2. Chapter Six Process Simulation Using Arena McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc. All rights reserved.

3. Chapter Six Learning Objectives Analyze queuing processes using Excel and Arena Develop and utilize Arena simulation models for a simple queuing process Use Arena to compare alternative queuing processes Develop new Arena modeling techniques by using Arena Example and Smart models

4. Chapter Six Worksheet Menu

5. Chapter Six Files

6. Chapter Six Outline Analyze queuing processes using Excel and Arena Arena Simulation Environment Other Queueing Process Models Other Arena Programs and Examples

7. Analysis and Simulation of Queuing Processes Queuing Process Analysis Using Excel M/M/1 Queue M/M/3 Queue Manual Simulation Using Excel Process Simulation Tasks Why Use Arena for Process Analysis and Improvement?

8. Queuing Process Analysis Using Excel Process BoundaryDefines process limits Arrival SourceSupplies process customers QueueAllows customers to wait for service ServerProvides customer service Exhibit 6-1 p. 155 Page: MM1

9. M/M/1 Queue MThe time between arrivals follows the exponential distribution MThe time for service follows the exponential distribution 1The process has 1 server Exhibit 6-2 p. 156 Sheet: Exponential Exponential Distribution f (x) = λe -λx, for 0 ≤ x < ∞ E (X) = 1/λ V(X) = 1/λ 2 F (x) = 1-e -λx, for 0 ≤ x < ∞

10. M/M/1 Queue Calculations Exhibit 6-3 p. 156 Sheet: MM1 Exhibit 6-4 p. 156 Sheet: MM1 Calculations

11. M/M/1 Queue Calculations Traffic Intensity = ρ = Mean Arrival Rate / Mean Service Rate =Mean Service Time / Mean Inter Arrival Time λ = 1 / 60 = 0.0167 Customers per Seconds = 0.0167 * 60 = 1.00 Customers per Minute μ = 1 / 55 = 0.0182 Customers per Seconds = 0.0182 * 60 = 1.09 Customers per Minute ρ = 1.00 / 1.09 = 0.917 Expected Number in Process = Lp = ρ / (1 - ρ) Expected Number in Queue = Lq = Lp - ρ = ρ2 / (1 - ρ) Exhibit 6-5 p. 167 Sheet: MM1

12. M/M/3 Queue Exhibit 6-6 p. 157 Sheet: MM3

13. Manual Simulation Using Excel Mean Inter Arrival Time in Seconds, 60 Mean Service Time in Seconds, 50 Arrival Option,0 = Fixed or 1 = Exponential Service Option, 0 = Fixed or 1 = Exponential F (60) / F (50) / 1Exhibits 6-7 & 6-8 M (60) / F (50) / 1Exhibits 6-9 & 6-10 M (60) / M (50) / 1Exhibits 6-11 & 6-12

14. Manual Simulation F (60) / F (50) / 1 Exhibit 6-8 p. 158 Sheet: Manual Simulation Exhibit 6-7 p. 158 Sheet: Manual Simulation

15. Manual Simulation M (60) / F (50) / 1 Exhibit 6-10 p. 159 Sheet: Manual Simulation Exhibit 6-9 p. 159 Sheet: Manual Simulation

16. Manual Simulation M (60) / M (50) / 1 Exhibit 6-12 p. 160 Sheet: Manual Simulation Exhibit 6-11 p. 160 Sheet: Manual Simulation

17. Process Simulation Tasks Exhibit 6-13 p. 160 Page: Simulation Tasks

18. Why Use Arena for Process Analysis and Improvement? Simulation History 1961 GPSS (Gordon – IBM) 1982 SIMAN (Pegden – Penn State) 1992 Arena (Systems Modeling Corp.) 2002 Arena Factory Analyzer (Rockwell Software) Other Simulation Products AutoMod Flexsim ProModel Simul8 Witness

19. Arena Simulation Environment Arena Modeling Environment Arena Template Panel Modules Arena Simulation Engine

20. Arena Modeling Environment Modeling Environment Exhibit 6-14 Template Panel Modules Exhibit 6-21 Simulation Engine Exhibit 6-33 VBA Interface Chapter 8 Stand Alone Programs Exhibit 6-59

21. Arena Modeling Environment Exhibit 6-14 p. 161 Model: MM1.doe Tool BarFlowchart Window Spreadsheet Window Project Bar Status Bar

22. Arena Modeling Environment Exhibit 6-15 p. 162 Sheet: Arena Components

23. Arena Modeling Environment Exhibit 6-16 p. 163 Page: Arena File Structure

24. Queueing Process Models MM1.doe MM3.doe Comparison.doe MV1.doe

25. MM1.doe @ 60 Minutes Exhibit 6-17 p. 163 TNOW = 60 Minutes

26. MM1.doe Exhibit 6-18 p. 164 Run Setup Dialog Exhibit 6-19 p. 164 Category Overview Report (Queue)

27. M/M/1 Queue Comparison: Theoretical versus Simulated Exhibit 6-20 p. 165 Sheet: MM1 Comparison

28. Arena Template Panel Modules Create Module Process Module Dispose Module Entity Spreadsheet Queue Spreadsheet Resource Spreadsheet Variable Spreadsheet

