Fine-Grained Mobility Characterization: Steady and Transient State Behaviors

1. Fine-Grained Mobility Characterization: Steady and Transient State Behaviors Wei Gao and Guohong Cao Dept. of Computer Science and Engineering Pennsylvania State University

2. Outline • Introduction • Node mobility formulation • Characterizing node mobility behaviors • Performance evaluation • Summary & future work

3. Mobility Characterization • Node mobility pattern • Needs to be characterized from node mobility observations • Predict node mobility in the future

4. 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

5. 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

6. Our Focus • Fine-grained mobility characterization • Mobility observation: geographical node movement • Accurate mobility prediction Characterized node mobility

7. 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

8. 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

9. 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

10. Outline • Introduction • Node mobility formulation • Characterizing node mobility behaviors • Performance evaluation • Summary & future work

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Outline • Introduction • Node mobility formulation • Characterizing node mobility behaviors • Performance evaluation • Summary & future work

18. 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

19. 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

20. 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

21. 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

22. 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

23. Outline • Introduction • Node mobility formulation • Characterizing node mobility behaviors • Performance evaluation • Summary & future work

24. Trace-based Evaluation • NCSU human mobility trace • Records the movement trajectory of human beings during a long period of time

25. Accuracy of Steady-State Mobility Prediction • Comparisons: • Auto-Regressive (AR) process • Order-2 Markov prediction linear regression coarse-grained 50% 70%

26. 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

27. Accuracy of Transient-State Mobility Prediction • Prediction error is lower than 20% for node mobility with less randomness

28. Mobility Inter-Dependency • The temporal and spatial mobility dependencies can be accurately characterized

29. 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?

30. Thank you! http://mcn.cse.psu.edu • The paper and slides are also available at: http://www.cse.psu.edu/~wxg139

31. HMM Parameter Re-estimation • Parameters to be re-estimated: Back

32. 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

33. 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

34. 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

35. KL Distance Measure between HMMs • KL distance between two probabilistic distributions and • KL distance between two HMMs and Stationary distribution Back

36. 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

37. Application of Mobility Inter-Dependency • Mobility-aware clustering • Nodes with higher SMD with its neighbors are better choices for clusterhead Back