1 Brief Survey of Mobility Models for Ad Hoc Networks and WLANs 2 A Mobility Model for Both Longterm

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(1) Brief Survey of Mobility Models for Ad Hoc
Networks and WLANs(2) A Mobility Model for Both
Long-term Mobility Characteristics and Timed
Location Prediction in WLANs

• Presented by Jong-Kwon Lee
• November 11, 2005

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Random Walk Model

• Originally proposed to emulate the unpredictable
  movement of particles in physics (referred to as
  Brownian Motion)
• Each node moves from its current location to a
  new location by randomly choosing a direction and
  speed in which to travel.
• For every interval t, randomly choose
• New Speed ? vmin, vmax
• New Direction ? (0, 2?
• No pause time

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Random Waypoint Model

• Widely used in mobile ad hoc network research
• Behavior of each node
• selects a random point in the simulation area as
  its destination, and a speed V from an input
  range vmin, vmax.
• Moves to its destination at its chosen speed.
• When the node reaches its destination, it rests
  for some pause time.
• After this pause time, it selects a new
  destination and speed, and repeats the process.

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Reference Point Group Mobility Model

• A mobility model with spatial dependency
• Represents the random motion of a group of mobile
  nodes as well as the random motion of each
  individual node within the group
• Group leader
• Movement of a group leader at time t
• Group members
• Mobility is assigned with a reference point that
  follows the group movement

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Obstacle Mobility Model (MobiCom03)

• Nodes move around pre-defined (rectangle)
  obstacles (e.g. buildings)
• Voronoi diagram is used to determine the path of
  mobile nodes.
• Planar graph whose edges are line segments that
  are equidistant from two obstacle corners
• A variation of Random Waypoint model
• The environment limits the trajectories of
  mobile nodes to the Voronoi graph.
• Obtain the shortest path between a nodes
  current location and its destination.

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Empirical Model

• Weighted Waypoint (WWP) model
• Based on surveys from sampled respondents on USC
  campus during 4 weeks
• Destinations are not randomly picked with the
  same weight across the simulation area.
• The parameters of a mobility model (e.g. pause
  time) are location-dependent and time-dependent.

5-state Markov model for mobile node transition
between categories
Topology of virtual-campus
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WLAN Mobility Model (Infocom05)

• Uses real-life mobility characteristics extracted
  from WLAN traces to generate mobility scenarios.

load environment description for every simulated
node do time 0 while time lt t_sim do
call PS select next destination call PT
generate timing move to next destination
time timecurrent_session end
while end for
Algorithm used by the WLAN mobility model to
generate node trajectories
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WLAN Mobility Model

• Consists of spatial process PS and temporal
  process PT
• Spatial process selects next destination
• The next cell can be either the same cell, one of
  the neighboring cells, or a non-neighboring cell
• gt (psame, pneigh, pnon_neigh) parameter sets
• Temporal process generates timing
• Duration of Inactive State uniform random
  distribution
• Duration of Active State
• Analyze persistence ( residence time at a
  given location) from WLAN traces ? approximated
  by a power-law function c1/x1.22
• Generated using a general Pareto distribution -gt
  approximation for c1/x1.22

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Model T (MobiCom05)

• Model only for spatial registration patterns
• Develop a model as a set of equations that
  characterize the salient features of the
  (training) data set
• No. and distribution of clusters
• No. of popular APs in a cluster size C
• Intra-cluster transition probability
• Intra-cluster trace length
• Inter-cluster transition probability
• Inter-cluster trace length

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A Semi-Markov Model for Estimating Steady-state
and Transient Behavior of User Mobility and Its
Application to Timed Location Prediction in WLANs
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Motivation

• Recent studies on characterization of user
  mobility and network usage in WLANs
• Few studies on how the user mobility is
  correlated in time (daily, weekly, monthly time
  scales).
• Existing prediction models for user locations in
  WLANs
• Predict only the next location w/o time
  information

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Semi-Markov Mobility Model

• Continuous-time Markov chain (CTMC)
• can characterize users state transitions as well
  as the sojourn times spent in each state.
• However, the sojourn time characteristics of
  users in campus-like WLAN do not follow an
  exponential distribution.
• Semi-Markov Processes
• Generalization of Markov processes with arbitrary
  distributed sojourn times.
• Can be used for obtaining both steady-state
  distribution and transient distribution
• ? characterize long-term usage of network
  resource timed location prediction with one
  model!

