Fine-Grained Mobility
Characterization: Steady and
Transient State Behaviors
Wei Gao and Guohong Cao
Dept. of Computer Science and Engineering
Pennsylvania State University
Outline
 Introduction
 Node mobility formulation
 Characterizing node mobility behaviors
 Performance evaluation
 Summary & future work
Mobility Characterization
 Node mobility pattern
Needs to be characterized from node mobility
observations
Predict node mobility in the future
Mobility Characterization
 Improve the performance of mobile computing
Forecast disconnection among mobile nodes
Avoid unreliable links for routing
Actively pre-fetch data before network partition
Coarse-Grained Mobility Characterization
 Mobility observation: association to wireless
Access Points (APs)
 Mobility pattern: transitions among APs
 Rough prediction on node movement in the future
Characterized node mobility
Node movement
Our Focus
 Fine-grained mobility characterization
Mobility observation: geographical node movement
Accurate mobility prediction
Characterized node mobility
Major Contributions
 Formulate node mobility at a fine-grained level
based on Hidden Markov Model (HMM)
 Mobility characterization based on the HMM
formulation
Mobility prediction at both steady-state and transientstate time scales
Temporal and spatial mobility inter-dependency
Hidden Markov Model
 Discrete state space
 State transition probability matrix
 Initial state distribution
 Observation probability distributions
Each state is “hidden” behind an observation PDF
For a state sequence
, a HMM has an
occurrence probability for each observation sequence
Why HMM?
 Discrete state space in a Markov process
Explicit correspondence to coarse-grained mobility
observations
 Each
state corresponds to an AP
No explicit correspondence to fine-grained mobility
observations
 Node
moves continuously
 Solution: bridge the gap through the observation
PDFs in HMM
Outline
 Introduction
 Node mobility formulation
 Characterizing node mobility behaviors
 Performance evaluation
 Summary & future work
Mobility Observation
 Each node periodically observes its own mobility
Each node is able to continuously locate itself
Hand-held GPS devices or triangulation localization
 Mobility observation: velocity vector
Including both the moving speed and direction
Observation period
Node locations
Mobility Stage
 Each stage corresponds to a range of the direction
of node velocity vectors
A sector-shaped area
 Uniform initialization
i-th stage:

: average of the first few
mobility observations
Mobility Stage
 Association of mobility stages to HMM states
Assume observation probability distribution as
Gaussian
Set the mean vector
to observation PDF
 Mobility stage allocation is adjusted based on
mobility observations
HMM parameter re-estimation
HMM Parameter Re-estimation
 HMM parameters are iteratively re-estimated
based on recent mobility observations to capture
the up-to-date mobility pattern
 Expectation-Maximization (EM) algorithm
For a set of mobility observations
estimation for the HMM
is to maximize
, re-
Parameters to be re-estimated:
Computational complexity:
 Being affected by various empirical parameters
Covariance
vector
of matrix of
InitialState
stateMean
transition
probability
probability
observation
observation
PDF PDF
Weighted Mobility Observations
 Mobility observations in a training set should not
be considered as equal
Mobility observations in past may be different from
the current node mobility
More recent mobility observations should have larger
weights during parameter re-estimation
Weighted Mobility Observations
 For a training set
, the weight of
is proportional to t, and controlled by a constant
factor
and a smoothing factor
as
P=0.3
P=0.5
P=0.7
P=0.9
Outline
 Introduction
 Node mobility formulation
 Characterizing node mobility behaviors
 Performance evaluation
 Summary & future work
Mobility Prediction
 Steady-state and transient-state time scales
Human mobility exhibits zig-zag movement pattern
Transient-state moving directions may vary
The cumulative moving direction remains unchanged
Mobility Prediction
 Steady-state prediction
The average direction over all the mobility stages
Stationary distribution of the HMM
 Transient-state prediction
For the recent mobility observations
find the best state sequence
maximizes
,
which
The distribution of the next mobility observation
Node Mobility Inter-Dependency
 Temporal Mobility Dependency (TMD)
 Current node mobility depends on the past history
 Spatial Mobility Dependency (SMD)
 The movement of a node relates to others
 Important in many mobile applications
Temporal Mobility Dependency (TMD)
 The TMD of node j at time t with HMM
defined as

: Kullback-Leibler distance
measure between HMMs
Discrete approximation:
 For
the k-th mobility observation period
Spatial Mobility Dependency (SMD)
 The SMD between two nodes i and j is defined as

 The SMD among a set S of nodes is defined as

Outline
 Introduction
 Node mobility formulation
 Characterizing node mobility behaviors
 Performance evaluation
 Summary & future work
Trace-based Evaluation
 NCSU human mobility trace
Records the movement trajectory of human beings
during a long period of time
Accuracy of Steady-State Mobility Prediction
 Comparisons:
Auto-Regressive (AR) process linear regression
coarse-grained
Order-2 Markov prediction
50%
70%
Simulations
 Performance evaluation in large-scale networks
50 mobile nodes in a
area
 Various mobility models
Random Way Point (RWP)
Gauss-Markov (GM)
 Temporal
correlation of node mobility is controlled by
Reference Point Group Mobility (RPGM)
 Spatial
correlation of node mobility is controlled by the
average number (n) of nodes per group
Accuracy of Transient-State Mobility Prediction
 Prediction error is lower than 20% for node
mobility with less randomness
Mobility Inter-Dependency
 The temporal and spatial mobility dependencies
can be accurately characterized
Summary
 HMM-based mobility formulation to bridge the
gap between discrete Markov states and
continuous mobility observations
 Fine-grained mobility characterization
Steady-state and transient-state mobility prediction
Temporal and spatial mobility inter-dependency
 Future work
Extension to multi-hop neighbors of mobile nodes
Correlation with existing mobility models?
Thank you!

http://mcn.cse.psu.edu
 The paper and slides are also available at:
http://www.cse.psu.edu/~wxg139
HMM Parameter Re-estimation
 Parameters to be re-estimated:


Back
Impact of Empirical Parameters
 T: period of mobility observation
Inversely proportional to the average node moving
speed
 L: size of training set of mobility observations
Larger L increases the accuracy of parameter reestimation
May not capture the up-to-date mobility pattern
 N: number of states in the HMM
Possible overfitting if N is too large
Regularization methods
Back
The Value of P
 P is adaptively adjusted according to the current
node moving velocity
 To ensure that
,
where
, and Vmax is the maximum node
speed in past
Back
Accuracy of Mobility Prediction
 Mainly depends on the randomness of node mobility
 Transient-state prediction is sensitive to the frequent
change of node moving direction
 Steady-state prediction is more reliable
 Error of node localization
 System error
 Eliminated
when velocity vector is used as mobility observation
 Random error
 HMM
parameters are re-estimated in an accumulative manner
over multiple mobility observations
Back
KL Distance Measure between HMMs
 KL distance between two probabilistic
distributions
and
 KL distance between two HMMs

and
Stationary distribution
Back
Application of Mobility Inter-Dependency
 Being used as network decision metrics
Mobility-aware routing: build routes between nodes
with higher SMD
Data forwarding in DTNs: a current relay which has
high TMD is also a good relay choice in the future
Application of Mobility Inter-Dependency
 Mobility-aware clustering
Nodes with higher SMD with its neighbors are better
choices for clusterhead
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