1. Department of Computer Science City University of Hong Kong Department of Computer Science City University of Hong Kong 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 2 Agenda Introduction Objective System Model Methodology Performance Analysis Conclusion

3. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 3 Introduction Modeling 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 t 1, at time t’ during [t 0,t 1 ], the position of A is predicted as: x’ = x 0 + v 0 * cosα 0 * (t’ – t 0 ); y’ = y 0 + v 0 * sinα 0 * (t’ – t 0 ) Mobile ObjectUpdate TimePositionSpeedDirection At0t0 v0v0 α0α0

4. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 4 Introduction What 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 5 Introduction Basic 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 6 Introduction Time-based Update Distance-based Update

7. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 7 Introduction Basic 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 8 Introduction Hybrid Method Speed-dead-reckoning

9. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 10 System Model The system architecture of a mobile computing system Location Database Server Query Processor Moving Objects Database Location Updates Moving Objects Continuous Queries Wireless Network

11. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 11 Uncertainty Model Definition 1 : Uncertainty Region An 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 PDF Uncertainty 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 13 Example of OLU

14. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 14 Example of QAU

15. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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 (x P, σ X ), Y ~ N (y P, σ Y ) An update will be issued if its actual position at time t exceeds the predicted position’s confidence interval c (x P - u (1-c)/2 * σ X, x P - u (1-c)/2 * σ X ) (y P - u (1-c)/2 * σ y, y P - u (1-c)/2 * σ y )

16. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 16 Generation of OLU Improvement in Generation of Object Location Update

17. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 17 Generation of OLU Condition : Update Threshold : Where

18. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 18 Generation of QAU In a range query, all moving objects are independent. We consider the calculation between O M and O Q. X M ~ N (x M P, σ x 2 ),Y M ~ N (y M P, σ y 2 ), X Q ~ N (x Q P, σ x ’2 ), Y Q ~ N (y Q P, σ y ’2 ) x M P = x M + v M * (t - t M ) * cos(α) y M P = y M + v M * (t - t M ) * sin(α) x Q P = x Q + v Q * (t - t Q ) * cos(β) y Q P = y Q + v Q * (t - t Q ) * sin(β)

19. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 19 Generation of QAU The relative movement of O M and O Q. X’ = X M -X Q => X’ ~ N (x M P -x Q P, σ x 2 +σ x ’2 ) Y’ = Y M -Y Q => Y’ ~ N (y M P - y Q P, σ y 2 +σ y ’2 ) The probability that the O M will cross the query boundary at time t. μ 1 = x M P - x Q P, μ 2 = y M P - y Q P σ 1 2 = σ x 2 +σ x ’2, σ 2 2 = σ y 2 +σ y ’2

20. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 20 Generation of QAU Integration Area Ω is different depending on M’s moving Direction

21. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 21 Prediction of the next QAU time

22. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 23 Performance Analysis Fidelity vs. Object Location Variance Number of updates vs. OLV

24. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 24 Performance Analysis Total number of updates vs. OLVFidelity vs. Number of Updates

25. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 28 Thank you!

29. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 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 S dbase (Q, t) is the result set of Q at time t from database S ideal (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. Department of Computer Science City University of Hong Kong Probabilistic Continuous Update Scheme in LDCQ 30 Simulation Metrics Fidelity of Continuous Range Query E (t) = f+ (Q, t) + f - (Q, t) < ε where E (t) is the error ratio of Q at time t and ε, the fidelity requirement, is a real-valued system parameter for Q.