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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
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Decomposing Replay Problems:A Case Study
Eric Verbeek and Wil van der Aalst
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
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Decomposition using Passages
Rule DescriptionR1 Incident arcs of places are equivalent
R2 Incident arcs of invisible transitions are equivalent
R3 Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label
PAGE 3
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
− SumPAGE 4
Case Study – Settings – Petri nets
Petri net Transitions Places Arcs LabelsRepairExample 12 12 26 8
A32 32 32 74 32
Bpic2012A 11 14 28 10
Bpic2012 58 44 124 36
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Case Study – Settings – Event logs
Event log Cases Events LabelsRepairExample 1104 11,855 12
A32f1n00 1000 24,510 32
A32f1n10 1000 24,120 32
A32f1n50 1000 22,794 32
Bpic2012A 13,087 60,849 10
Bpic2012 13,087 262,200 36
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Case Study – Settings – Replay results
Event log Running time (secs) CostsRepairExample 0.25 0.197
A32f1n00 11.00 0.000
A32f1n10 17.00 0.993
A32f1n50 32.00 4.521
Bpic2012A 0.59 1.293
Bpic2012 480.00 14.228
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Case Study – Decomp. Replay Results
Event log Passages Running time CostsRepairExample 6 0.43 171% 0.196 99%
A32f1n00 30 1.30 12% 0.000 100%
A32f1n10 30 1.10 7% 0.444 45%
A32f1n50 30 1.20 4% 2.155 48%
Bpic2012A 8 2.20 378% 0.629 49%
Bpic2012 12 DNF
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Bpic2012
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Bpic2012 – Problematic Passage
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BPIC2012 – Attempt 1
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Running time Costs470.00 98% 8.722 61%
BPIC2012 – Attempt 2
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Running time Costs190.00 40% 6.676 47%
BPIC2012 – Attempt 3a
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Rule DescriptionR1 Incident arcs of places are equivalent
R2 Incident arcs of invisible transitions are equivalent
R3 Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label
R4 The 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
Case Study – Attempt 3a – Results
Event log Passages Running time CostsRepairExample 2 0.31 136% 0.197 100%
A32f1n00 4 1.90 18% 0.000 100%
A32f1n10 4 2.10 13% 0.929 94%
A32f1n50 4 3.10 10% 4.322 96%
Bpic2012A 1 0.74 125% 1,293 100%
Bpic2012 1 480.00 101% 14.228 100%
PAGE 14
BPIC2012 – Attempt 3b
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Rule DescriptionR1 Incident arcs of places are equivalent
R2 The i-th input arc of an invisible transition is equivalent to the i-th output arc of that transition, it both exist
R3 Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label
R4 The 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
Case Study – Attempt 3b – Results
Event log Passages Running time CostsRepairExample 2 0.31 136% 0.197 100%
A32f1n00 4 1.90 18% 0.000 100%
A32f1n10 4 2.10 13% 0.929 94%
A32f1n50 4 3.10 10% 4.322 96%
Bpic2012A 3 2.30 391% 1.272 98%
Bpic2012 3 400.00 83% 14.227 100%
PAGE 16
BPIC2012 – Attempt 3c
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Rule DescriptionR1 Incident arcs of places are equivalent
R2 The i-th input arc of an invisible non-milestone transition is equivalent to the i-th output arc of that transition, it both exist
R3 Incident arcs of visible transitions with non-unique labels are equivalent to incident arcs of all transitions with the same label
R4 The 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
BPIC2012 – Attempt 3c - Milestones
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Running time Costs100.00 22% 11.722 82%
Wrapping Up
Event log Passages Running time CostsA32f1n00 1
411.01.9 18%
0.0000.000 100%
A32f1n10 14
17.02.1 13%
0.9930.929 100%
A32f1n50 14
32.03.1 10%
4.5214.332 96%
Bpic2012 14
480.0100.0 22%
14.22811.722 82%
PAGE 19
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?
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Bpic2012 – Attempt 1
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Bpic2012 – Attempt 2
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Bpic2012 – Attempt 3c
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Subnet Running time Costs
A 100.0 7.102
B 66.0 0.951
C 2.8 0.863
D 97.0 2.806
Total 260.0 11.722
A
BC
D
Tool Implementation – ProM 6
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