1. A Discourse on Complexity of Process Models J. CardosoUniversidade da Madeira J. MendlingVienna University of Economics G. NeumannVienna University of Economics H.A. ReijersTU Eindhoven

2. Folie 2 Is this complex?

3. Folie 3 Problems? deadlock

4. Folie 4 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

5. Folie 5 Agenda Errors due to Complexity? The SAP Reference Model

6. Folie 6 Verification Approach Mendling et al. 2006: A Quantitative Analysis of Faulty EPCs in the SAP Reference Model. BPM Center Report.

7. Folie 7 Results

8. Folie 8 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 R 2 : 0.30 and 0.26 in significant models Correct Classification: about 95%

9. Folie 9 Agenda From Software Metrics to Process Metrics

10. Folie 10 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

11. Folie 11 How complex is this? No. of Act.: 43 No. of Act.+Splits: 52 No. of Act.+Splits+Joins: 67

12. Folie 12 Adapting McCabe‘s Cyclomatic Complexity In Software Engineering: edges – nodes +2 For Business Processes: CFC = Σ xor fan-out(xor) + Σ or 2 fan-out(or) -1 + Σ and 1

13. Folie 13 How complex is this? No. of AND-Splits: 6 No. of OR-Splits: 2 No. of XOR-Splits: 1 CFC: 43

14. Folie 14 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)

15. Folie 15 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

16. Folie 16 Adapting Henry&Kafura Information Flow In Software Engineering: Σ activity Length * (Fan-in * Fan-out) 2 For Business Processes: Σ activity 1 * (inputs * outputs) 2

17. Folie 17 How complex is this? Σ activity 1 * (inputs * outputs) 2 = 312

18. Folie 18 Agenda From Graph Metrics to Process Metrics

19. Folie 19 Adapting Network Complexity In Graph Theory: no. of arcs / no. of nodes For Business Processes: no. of arcs / no. of nodes

20. Folie 20 How complex is this? no. of arcs / no. of nodes = 122 / 107 = 1,14

21. Folie 21 Adapting Restrictiveness Estimator In Graph Theory: 2 * Σr ij – 6*(N-1) / (N-2)*(N-3) For Business Processes: 2 * Σr ij – 6*(N-1) / (N-2)*(N-3)

22. Folie 22 How complex is this? 2 * Σrij – 6*(N-1) / (N-2)*(N-3) = 2* 3389 – 6*(106) / (105)*(104)= 0,5625

23. Folie 23 Agenda Conclusion

24. Folie 24 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

25. Folie 25 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