1. Decomposing Replay Problems: A Case Study Eric Verbeek and Wil van der Aalst

2. Replay In Event log Traces −Events −Activity Petri net Labeled transitions −Activity Initial marking Final markings Cost structure Out Alignments Transition sequence −Activity −Synchronous −Net only −Silent transition Trace −Activity −Synchronous −Log only Minimal costs PAGE 1

3. Decomposition using Passages RuleDescription R1Incident arcs of places are equivalent R2Incident arcs of invisible transitions are equivalent R3Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label PAGE 2

4. Decomposed Replay Decompose Petri net into subnets Using passages (subsuming activities) Adapt cost structure Decompose Event log into sublogs Empty traces! Replay every sublog on corresponding subnet Idea: Replaying sublogs on subnets is more efficient than replaying event log on Petri net Can easily be done on multiple cores Merge replay results Aggregate costs −Sum PAGE 3

5. Case Study – Settings – Petri nets Petri netTransitionsPlacesArcsLabels RepairExample12 268 A3232 7432 Bpic2012A11142810 Bpic2012584412436 PAGE 4

6. Case Study – Settings – Event logs Event logCasesEventsLabels RepairExample110411,85512 A32f1n00100024,51032 A32f1n10100024,12032 A32f1n50100022,79432 Bpic2012A13,08760,84910 Bpic201213,087262,20036 PAGE 5

7. Case Study – Settings – Replay results Event logRunning time (secs)Costs RepairExample0.250.197 A32f1n0011.000.000 A32f1n1017.000.993 A32f1n5032.004.521 Bpic2012A0.591.293 Bpic2012480.0014.228 PAGE 6

8. Case Study – Decomp. Replay Results Event logPassagesRunning timeCosts RepairExample60.43171%0.19699% A32f1n00301.3012%0.000100% A32f1n10301.107%0.44445% A32f1n50301.204%2.15548% Bpic2012A82.20378%0.62949% Bpic201212DNF PAGE 7

9. Bpic2012 PAGE 8

10. Bpic2012 – Problematic Passage PAGE 9

11. BPIC2012 – Attempt 1 PAGE 10 Running timeCosts 470.0098%8.72261%

12. BPIC2012 – Attempt 2 PAGE 11 Running timeCosts 190.0040%6.67647%

13. BPIC2012 – Attempt 3a PAGE 12 RuleDescription R1Incident arcs of places are equivalent R2Incident arcs of invisible transitions are equivalent R3Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label R4The i-th input arc of a visible transition with unique label is equivalent to the i-th output arc of that transition, if both exist

14. Case Study – Attempt 3a – Results Event logPassagesRunning timeCosts RepairExample20.31136%0.197100% A32f1n0041.9018%0.000100% A32f1n1042.1013%0.92994% A32f1n5043.1010%4.32296% Bpic2012A10.74125%1,293100% Bpic20121480.00101%14.228100% PAGE 13

15. BPIC2012 – Attempt 3b PAGE 14 RuleDescription R1Incident arcs of places are equivalent R2The i-th input arc of an invisible transition is equivalent to the i-th output arc of that transition, it both exist R3Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label R4The i-th input arc of a visible transition with unique label is equivalent to the i-th output arc of that transition, if both exist

16. Case Study – Attempt 3b – Results Event logPassagesRunning timeCosts RepairExample20.31136%0.197100% A32f1n0041.9018%0.000100% A32f1n1042.1013%0.92994% A32f1n5043.1010%4.32296% Bpic2012A32.30391%1.27298% Bpic20123400.0083%14.227100% PAGE 15

17. BPIC2012 – Attempt 3c PAGE 16 RuleDescription R1Incident arcs of places are equivalent R2The i-th input arc of an invisible non-milestone transition is equivalent to the i-th output arc of that transition, it both exist R3Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label R4The i-th input arc of a visible non-milestone transition with unique label is equivalent to the i-th output arc of that transition, if both exist

18. BPIC2012 – Attempt 3c - Milestones PAGE 17 Running timeCosts 100.0022%11.72282%

19. Wrapping Up Event logPassagesRunning timeCosts A32f1n001414 11.0 1.918% 0.000 100% A32f1n101414 17.0 2.113% 0.993 0.929100% A32f1n501414 32.0 3.110% 4.521 4.33296% Bpic20121414 480.0 100.022% 14.228 11.72282% PAGE 18

20. Take-Home Points Decomposed Replay can be faster At acceptable costs Decomposed Replay can be slower, much slower What are good passages? Given the replayer we’re using Chaining passages seems to help Sparsest cuts through the net? PAGE 19

21. Bpic2012 – Attempt 1 PAGE 20

22. Bpic2012 – Attempt 2 PAGE 21

23. Bpic2012 – Attempt 3c PAGE 22 SubnetRunning timeCosts A100.07.102 B66.00.951 C2.80.863 D97.02.806 Total260.011.722 A B C D

24. Tool Implementation – ProM 6 PAGE 23