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GAME THEORY IN TOPOLOGY CONTROL

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GAME THEORY. IN TOPOLOGY CONTROL. Robert P. Gilles. 11/18/05 ... algorithm design must account for selfish node behavior ! Non Cooperative Game Framework ... – PowerPoint PPT presentation

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Title: GAME THEORY IN TOPOLOGY CONTROL


1
GAME THEORY IN TOPOLOGY CONTROL
  • Robert P. Gilles
  • 11/18/05

2
Presentation Overview
  • Ad-Hoc Networks
  • Motivation
  • Problem Statement
  • Game Theoretic Framework
  • Topology Control Game
  • Potential Game
  • Convergence
  • Results

3
Elements of an ad-hoc network
Heterogeneous nodes- different functionality and
capability Wireless medium
4
Transmission pattern
  • nodes can only transmit to other nodes within
    link coverage
  • communication graph

5
Variable transmission range
nodes can adjust their transmission power to
conserve energy
self organizing network nodes route amongst
themselves
6
Abstraction
construction of symmetric communication graph
7
Motivation
  • Issues
  • Energy and Capacity
  • Limiting resources in Ad-hoc networks.
  • Improper topology
  • Too sparse (high end-to-end delay, less robust to
    node failure)
  • Too dense (limited spatial reuse, reduced
    capacity)

8
Motivation
  • Problem
  • Connectivity
  • a basic requirement
  • How should the nodes select an appropriate
    transmit power?
  • Underlying graph is connected
  • Total energy consumption is minimized

Solution ? TOPOLOGY CONTROL
9
Before Topology Control…
10
After Topology Control…
Topology Control- Choosing a subset of links and
nodes
11
Notations and Assumptions
  • Network abstracted as undirected graph H(V,E)
  • Let power required to support edge (i,j)
  • Individual transmission power p(i)
  • Connected graph with pi,max(with redundancies)
  • Symmetric channel
  • Multi-hop path between source and destination

p(i)
12
Problem Statement
  • The (design) problem of choosing per node
    (optimal) transmission ranges (variables) that
    preserves network connectivity (constraints).
  • Formally…
  • Power assignment such that
    determines . Sub-graph G(V,E)
    must be efficient and preserve connectivity of
    H induced by

13
Existing TC Algorithms
  • nodes forced to cooperate to achieve global
    objective
  • altruism may not hold when nodes competing for
    resources
  • algorithm design must account for selfish node
    behavior !

14
Non Cooperative Game Framework
  • Each node independent, selfish
  • Considers power level of other nodes when
    assigning transmission power somewhat fair
    (power level assignment)
  • Best response to current state topology
    (overhead), but works even with local information
    (localized)
  • Once a node determines its transmission power
    (utility maximizer), it will cooperate and
    forward.

Topology update Cycle Payoff better
connectivity,..
Actions (Power level)
Individual payoff
Neighborhood
Topology (Set of links)
15
Framework
  • Let
  • Utility of node i
  • Benefit of node i, , from being a
    part of topology g
  • Cost to node i its transmission power pi
  • Transmit power level vector
    induces a topology given by
  • Let be the maximum-power- connected-graph
  • Goal Generate that is energy
    efficient and preserves the connectivity of gmax

16
Energy Efficiency
  • A network gp is locally energy efficient if no
    node can reduce its transmission power without
    disconnecting the network

A network gp is globally energy efficient if sum
of every nodes transmission power is minimum
17
Topology Control Game I
  • Consider where
  • and . f is the number of nodes
    that can be reached (multi-hop). Assume,
  • This game is an OPG with

18
Corollary
  • For the BR algorithm converges
    to NE that is locally energy efficient and
    preserves connectivity.
  • Proof (Connectivity) Suppose not.
  • Contradiction.
  • Thus topology always connected at every stage.
    So . Power minimization problem,
    implies, locally energy efficient.

19
Corollary
  • For the steady state topology is
    also globally energy efficient.
  • Proof We have . Potential maximizer
    . But by previous corollary
    . Therefore,
  • .Thus g(p) is globally efficient.

20
Topology Control Game II
  • Consider where
  • This game is an EPG with EPF given by
  • Utilities exhibit 0-1 around a power level
    threshold. So BR algorithm converges to a power
    profile just to the right of this threshold

21
Simulation results (I)
22
Simulation results
23
Simulation results
24
Simulation results
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