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Semi-Markov Mobility Model

• Discrete state space S1, , m
• Markov renewal process (Xn, Tn) n?0
• (Time homogeneous) semi-Markov process

Transition prob. from i to j
Sojourn time distribution in state i when the
next state is j
Transition prob. matrix of the embedded Markov
chain
Sojourn time distribution in state i regardless
of the next state
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Steady-state User Distribution over APs

• Association trace ? Build transition probability
  matrix P mean residence time vector
• From P and ,
• gt Long-term average user distribution over APs

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Steady-state User Distribution over APs

• During 11/1/2003 2/29/2004
• 786 active users

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Similarity of Mobility Patterns between Different
Periods

• Use of similarity measures to check the
  correlation of the mobility behavior
• Cosine distance ( correlation coefficient) a
  pattern similarity measure
• 0? sim(p,q) ? 1sim(p,q) 1 ? Identical
  Pattern

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Monthly Correlation

• 1 month 4 weeks
• 8 months (11/2/2003 6/12/2004)
• ? More similar between consecutive periods

3/21/20044/17/2004
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Weekly Correlation

• 14 weeks (2/1/20045/8/2004)

3/21/20044/17/2004
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Daily Correlation

• For each day of week (Sunday, Monday, ,
  Saturday)
• 8 weeks (11/2/200312/27/2003)

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Different User Groups
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Ping-Pong Phenomena

• Ping-pong transition for APs i, j, and k,
• (i?j?i?j) or (i?j?k?i)
• For each user,
• Ping-pong ratio of ping-pong transitions /
  of all transitions
• For 786 users,
• Average ping-pong ratio 0.40
• Median 0.38
• ? Ping-pong happens quite oftenand should not be
  ignored !
• gt The transition probability and residence time
  characteristics at each AP with the original
  association patterns can distort the actual
  mobility behavior.

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Mobility Change Due to Ping-Pong Phenomena

• Elimination of ping-pong transitions from the
  original association history of each user
• Identify a sequence of ping-pong transitions
• Cluster the states (i.e. APs) in the sequence of
  the ping-pong transitions into an Aggregate State
  (AS)
• Replace the sequence of the ping-pong transitions
  with just one transition to the dominant AP with
  which the user has mostly associated among the
  APs in the same ASex) a-gt1-gt4-gt1-gt4-gtb gt
  a-gt1-gtb if 1 is dominant in AS1,4
  a-gt4-gtb if 4 is dominant in AS1,4

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Mobility from Corrected Data (after Elimination
of Ping-Pong)
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Mobility from Original Data
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Change in Residence Time
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Timed Prediction of User Location

• Transient behavior of semi-Markov model

Numerical solution discretize by t kh
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Timed Prediction of User Location

• Predict users location at every k time step

s
k
i
j
nk
(n-1)k
(n1)k
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Timed Prediction of User Location Results

• h 600, K 12, Tp 1800

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Application Mobility-aware Load Balancing in WLAN

• Lets take advantage of ping-pong phenomena.
• Rationale APs in the same AS has served in turn
  the user with the acceptably high SNR.
• Basic idea of load balancing over APs
• Assume the load at each AP is the number of users
  at the AP. (We may later extend this to the case
  of traffic amount at each AP.)
• Move users at overloaded APs to a lightly loaded
  AP in the same AS.
• Balance Index
• where m of APs, Li load at AP i
• ? 1 All Lis have the same
  value. ? ? 1/n Heavily unbalance.

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Overview of the Mobility-aware Load Balancing
Algorithm

• Incorporating timed location prediction
• Can predict future load distribution.
• Can avoid load unbalance in advance.
• Use a 1xm bit vector AC to control the
  association of users to APs (m of APs)
• Initially, AC(i) 1 for all AP i
• If the load at AP i is predicted to be greater
  than a threshold L, AC(i) ? 0.
• AC(i) is reset to 1 if the load at AP i is under
  L (either expectedly or actually).
• When a user moves to a new location,
• First checks the AC bit corresponding to the AP
  having highest signal strength.
• If it is 0 (i.e. it is overloaded), the user
  tries to associate to alternative APs in the same
  AS as that AP.
• If the overloaded AP belongs to no AS, or there
  are no alternative APs having sufficient signal
  strength, the user is allowed to associate to the
  overloaded AP.

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Simulation Results

• Total users 786, OFF users 509, Active users
  277
• Original distribution Balance Index
  0.180823 with max load 9 at AP 361
• After load balancing Balance Index 0.327917
  with max load 3 at AP 373

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Simulation Results More Active Users

• Total users 786, OFF users 201, Active users
  585 (OFF users artificially reduced)
• Original distribution Balance Index
  0.284616 with max load 12 at AP 361
• After load balancing Balance Index 0.506377
  with max load 4 at AP 275