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

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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%

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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%

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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%

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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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