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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

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Fine grained mobility characterization steady and transient state behaviors

Fine-Grained Mobility Characterization: Steady and Transient State Behaviors

Wei Gao and Guohong Cao

Dept. of Computer Science and Engineering

Pennsylvania State University


Outline

Outline

  • Introduction

  • Node mobility formulation

  • Characterizing node mobility behaviors

  • Performance evaluation

  • Summary & future work


Mobility characterization

Mobility Characterization

  • Node mobility pattern

    • Needs to be characterized from node mobility observations

    • Predict node mobility in the future


Mobility characterization1

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

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

Our Focus

  • Fine-grained mobility characterization

    • Mobility observation: geographical node movement

    • Accurate mobility prediction

Characterized node mobility


Major contributions

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 transient-state time scales

    • Temporal and spatial mobility inter-dependency


Hidden markov model

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

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


Outline1

Outline

  • Introduction

  • Node mobility formulation

  • Characterizing node mobility behaviors

  • Performance evaluation

  • Summary & future work


Mobility observation

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

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 stage1

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 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 , re-estimation for the HMM is to maximize

    • Parameters to be re-estimated:

    • Computational complexity:

  • Being affected by various empirical parameters

Covariance matrix of observation PDF

Mean vector of observation PDF

Initial state probability

State transition probability


Weighted mobility observations

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 observations1

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


Outline2

Outline

  • Introduction

  • Node mobility formulation

  • Characterizing node mobility behaviors

  • Performance evaluation

  • Summary & future work


Mobility prediction

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 prediction1

Mobility Prediction

  • Steady-state prediction

    • The average direction over all the mobility stages

  • Transient-state prediction

    • For the recent mobility observations , find the best state sequence which maximizes

    • The distribution of the next mobility observation

Stationary distribution of the HMM


Node mobility inter dependency

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

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

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


Outline3

Outline

  • Introduction

  • Node mobility formulation

  • Characterizing node mobility behaviors

  • Performance evaluation

  • Summary & future work


Trace based evaluation

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

Accuracy of Steady-State Mobility Prediction

  • Comparisons:

    • Auto-Regressive (AR) process

    • Order-2 Markov prediction

linear regression

coarse-grained

50%

70%


Simulations

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

Accuracy of Transient-State Mobility Prediction

  • Prediction error is lower than 20% for node mobility with less randomness


Mobility inter dependency

Mobility Inter-Dependency

  • The temporal and spatial mobility dependencies can be accurately characterized


Summary

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

    Thank you!

    http://mcn.cse.psu.edu

    • The paper and slides are also available at:

      http://www.cse.psu.edu/~wxg139


    Hmm parameter re estimation1

    HMM Parameter Re-estimation

    • Parameters to be re-estimated:

    Back


    Impact of empirical parameters

    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 re-estimation

      • 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

    The Value of P

    • P is adaptively adjusted according to the current node moving velocity

    • To ensure that ,

      • where , and Vmaxis the maximum node

        speed in past

    Back


    Accuracy of mobility prediction

    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 Measure between HMMs

    • KL distance between two probabilistic distributions and

    • KL distance between two HMMs and

    Stationary distribution

    Back


    Application of mobility inter dependency

    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 dependency1

    Application of Mobility Inter-Dependency

    • Mobility-aware clustering

      • Nodes with higher SMD with its neighbors are better choices for clusterhead

    Back


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