Fine-Grained Mobility Characterization: Steady and Transient State Behaviors

Wei Gao and Guohong Cao

Dept. of Computer Science and EngineeringPennsylvania State University

Outline

IntroductionNode mobility formulationCharacterizing node mobility behaviorsPerformance evaluationSummary & future work

Mobility CharacterizationNode 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 nodesAvoid unreliable links for routingActively pre-fetch data before network partition

Coarse-Grained Mobility Characterization

Mobility observation: association to wireless Access Points (APs)

Mobility pattern: transitions among APsRough prediction on node movement in the future

Node movement

Characterized node mobility

Our FocusFine-grained mobility characterization

Mobility observation: geographical node movementAccurate mobility prediction

Characterized node mobility

Major ContributionsFormulate node mobility at a fine-grained level

based on Hidden Markov Model (HMM)Mobility characterization based on the HMM

formulationMobility prediction at both steady-state and transient-

state time scalesTemporal and spatial mobility inter-dependency

Hidden Markov ModelDiscrete state spaceState transition probability matrix Initial state distribution Observation probability distributions

Each state is “hidden” behind an observation PDFFor 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

IntroductionNode mobility formulationCharacterizing node mobility behaviorsPerformance evaluationSummary & future work

Mobility ObservationEach node periodically observes its own mobility

Each node is able to continuously locate itselfHand-held GPS devices or triangulation localization

Mobility observation: velocity vectorIncluding both the moving speed and direction

Observation period Node locations

Mobility StageEach stage corresponds to a range of the direction

of node velocity vectorsA sector-shaped area

Uniform initializationi-th stage: : average of the first few

mobility observations

Mobility StageAssociation of mobility stages to HMM states

Assume observation probability distribution as Gaussian

Set the mean vector to observation PDFMobility stage allocation is adjusted based on

mobility observationsHMM parameter re-estimation

HMM Parameter Re-estimationHMM parameters are iteratively re-estimated

based on recent mobility observations to capture the up-to-date mobility pattern

Expectation-Maximization (EM) algorithmFor 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 parametersInitial state probabilityState transition probabilityMean vector of

observation PDFCovariance matrix of observation PDF

Weighted Mobility ObservationsMobility observations in a training set should not

be considered as equalMobility observations in past may be different from

the current node mobilityMore recent mobility observations should have larger

weights during parameter re-estimation

Weighted Mobility ObservationsFor 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

IntroductionNode mobility formulationCharacterizing node mobility behaviorsPerformance evaluationSummary & future work

Mobility PredictionSteady-state and transient-state time scales

Human mobility exhibits zig-zag movement patternTransient-state moving directions may varyThe cumulative moving direction remains unchanged

Mobility PredictionSteady-state prediction

The average direction over all the mobility stages

Transient-state predictionFor 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 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

IntroductionNode mobility formulationCharacterizing node mobility behaviorsPerformance evaluationSummary & future work

Trace-based EvaluationNCSU 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) processOrder-2 Markov prediction

linear regressioncoarse-grained

50% 70%

SimulationsPerformance evaluation in large-scale networks

50 mobile nodes in a areaVarious 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-DependencyThe temporal and spatial mobility dependencies

can be accurately characterized

SummaryHMM-based mobility formulation to bridge the

gap between discrete Markov states and continuous mobility observations

Fine-grained mobility characterizationSteady-state and transient-state mobility predictionTemporal and spatial mobility inter-dependency

Future workExtension to multi-hop neighbors of mobile nodesCorrelation 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-estimationParameters to be re-estimated:

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Impact of Empirical ParametersT: period of mobility observation

Inversely proportional to the average node moving speed

L: size of training set of mobility observationsLarger L increases the accuracy of parameter re-

estimationMay not capture the up-to-date mobility pattern

N: number of states in the HMMPossible overfitting if N is too largeRegularization methods Back

The Value of PP 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

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KL Distance Measure between HMMsKL distance between two probabilistic

distributions and

KL distance between two HMMs and

Stationary distribution

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Application of Mobility Inter-Dependency

Being used as network decision metricsMobility-aware routing: build routes between nodes

with higher SMDData 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 clusteringNodes with higher SMD with its neighbors are better

choices for clusterhead

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