A Discourse on Complexity of Process Models

A Discourse on Complexity of Process Models

J. Cardoso Universidade da MadeiraJ. Mendling Vienna University of EconomicsG. Neumann Vienna University of EconomicsH.A. Reijers TU Eindhoven

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Is this complex?

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Problems?

deadlock

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Agenda

1. Errors due to Complexity? The SAP Reference Model

2. From Software Metrics to Process Metrics

3. From Graph Metrics to Process Metrics

4. Conclusion

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Agenda

Errors due to Complexity? The SAP Reference Model

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Verification Approach

V

V

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SAP Reference Model

EPC to YAWL

Generated YAWL Models

Model Analyzer

WofYAWL <warning>Task or (ahvi) may not forward control to task xor (aho7)</warning><warning>Task or (ahvi) may not forward control to task and (ahql)</warning>...

WofYAWL Analysis Output

<model><treenr>Asset Accounting</treenr><modelnr>1</modelnr><modeltype>MT_EEPC</modeltype><level>5</level><name>Index Series</name><events>0</events><andsplits>0</andsplits><arcs>2</arcs><hasCycles>false</hasCycles>...

Model Characteristics Table Generator

# # # # # ## ## # # # # ## ## # # # # ## ## # # # # ## ## # # # # ## ## # # # # ## #

Analysis Table

Mendling et al. 2006: A Quantitative Analysis of Faulty EPCs in the SAP Reference Model. BPM Center Report.

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Results

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Why Errors

• Hypotheses:

• Model Size

• Model Complexity

• Error Patterns

• Independent variables:

• Number of each element type

• Cycles

• Complexity metrics based on state space

• Logistic Regression:

• Explain error (yes/no)

• Nagelkerke R2: 0.30 and 0.26 in significant models

• Correct Classification: about 95%

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Agenda

From Software Metrics to Process Metrics

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Adapting the LOC Metric

• In Software Engineering:

• Lines of Code

• For Business Processes:

• Number of Activities

• Number of Activities and Splits

• Number of Activities, Splits, and Joins

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How complex is this?

No. of Act.: 43

No. of Act.+Splits: 52

No. of Act.+Splits+Joins: 67

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Adapting McCabe‘s Cyclomatic Complexity

• In Software Engineering:

• edges – nodes +2

• For Business Processes:

• CFC = Σxor fan-out(xor) + Σor 2fan-out(or)-1 + Σand 1

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How complex is this?

No. of AND-Splits: 6

No. of OR-Splits: 2

No. of XOR-Splits: 1

CFC: 43

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Adapting Halstead Complexity

• In Software Engineering:

• n1: No. of unique operators

• n2: No. of unique operands

• N1: No. of operator occurences

• N2: No. of operand occurences

• For Business Processes:

• n1: No. of node types

• n2: 1

• N1: No. of nodes

• N2: 1

• Halstead Metrics:

• Process Length: n1*log(n1)+n2*log(n2)

• Process Volume:(N1+N2)*log(n1+n2)

• Process Difficulty:(n1/2)*(N2/n2)

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How complex is this?

n1: F+E+ANDj+ANDs+XORj+XORs+ORj+ORs

n2: 1

N1: 107

N2: 1

Process Length: 8*log(8)+1*log(1) = 24

Process Volume:(108)*log(9) = 342,35

Process Difficulty:(4)*(1) = 4

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Adapting Henry&Kafura Information Flow

• In Software Engineering:

• Σactivity Length * (Fan-in * Fan-out)2

• For Business Processes:

• Σactivity 1 * (inputs * outputs)2

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How complex is this?

Σactivity 1 * (inputs * outputs)2 = 312

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Agenda

From Graph Metrics to Process Metrics

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Adapting Network Complexity

• In Graph Theory:

• no. of arcs / no. of nodes

• For Business Processes:

• no. of arcs / no. of nodes

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How complex is this?

no. of arcs / no. of nodes = 122 / 107 = 1,14

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Adapting Restrictiveness Estimator

• In Graph Theory:

• 2 * Σrij – 6*(N-1) / (N-2)*(N-3)

• For Business Processes:

• 2 * Σrij – 6*(N-1) / (N-2)*(N-3)

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How complex is this?

2 * Σrij – 6*(N-1) / (N-2)*(N-3) = 2* 3389 – 6*(106) / (105)*(104)=

0,5625

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Agenda

Conclusion

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Processes Compared

No. of Act.: 3 vs. 43

No. of Act.+Splits: 7 vs. 52

No. of Act.+Splits+Joins:8 vs. 67

CFC: 14 vs. 43

Process Length: 19,65 vs. 24

Process Volume: 57 vs. 342,35

Process Difficulty: 3,5 vs. 4

Henry&Kafura: 36 vs. 312

Arcs/Nodes: 1 vs. 1,14

Restrictiveness Est.: 0,66 vs. 0,5615

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Conclusion

• Metrics from Software Engineering and Graph Theory can be adapted

• Empirical Correlation of metrics with errors, maintainability, etc. to be tested

• Further Research into graph metrics required

• Future research:

• test correlation of perceived process complexity and metrics

• test predictive power of metrics for error probability