1. Evaluating Window Joins over Unbounded Streams Jaewoo Kang Jeffrey F. Naughton Stratis D. Viglas {jaewoo, naughton, viglas}@cs.wisc.edu Univ. of Wisconsin-Madison ICDE’03 Bangalore, India

2. Outline of the talk Introduction: Continuous Queries over Unbounded Streams Measuring the Cost of Sliding Window Joins On Maximizing the Efficiency of Processing Joins Summary

3. Sliding Windows Handling internal states is big challenge. Approximate answers Sliding windows – toss out expired tuples Synopses – resort to reduced answer precision

4. A Simple Sliding Window Query On arrival of a new tuple to window A 1. Scan window B and propagate matching tuples 2. Insert new tuple into window A 3. Invalidate all expired tuples in window A λaTaλaTa λaλa λbλb λbTbλbTb AB

5. Some interesting questions How should we measure the efficiency of a sliding window join evaluation strategy? Can a sliding window join algorithm take advantages of asymmetries in two input stream speeds?

6. Interesting questions (Cont’d) How should we allocate computing resources between the two windows to maximize join efficiency? If memory is the bottleneck, how should we allocate memory between the two windows for the two inputs?

7. Interesting questions How should we measure the efficiency of a sliding window join evaluation strategy? Can a sliding window join algorithm take advantages of asymmetries in two input stream speeds?

8. Outline of the talk Introduction: Continuous Queries over Unbounded Streams Measuring the Cost of Sliding Window Joins On Maximizing the Efficiency of Processing Joins Summary

9. Cost Model Unit-time basis cost model Aggregate cost of processing tuples arriving in each window in a time unit λaTaλaTa λaλa λbλb λbTbλbTb AB

10. Cost Model (Cont’d) Cost formula can be divided into two independent groups, one for each input stream Thus, can evaluate join algorithms for each join direction independently λaTaλaTa λaλa λbλb λbTbλbTb AB

11. Cost of One-way NLJ P(D) - cost of accessing one tuple in data structure D during search operation I(D) - cost of accessing one tuple in data structure D during update operation Total number of tuples processed in a time unit multiplied by the tuple access cost

12. Cost of One-way HJ |B| -- #of hash buckets in window B B/|B| -- #of tuples in a hash bucket Implement hash bucket to preserve tuple arrival order – avoid invalidation overhead.

13. Cost of One-way T-tree INLJ N – size of a T-tree node (#of tuples) B/N – total #of nodes in a T-tree

14. Implementation Implemented: Four join algorithms: NLJ, HJ, BJ, and TJ. Asymmetric join operator Stream emulator System: Java HotSpot VM 1.4 AMD Athlon XP 1533Mhz, 1GB memory Windows XP Professional

15. Fitting Parameters in the Model Process 60 seconds worth of tuples without intermittent delays, at 20 different points with increasing workload rates. Then, equate the measured values with the cost formula, and solve the equation. Hash bucket size = 10, T-tree node size = 100 used P(N) = 3x10 -4 P(H) = 5.5x10 -4 P(BT) = 2.6x10 -4 P(TT) = 2.6x10 -4 I(N) = 1x10 -4 I(H) = 7.8x10 -4 I(BT) = 2.6x10 -4 I(N) = 2.7x10 -4

16. Outline of the talk Introduction: Continuous Queries over Unbounded Streams Measuring the Cost of Sliding Window Joins On Maximizing the Efficiency of Processing Joins Summary

17. Interesting questions How should we measure the efficiency of a sliding window join evaluation strategy? Can a sliding window join algorithm take advantages of asymmetries in two input stream speeds?

18. Taking Advantage of Asymmetry There are cases where an asymmetric combination of join algorithms outperforms symmetric counterparts! E.g. for some A, B

19. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

20. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

21. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

22. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

23. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

24. Join Cost Estimation using Cost Model Size of window A = 5000 Size of window B = 5000 Five winning combinations: TN, TH, HH, HT, NT

25. Measured Join Cost (CPU Time) A=5000, B=5000 Memory utilization: HJ (h=10) consumed 5% more than TJ (n=100). Same five winners: TN, TH, HH, HT, NT Cost model prediction was accurate for both overall shape and crossover points. What if we increase window A and decrease window B? (e.g. A=7000, B=3000 as opposed to current 5000:5000)

26. Cross-over Point TN-TH TN-TH only dependent on window size B TN-TH = 0.0094 (B=500), meaning TNJ will outperform THJ when stream B is more than 106 times faster than stream A. TN-TH = 0.0555 (B=100), 18 times. λaTaλaTa λaλa λbλb λbTbλbTb AB

27. Cross-over Point TH-HH TH-HH only dependent on the size of window A If the size of window A increases the crossover point TH-HH will move toward left, and vice versa.

28. A=9500, B=500, λa=2, λb=998 Join Performance A=7000, B=3000, λa=800,λb=200

29. Interesting questions (Cont’d) How should we allocate computing resources between the two windows to maximize join efficiency? If memory is the bottleneck, how should we allocate memory between the two windows for the two inputs?

30. Resource Allocation & Join Performance Focus on cases where system resources are insufficient to fully support queries and workloads. Input streams are simply too fast to keep up with. Evaluating expensive join operator and its service rate is lower than the input rates. System memory cannot hold both windows.

31. Resource Allocation & Join Performance (Cont’d) Approximate answers may be acceptable E.g. query involving aggregate (e.g. average) over join Question is how to maximize the accuracy of the approximate answers, given the limited resources. We use insight that larger samples produce better answers Goal is to maximize the #of join result tuples Care must be taken to ensure that the result produced is statistically comparable to a random sample of the full join result.

32. Limited Computing Resources λa=800, λb=200 A=100, B=200  =0.01, μ=100 Window Join Output Rate : w/ Effective Rates =

33. Limited Memory Resources λa=10, λb=50 M=1000,  =0.005 Window Join Output Rate =

34. Limited Memory & Computing Resources μ=10, M=100  =0.01 Best performers are groups that allocate maximum computing resources to one stream and maximum memory to the another.

35. Summary Introduced unit-time basis cost model and experimentally validated it. Extended traditional join framework to include asymmetric combinations of join algorithms. Investigated resource allocation strategies for improving the accuracy of approximate answers. Developed powerful optimization framework for sliding window join queries by addressing these issues in a unified manner.