Sound Mobility Model

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• Sound Mobility Model
• By Jungkeun Yoon, Mingyan Liu, Brian Noble
• Mobicom 2003
• Mobility Models for Ad hoc Network Simulations
• Guolong Ling, Guevara Noubir, Rajmohan Rajaraman,
  Northeastern University
• Infocom 2004

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Sound Mobility Model

• By Jungkeun Yoon, Mingyan Liu, Brian Noble
• Mobicom 2003
• Presented by Honghai Zhang

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Outline

• Introduction of mobility models
• Main Result
• Speed decay, Esteady speed lt Einitial speed
  for some commonly used mobility model (random
  waypoint)
• Derivation of the result
• Eliminating speed decay.

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Introduction to Mobility Models

• Each node selects two or more of the followings
  according to some random distributions
• A destination x in a space U
• Traveling speed v
• Angle ?
• Distance d
• Travel time t
• After reaching d or traveling for t, it may pause
  before repeating the above process.

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Classification of random mobility models
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Classification of random mobility models (cont)

• Another classifications
• Entity model
• Individual nodes move independently
• Group model
• Movement of nodes in a group is correlated

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Main Results

• Speed, time independent
• No speed decay
• Speed, distance independent
• There is speed decay

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Initial Average Speed

• Initial State
• With probability Pmove in move state, speed is
  randomly distributed in Vmin, Vmax with certain
  distribution Vmin gt 0.
• With probability Ppause in pause state, for a
  time period randomly distributed with certain
  distribution.
• Pmove1 Ppause is the probability that a node
  is found in move state when the mobility model
  reaches equilibrium.
• EVinit EVPmove

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Speed, time indepedent

• V- speed in the move state
• V- speed in the pause state, 0
• Model the distribution of V as a delta
  function, ?
• Vss steady state speed.
• S time duration of moving once
• P time duration of pausing once
• R distance during one move.

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Speed, time independent (cont)
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Speed, time independent (cont)
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Speed, distance independent
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Speed, distance independent (cont)
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Intuitive explanation

• When speed and distance are chosen independently,
  a lower speed results in a longer trip.
• So a node has more time in a lower-speed state.
• Average speed is weighted by travel time. Average
  speed is lower than the system set average speed,
  or the initial speed.

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Eliminating Speed Decay

• Determine whether a node starts from a move state
  or a pause state, with probability Pmove and
  Ppause, respectively.
• If a node starts from a move state, use fvss to
  generate the travel speed.
• If a node starts from a pause state, use fpss to
  choose a pause time.
• After the first trip (either move or pause) of a
  node, use fv(v) or fP(p) to select all subsequent
  travel speeds any pause times, respectively.

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Simulation Results
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Mobility Models for Ad hoc Network Simulations

• Guolong Ling, Guevara Noubir, Rajmohan Rajaraman
• Northeastern University

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Outline

• Original Mobility Model
• Steady State Speed Distribution
• Revised Mobility Model
• Speed Distribution of the Revised Model
• Simulation results

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Mobility Model S1A

• Each nodes movement is characterized by a
  non-overlapping time period X1, X2, .
• In each period X1, independently randomly choose
  a distance Di and speed Vi
• Distribution function of Di,Vi are FD and FV

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Theorem 1 Steady State Speed Distribution
Function

• Vt-speed at time t.
• Fvt, fvt, is the cdf and pdf of Vt

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Application of Theorem 1

• Random Waypoint mobility model w/o pause
• V uniformly from Vmin to Vmax

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Thm2 Residual distance ?t
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Revised Mobility Model S1B

• In the first period, travel speed, distance are
  chosen according to
• Fv?,FD?. In the remaining period, they are
  chosen according to Fv,FD.

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Thm3 Stationary Property of the Revised Model
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Simulation Results
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Renewal theory

• Renewal-type equation
• where H is a uniformly bounded function.
• is a
  solution of the renewal-type equation. If H is
  bounded on finite intervals then u is bounded on
  finite intervals and is the unique solution.
• , Fk(t) is k times convolution
  of F(t).
• Elementary renewal theory

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Key Renewal Theory

• If g 0,?)-gt0, ?) is such that
• (a) g(t) gt 0 for all t,
• (b) ,
• (c) g is a non-increasing function,
• Xi is a non-arithmetic function,

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