Staffer Day Template

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Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project

• Competitive Scheduling in Wireless Networks with
  Correlated Channel State
• Ozan Candogan, Ishai Menache, Asu Ozdaglar,
  Pablo Parrilo

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Competitive Scheduling in Wireless Collision
Channels withCorrelated Channel State (Candogan,
Menache, Ozdaglar, Parrilo)

• Aggregate utility maximization problem is
  non-convex and difficult to solve. Instead, a
  simple distributed framework is suggested.
• Robust system design in the presence of
  non-cooperative users is achieved and efficiency
  loss due to selfishness of users is bounded.

• Existing work on scheduling focuses on hard to
  analyze centralized schemes with single
  performance objective
• Competitive scheduling models allow the
  flexibility to incorporate different user
  objectives, but focus mainly on users with
  independent channel models
• Correlated channels are more realistic extensions
  of the current model as they incorporate joint
  fading effects

• Achievement
• Convergent dynamics and equilibria
  characterization for competitive scheduling in
  collision channels
• Bounds on price of stability (efficiency losses
  due to selfishness)
• Equilibrium paradoxes Bad-quality states can be
  used more frequent than good states.
• How it works
• Best response dynamics (or fictitious play) and
  potential game property imply convergence
• Characterization of the social optimum in order
  to find efficiency losses due to selfishness.
• Bounds on price of stability is achieved by
  bounding the change in aggregate utility when a
  Nash equilibrium is obtained by perturbing the
  social optimum
• Assumptions and limitations
• Perfect correlation across channel state
  processes of users
• Symmetric-rate assumption for a more tractable
  analysis

• Combine tools from optimization and game theory
• Selfish utility maximization framework for
  collision channels
• Use tools from optimization theory to analyze
  wireless network games
• Potential games and convergence algorithms

Principle When user 3 updates its strategy
through best-response, the potential function
increases after each update

• Extend the results to partial channel
  state-correlation (local central fading
  components)?
• Additional channel models (e.g., CDMA)?
• Convergence of dynamics with asynchronous updates
  and with limited information
• Extending the results to general networks models
  which also include routing

Robust scheduling and power allocation in
wireless networks with selfish users
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Motivation

• Centralized resource allocation in wireless
  networks is usually
• Hard to implement and sustain
• not robust to selfishness of users
• Hence, there is an increasing interest in
  distributed resource allocation in wireless
  networks under the presence of self-interested
  users.
• One of the most distinctive features of wireless
  networks is the time-varying nature of the
  channel quality, an effect known as fading.
• Users may base their transmission decision on the
  current channel quality. This decision model
  naturally leads to a non-cooperative game, since
  each users decision affects other users through
  the commonly shared channel.

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Motivation

• Unlike existing work in the area which assumes
  independent state-processes for different users,
  we consider the case where the channel state is
  correlated across users.
• This correlated-fading model allows to capture
  global network elements that affect all mobiles.

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Goals and Relevance

• Goals
• Study the equilibria of the competitive
  scheduling game
• Establish tight bounds on efficiency loss due to
  noncooperative behavior of the users
• Suggest network dynamics that converge to desired
  equilibrium points.
• Relevant examples
• Satellite networks
• Any uplink wireless network in which global noise
  effects are possible.

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The Model

• We consider a finite set of mobiles transmitting
  to a common base-station.
• Time is slotted, and the channel quality is
  revealed to the user prior to each transmission.
• Each user may base its transmission decision on
  the current channel state.
• In the present work, we assume perfect
  correlation, meaning that all users observe the
  same channel state, yet may obtain different
  rates for a given state.

User 1, p1
User 2, p2
User 3, p3
Due to perfect correlation, all users observe the
same fading state at a given time slot

• Let be the state space. We
  denote by the rate that user m will
  obtain in state j, provided that there are no
  simultaneous transmissions
• Monotonicity assumption If jlti then
  for every user m.

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The Model

• Underlying fading process is assumed to be
  stationary-ergodic. We denote by the
  state-state probability for channel state i.
• Reception Model We assume a collision channel
  Simultaneous transmissions are lost. A single
  transmission is always successful.
• Users are assumed to adopt stationary
  strategies,
• policy of user
  m, where
• transmission probability of user m in state j

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The Noncooperative Game

• Performance measures Average power and average
  throughput
• Average power
• Average throughput
• Each user is interested in maximizing its
  throughput with minimal power investment. We
  capture this tradeoff via the following utility
• where is a positive constant.
• Each user is interested in maximizing the above
  utility subject to an individual power
  constraint, i.e.,
• Nash equilibrium

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Centrally Optimal Scheduler

• Central optimization problem
• The central optimization problem is non-convex
  and hard to characterize.
• Partial characterization There exists an
  optimal solution of the central optimization
  problem where users utilize threshold policies -
  meaning that for each user m there exist at most
  a single state j so that

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Equilibrium Characterization

• A Nash equilibrium point always exists.
• There can be infinitely many Nash equilibria.
• For the case where , best equilibrium
  coincides with the social optimum (i.e., price of
  stability is one).
• Price of anarchy (upper bound on the performance
  ratio between the social optimum and the worst
  Nash equilibrium) can be arbitrary large.
• Bad quality states might be utilized more
  frequently than good states, where utilization is
  defined as the overall transmission probability
  at a given state

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Convergence to Equilibrium

• Additional assumption Assume that rates are
  user independent, i.e.,
• Potential games are games in which a change in a
  single users payoff is equivalent to a change in
  a systems potential function. An important
  property of such games is the convergence of
  sequential best-response dynamics.
• Thus, under the above assumption, our game
  convergences to an equilibrium in case that users
  update their strategies in a sequential manner.
• Convergence properties without the above
  assumption are under current study.

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Future Work

• Further characterization of equilibrium points.
  Explicit bounds on price of stability/anarchy for
  special cases of interest.
• Partial state-correlation models.
• Asynchronous best response dynamics and their
  properties
• Multi-hop networks.
• Additional reception models (such as CDMA based
  networks).?