Analysis of workflows : Verification, validation, and performance analysis .

1. Eindhoven University of Technology Faculty of Technology Management Department of Information and Technology P.O. Box 513 5600 MB Eindhoven The Netherlands w.m.p.v.d.aalst@tm.tue.nl Analysis of workflows: Verification, validation, and performance analysis. Wil van der Aalst

2. Design-time and run-time questions Run-time Design-time • verificationvalidationperformance analysis • process mining

3. Techniques to analyze workflows (design-time) • Validation is concerned with the relation between the model and reality. • Verification is typically used to answer qualitative questions • Is there a deadlock possible? • It is possible to successfully handle a specific case? • Will all cases terminate eventually? • It is possible to execute two tasks in any order? • Performance analysis is typically used to answer quantitative questions • How many cases can be handled in one hour? • What is the average flow time? • How many extra resources are required? • How many cases are handled within 2 days?

4. Verification: analysis techniques can be used to avoid logical errors. c3 check_policy send_letter c4 c1 c2 c5 start register ready check_damage pay_damage c6 Is this a correct workflow? If not, how to correct it?

5. It this process correct?

6. Error 1: dangling tasks task4 task5 begin task1 task2 task3 end

7. Error 2: deadlock (task2) task2 begin task1 end

8. Error 3: unbounded and never-ending begin task1 task2 task3 end

9. Error 4: deadlock before or after termination begin task1 task2 task3 end

10. Soundness property Eventually the case terminates and the moment it terminates all references have been removed. process definition • The soundness property corresponds to two standard Petri-net properties (liveness and boundedness). • Standard Petri-net-based tools can be used. • For (almost) free-choice nets this can be checked in polynomial time! begin end

11. problem toolbox modeling Petri net description analysis structural analysis reachability analysis Markovian analysis OR-techniques simulation answers Petri-nets: a solver-independent medium

12. red1 red2 safe yr1 yr2 yellow1 yellow2 rg1 rg2 gy1 gy2 green1 green2 Reachability analysis

13. Reachability graph • Each node corresponds to a reachable state. • Done by a computer. • A computer can cope with reachability graphs with millions of nodes. The traffic lights are safe!

14. Exercise: construct reachability graph c3 check_policy send_letter c4 c1 c2 c5 start register ready check_damage pay_damage c6

15. Structural analysis Many techniques are available: • place invariants • transition invariants • traps and siphons • reduction rules • decomposition techniques • S-covers/T-covers • special techniques for subclasses: • state machines • marked graphs • free-choice nets • asymmetric free-choice nets

16. Place invariants • A place invariant assigns a weight to each place such that the weighted token sum remains constant. man couple marriage divorce • 1man + 1woman+2couple =constant (man+woman+2couple=7) • woman + couple • man + couple • man - woman woman

17. red1 red2 safe yr1 yr2 yellow1 yellow2 rg1 rg2 gy1 gy2 green1 green2 Example red1+yellow1+green1 = 1 red2+yellow2+green2 = 1 safe + green1 + green2 + yellow1 + yellow2 = 1 red1 + red2 - safe = 1

18. Place invariants can be used to check detect errors • There should be a positive place invariant assigning positive weights to all places and identical weights to begin and end. • 1.begin + 1.end + ..... = constant begin end

19. Exercise c3 send_letter check_policy c1 c4 c5 c2 start register ready check_damage pay_damage c6 Use place invariants to motivate the correctness of the process definition.

20. Example process_form send_form c1 c5 archive c3 time-out evaluate start register ready c7 c2 c6 c4 check_proc Sound? P-inv.? process_complaint

21. Example (2) process_form send_form c1 c5 archive c3 time-out evaluate start register ready c2 c6 c4 check_proc Sound? P-inv.? process_complaint

22. Example (3) process_form send_form c1 c5 archive c3 time-out evaluate c8 start register ready c7 c2 c6 c4 check_proc Sound? P-inv.? process_complaint

23. Example (4) process_form send_form c1 c5 archive c3 time-out evaluate start register ready c7 c2 c6 check_proc c4 Sound? P-inv.? process_complaint

24. Example (5) process_form send_form c1 c5 archive c3 time-out evaluate start register ready c7 c2 c6 c4 check_proc Sound? P-inv.? process_complaint

25. Transition invariants • A transition invariant assigns a weight to each transition such that the net effect of firing each transition the specified number of time is zero, i.e., the initial marking is reproduced. man couple marriage divorce • marriage + divorce • 2.marriage + 2.divorce woman

26. Transition invariants can be used to detect errors short-circuited net • There should be a positive transition invariant assigning positive weights to all transitions. begin end

27. Example • Give transition invariants of short-circuited net. c3 check_policy send_letter c4 c1 c2 c5 start register ready check_damage pay_damage c6

28. Why invariants? • Can be calculated efficiently (polynomial time for a basis). • Independent of initial marking. • However, the main reason is didactical! You only truly understand a model if you think about it in terms of invariants!

