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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