Probabilistic Continuous Update Scheme in Location Dependent Continuous Queries

1. Probabilistic Continuous Update Scheme in Location Dependent Continuous Queries Song Han and Edward Chan Department of Computer Science, City University of Hong Kong 83 Tat Chee Avenue, Kowloon, HONG KONG

2. Agenda • Introduction • Objective • System Model • Methodology • Performance Analysis • Conclusion

3. IntroductionModeling of Moving Object • Moving Object Spatio -Temporal (MOST) Model • For location management and location prediction • To reduce the update cost (frequency of Update) • Predictive Approach • If next update time is t1, at time t’ during [t0 ,t1], the position of A <x’,y’> is predicted as: x’ = x0 + v0 * cosα0 * (t’ – t0); y’ = y0 + v0 * sinα0 * (t’ – t0)

4. IntroductionWhat is a LDCQ? • Example: A user walking along a road wants to know whether there exists a taxi inside the range of 1km around him from now to 10 min later. • Special Features: • 1. Location Dependent • Different time, Different Position, Different Query Result • 2. Continuous Query • The active period of the query is from now to 10 min later

5. IntroductionBasic Location Update Methods • Time-based Location Update (TB) • A periodic update scheme • Generate an update every fixed time threshold T • How to define T? • Distance-based Location Update (DB) • If the difference between current location and last update location is larger than the distance threshold D, an update is generated • How to define D?

6. Introduction Time-based Update Distance-based Update

7. IntroductionBasic Location Update Methods • Hybrid (time-based + distance-based) • Either condition from Time-based Location Update or Distance-based Location Update is satisfied, an update is generated. • Speed-dead-reckoning (SDR) • An update is generated if the deviation of its current location is greater than the predicted location by a pre-defined distance threshold

8. Introduction Hybrid Method Speed-dead-reckoning

9. Objective • To formulate an update strategy to meet user fidelity requirement. • To related the update frequency to the overall accuracy of the query.

10. Location Updates Location Database Server Wireless Network Query Processor Continuous Queries Moving Objects Moving Objects Database System Model The system architecture of a mobile computing system

11. Uncertainty Model Definition 1 : Uncertainty RegionAn Uncertainty Region of mobile object M at time t, U (p, t), is a closed region such that M can be found inside this region with a probability p.Definition 2 : Uncertainty PDFUncertainty Probability Density Function of a mobile object M at time t, f (x, y, t), is the probability density function of M ’s location at time t and

12. Methodology Probabilistic Continuous Update Scheme • Object Location Update (OLU): • Issued by both Query Object and Moving Object • To guarantee at time t, the mobile object ’s position will not be outside its uncertainty region U (p, t). • Query Accuracy Update (QAU): • Issued only by Moving Object • When the change of the moving object’s uncertainty region will affect the answer set for a certain Q with a probability p which is specified by the user.

13. Example of OLU

14. Example of QAU

15. Generation of OLU • Calculation is independent and same for moving objects and query objects • The uncertainty PDF for the position of MO satisfy normal distribution • X ~ N (xP, σX), Y ~ N (yP, σY) • An update will be issued if its actual position at time t exceeds the predicted position’s confidence interval c • (xP - u (1-c)/2 * σX, xP - u (1-c)/2 * σX) (yP - u (1-c)/2 * σy, yP - u (1-c)/2 * σy)

16. Generation of OLU Improvement in Generation of Object Location Update

17. Generation of OLU Condition :Update Threshold :Where

18. Generation of QAU • In a range query, all moving objects are independent. We consider the calculation between OM and OQ. • XM ~ N (xMP, σx2),YM ~ N (yMP, σy2), • XQ ~ N (xQP, σx’2), YQ ~ N (yQP, σy’2) • xMP = xM + vM * (t - tM) * cos(α) • yMP = yM + vM * (t - tM) * sin(α) • xQP = xQ + vQ * (t - tQ) * cos(β) • yQP = yQ + vQ * (t - tQ) * sin(β)

19. Generation of QAU • The relative movement of OM and OQ. <X’, Y’> • X’ = XM -XQ => X’ ~ N (xMP-xQP, σx2+σx’2) • Y’ = YM -YQ => Y’ ~ N (yMP- yQP, σy2 +σy’2) • The probability that the OM will cross the query boundary at time t. μ1 = xMP - xQP, μ2 = yMP - yQP σ12 = σx2 +σx’2, σ22 = σy2 +σy’2

20. Generation of QAU Integration Area Ω is different depending on M’s moving Direction

21. Prediction of the next QAU time

22. Simulation Model • Random Waypoint Mobility Model • Continuous query length: 1000 sec • Query Boundary: 200 m • Number of Moving Object: 100 • Size of the area: 1000 m * 1000 m • Fidelity Requirement: 95% • Confidence Level: 95% • Speed of the moving object: U [12km/h, 60km/h]

23. Performance Analysis Fidelity vs. Object Location Variance Number of updates vs. OLV

24. Performance Analysis Total number of updates vs. OLV Fidelity vs. Number of Updates

25. Conclusion • Probabilistic Continuous Update Scheme is proposed to meet user fidelity requirement • Goes beyond traditional location update schemes • Related the update frequency to the overall accuracy of the query.

26. Future Work • Adaptive OLU generation • How to calculate the predicted update time directly • How to reduce to calculation complexity in calculating the predicted update time • Extend Entity Query to Count Query • Extend RQ to NNQ and kNNQ

27. References • [1] M. H. Dunham and V. Kumar, Location Dependent Data and its Management in Mobile Database, Database and Expert Systems Applications, 1998, Proc. 9h International Workshop on Database and Expert Systems Applications, 1998. • [2] A. P. Sistla, O. Wolfson, S. Chamberlain, and S. Dao, Querying the Uncertain Position of Moving Objects, Temporal Database – Research and Practice Lecture Notes in Computer Science 1399, 1998. • [3] O. Wolfson, S. Chamberlain, S. Dao, L. Jiang and G. Mendez, Cost and Imprecision in Modeling the Position of Moving Objects, Proc. 14th International Conference on Data Engineering, 1998. • [4] Reynold Cheng, Dmitri V. Kalashnikov, and Sunil Prabhakar, Querying imprecise data in moving object environments, IEEE Trans. on Knowledge and Data Engineering, Vol. 16(7), July 2004. • [5] Jinfeng Ni and C. V. Ravishankar, Probabilistic Spatial Database Operations, Proc. 8th Intl. Symposium on Spatial and Temporal Databases (SSTD), 2003.

28. Thank you!

29. Simulation Metrics • Fidelity of the Probabilistic Range Query • It measures the deviation of the results in the database from the correct results for a range query Q. • Based on the concepts of false positives and false negatives • Sdbase (Q, t) is the result set of Q at time t from database • Sideal (Q, t) is the result set of Q at time t from actual location • f+ (Q, t) measures the fraction of objects wrongly included into the answer of Q and f - (Q, t) measures the portion of objects that are missing in the correct answer of Q.

30. Simulation Metrics • Fidelity of Continuous Range Query • E (t) = f+ (Q, t) + f - (Q, t) < εwhere E (t) is the error ratio of Q at time t and ε, thefidelity requirement, is a real-valued system parameter for Q.