29. Performance analysis Questions: • throughput, waiting and service times • service levels • occupation rates Techniques: • simulation • queuing theory • Markovian analysis

30. Example: sequential (1) 24 arrivals per hour • average throughput time : 22.2 minutes • service time: 8.0 minutes • waiting time: 14.2 minutes 2 resources, average service time of 4 minutes 2 resources, average service time of 4 minutes c1 task1 c2 task2 c3

31. Parallel (2) 24 arrivals per hour 2 resources, average service time of 4 minutes • average throughput time : 15 minutes • service time: 4 minutes • waiting time: 11 minutes c21 c23 task1 c1 c3 task2 c22 c24 2 resources, average service time of 4 minutes

32. Compose (3) • average throughput time : 9.5 minutes • service time: 7.0 minutes • waiting time: 2.5 minutes 24 arrivals per hour 4 resources, average service time of 7 minutes c1 task12 c3

33. Flexible resources (4) • average throughput time : 14.0 minutes • service time: 8.0 minutes • waiting time: 6.0 minutes 24 arrivals per hour 4 resources, average service time of 4 minutes c1 task1 c2 task2 c3

34. Triage (5) 1 resource, average service time of 8 minutes • average throughput time : 31.1 minutes • service time: 8.0 minutes • waiting time: 23.1 minutes difficult cases 2 resources, average service time of 4 6 difficult c21 minutes cases per hour task1a c1 c23 task2 c3 task1b 18 easy cases c22 per hour easy cases 1 resource, average service time of 2.66 minutes

35. Priority (6) easy cases have priority 2 resources, average service time 8 (difficult case) or • average throughput time : 14 minutes • service time: 8 minutes • waiting time: 6 minutes 2.66 (easy case) minutes 6 difficult cases per hour task2 c1 task1 c2 c3 18 easy cases per hour easy cases have priority 2 resources, average service time 8 (difficult case) or 2.66 (easy case) minutes

36. situation description average average average throughput t. service time waiting t. Situation 1 sequential 22.2 8.0 14.2 Situation 2 parallel 15 4(8) 11(7) Situation 3 compose 9.5 7.0 2.5 Situation 4 flexibility 14.0 8.0 6.0 Situation 5 triage 31.1 8.0 23.1 Situation 6 priorities 14.0 8.0 6.0 Results

37. Queuing models service Basic characteristics: • average number of arrivals per time unit: l (mean arrival rate) • average number that can be handled by one server per time unit: m (mean service rate) • number of servers: c waiting arrivals l c m

38. Basic relationships: average time between arrivals: 1/l average service time: 1/m occupation rate: r = l/(c*m) average number being served: r = l/m Queuing models (2) l c m W,Lq S,L W (S) = average time in queue (system) Lq (L) = average number in queue (system) • L = Lq + r • S = W + 1/m • Lq = l * W • L = l * S (Little’s formula)

39. M/M/1 queue • Lq = (l* l)/(m * (m-l)) • L = l/(m-l) = r/(1-r) • W = r/(m-l) • S = 1/(m-l) l 1 m • Assumptions: • time between arrivals and service time follow a negative expontential distribution • 1 server (c = 1) • FIFO Also formulas for M/Er/1, M/G/1, M/M/c, ... !

40. Exercise 1 resource, average service time of 8 minutes difficult cases 1 resource, average Calculate: • occupation rates, • average waiting time, • average throughput time, • average number in system. service time of 2 6 difficult c21 minutes cases per hour task1a c1 c23 task2 c3 task1b 18 easy cases c22 per hour easy cases 1 resource, average service time of 2.66 minutes • Increase the occupation rate until 90%: • average waiting time, • average throughput time, • average number in system.

41. Simulation • Random walk through the reachability graph • Computer experiment • pseudo random numbers • random generator • Validation • Statistical aspects • start run • subruns • Animation • Flexible • No proof!

42. Simulation using Protos/ExSpect