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Fine-Grained Mobility Characterization: Steady and Transient State Behaviors

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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

- Introduction
- Node mobility formulation
- Characterizing node mobility behaviors
- Performance evaluation
- Summary & future work

- Node mobility pattern
- Needs to be characterized from node mobility observations
- Predict node mobility in the future

- Improve the performance of mobile computing
- Forecast disconnection among mobile nodes
- Avoid unreliable links for routing
- Actively pre-fetch data before network partition

- 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

- Fine-grained mobility characterization
- Mobility observation: geographical node movement
- Accurate mobility prediction

Characterized node mobility

- 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

- 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

- 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

- Explicit correspondence to coarse-grained mobility observations
- Solution: bridge the gap through the observation PDFs in HMM

- Introduction
- Node mobility formulation
- Characterizing node mobility behaviors
- Performance evaluation
- Summary & future work

- 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

- 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

- 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 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

- 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

- 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

- Introduction
- Node mobility formulation
- Characterizing node mobility behaviors
- Performance evaluation
- Summary & future work

- 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

- 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

- 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

- 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

- The SMD between two nodes i and j is defined as
- The SMD among a set S of nodes is defined as

- Introduction
- Node mobility formulation
- Characterizing node mobility behaviors
- Performance evaluation
- Summary & future work

- NCSU human mobility trace
- Records the movement trajectory of human beings during a long period of time

- Comparisons:
- Auto-Regressive (AR) process
- Order-2 Markov prediction

linear regression

coarse-grained

50%

70%

- 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

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

- The temporal and spatial mobility dependencies can be accurately characterized

- HMM-based mobility formulation to bridge the gap between discrete Markov states and continuous mobility observations

- Steady-state and transient-state mobility prediction
- Temporal and spatial mobility inter-dependency

- Extension to multi-hop neighbors of mobile nodes
- Correlation with existing mobility models?

http://mcn.cse.psu.edu

- The paper and slides are also available at:
http://www.cse.psu.edu/~wxg139

- Parameters to be re-estimated:

Back

- 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

- P is adaptively adjusted according to the current node moving velocity
- To ensure that ,
- where , and Vmaxis the maximum node
speed in past

- where , and Vmaxis the maximum node

Back

- 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

- System error

Back

- KL distance between two probabilistic distributions and
- KL distance between two HMMs and

Stationary distribution

Back

- 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

- Mobility-aware clustering
- Nodes with higher SMD with its neighbors are better choices for clusterhead

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