTIncrease Trust!Change Path!
4
6
3
5
8
Optimal Path p, trust value t
64
Tolerances for any Optimization Semiring

• Optimization semirings ? is min or max
• ?-minimal (maximal) tolerance ae (ße) 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.

• If e ? p

• If e ? p

65
Tolerances for the Trust Semiring

• Assume (max, ) semiring essentially equivalent
  to our trust semiring.
• Tolerances

• If e ? p

• If e ? p

66
Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graphs
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

67
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 execute actions
  ---- 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.

68
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.

69
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 !
70
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

71
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 VV
• 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

72
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

73
Current Autonomic Wireless Nets Performance Very
Poor
From Tim Krout
74
Overhead (OH) vs Performance
From Ananthram Swami
75
Cross-Linked Executable, Formal and Performance
Models for MANET Protocols
76
Cross-Linked Models

• Executable system 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.

77
Cross-Linked Models

• 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.

78
Cross Linked Models

• 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, verification
  and 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.

79
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)

80
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 this systems
  engineering or component based analysis and
  synthesis subject to various formal model
  constraints

81
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

82
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

83
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 its 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 its up or
  down.

84
Subcomponents for AODV

• AODV
• Route Discovery Component Subcomponents
• Expanding_ring RREQs TTL incremented by
  TTL_increment in each retransmission for
  RREQ_timeout.
• Hop_defined Hops traversed by RREQ arent
  encapsulated into packet. Next hop is stored in
  Route_Cache_Table.
• Cached_RREP Intermediate node on RREQs 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 packets
  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 nodes 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.

85
Subcomponents for DSR

• DSR
• Route Discovery Component Subcomponents
• Fixed_ring RREQs 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 RREQs 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
  dont 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.

86
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

87
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

88
AODV Structure
89
Route Discovery Behavior Model
Description When the Intermediate Node receives
RREQ or RREP it initiates its own Route Discovery
Process
90
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.
91
Topology Database Maintenance
Description This component describes the
current topology of the network. Each node
knows if it is connected to its 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.
92
Component Relationships
Route Discovery
NODE
Route Maintenance
Topology Database Maintenance
LINK
Packet Forwarding
Routing Protocol
93
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)

94
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

95
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

96
Performance Metrics for Routing Components (cont)

• 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

97
Performance of ComponentsRoute 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

98
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).

99
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

100
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 components metrics(e.x Path
  Discovery Delay).
• Figure out bottleneck component.
• Trace Data Packet
• Differentiate each component .
• Record component metrics value.

101
Packet Registration Table

• Create registration table for each component.
• Route Discovery Component Pkt_Enroll_Route_Disc.
  
• Route Maintenance Component Pkt_Enroll_Route_Main
  t.
• Data Packet Forwarding Pkt_Enroll_Data_Forward.
• Topology Database Maintenance Pkt_Enroll_Topo_Mai
  nt.

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
102
Route Discovery Delay vs End to End Delay

• Simulation Scenarios

• 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.

103
Route Discovery Delay vs End 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.

104
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.

105
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.

106
Outline

• Networks
• Constrained Coalitional Games
• Iterative Dynamics on Graph
• Trust and Collaboration
• Direct and Indirect Trust Computation
• Component Based Networking
• Network Design and Trade-offs

107
MANET Network Design-Dimensioning
Fundamental Trade-Off Benefits vs Cost of
Collaboration

• 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

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