29. Arena Template Panel Modules Exhibit 6-21 p. 165 Sheet: Arena Components

30. Arena Basic Process Template Exhibit 6-22 p. 166 Sheet: Arena Modules Exhibit 6-23 p. 166 Arena Basic Process Panel Module Icons

31. Create Module Exhibit 6-24 p. 166 MM1.doe Create Module Dialog Box

32. Process Module Exhibit 6-25 p. 167 MM1.doe Process Module Dialog Box

33. Resource Detail Exhibit 6-26 p. 168 MM1.doe Process Module Resource Detail Dialog Box Exhibit 6-27 p. 168 Arena Resource Picture Placement Window

34. Dispose Module Exhibit 6-28 p. 168 MM1.doe Dispose Module Dialog Box

35. Entity Spreadsheet Exhibit 6-29 p. 169 MM1.doe Entity Spreadsheet

36. Queue Spreadsheet Exhibit 6-30 p. 169 MM1.doe Queue Spreadsheet

37. Resource Spreadsheet Exhibit 6-31 p. 169 MM1.doe Resource Spreadsheet

38. Variable Spreadsheet Exhibit 6-32 p. 169 MM1.doe Variable Spreadsheet

39. Arena Simulation Engine Entity Simulation Clock and Event Calendar Random Number Generator Statistic Collection Tools Crystal Reports Statistic Output

40. Arena Simulation Engine Exhibit 6-33 p. 170 Sheet: Arena Components

41. Entity Entities are the dynamic elements in the Arena model Entities enter the model via a Create module and exit via a Dispose module While a large arena model may contain thousands of entities at any one point in time, or one entity is active. The active entity attempts to move as far as possible through the logic modules of the model. In model MM1.doe, the only point at which an entity can be delayed is the process module. When an entity enters the Service Process module, either the service function is started immediately or the entity is held in the Service.Queue. If Resource Server is available, the duration of the service is determined based on the random expression illustrated previously. The Arena simulation engine schedules an End-Of-Service event on the Event Calendar to take place at a future point in time. If Resource Server is not available, the duration of the time in queue cannot be determined. The entity will be released from the queue only after the server has processed all previously waiting entities.

42. Simulation Clock and Event Calendar The Simulation Clock control the advance of simulation time When the active entity is halted The movement of another entity may be started or The clock advances to the next scheduled event, starting the associated entity

43. Simulation Clock and Event Calendar Exhibit 6-34 p. 171 MM1.doe Trace Report Extract

44. Random Number Generators Statistical Distributions BETA (Alpha1, Alpha2) EXPOnential (Mean) GAMMa (Beta, Alpha) JOHNson (gamma, delta, lambda, xi) ERLAng (Mean, k) LOGNormal (LogMean, LogStd) NORMal (Mean, SD) POISson (Mean) TRIAngular (Min, Mode, Max) UNIForm (Min, Max) WEIBull (Beta, Alpha) Empirical Data CONTinuous (Prob1, Value1, Prob2, Value2,... ) DISCrete (Prob1, Value1, Prob2, Value2,... )

45. Random Number Generator Example Disc (0.11, 1, 0.28, 2, 0.46, 3, 0.69, 4, 0.90, 5, 1, 6) Exhibit 6-35 p. 172 Sheet: D&E Order Size

46. Statistic Collection Tools Counter Tally Time Persistent Output Frequency

47. Counter Exhibit 6-36 p. 173 MM1.doe Record Number Served

48. Crystal Reports Statistic Output Exhibit 6-37 p. 173 MM1.doe Advanced Process Statistics Module Exhibit 6-42 p. 176 MM1.doe User Specified Report

49. Tally Exhibit 6-38 p. 173 MM1.doe Record Time Between

50. Time Persistent Exhibit 6-39 p. 174 Arena Expression Builder, Current Number in Queue

51. Output Exhibit 6-40 p. 174 Arena Expression Builder, Number In Entity

52. Frequency Report Exhibit 6-42 p. 176 MM1.doe Frequencies Report

53. MM3.doe Exhibit 6-43 p. 177 MM3.doe Network Logic Flow

54. MM3.doe @ 60 Minutes Exhibit 6-44 p. 177 MM3.doe at TNOW = 60 Minutes

55. MM3.doe Report Exhibit 6-45 p. 177 MM3.doe Category Overview Report (Queue)

56. Comparison.doe Separate Module Assign Module Variables Attributes Entity Type Entity Picture Other Entity Icon Simulation Results

57. Comparison.doe Exhibit 6-46 p. 178 Page: Comparison

58. Comparison.doe Exhibit 6-47 p. 178 Comparison.doe Network Logic Flow

59. Separate Module Exhibit 6-48 p. 179 Comparison.doe Module Separate 1

60. Assign Module Exhibit 6-49 p. 179 Comparison.doe Module Assign as Parallel Exhibit 6-50 p. 179 Comparison.doe Assignments Dialog

61. Assign Module Types Variables (Available throughout model) Attributes (Available for each entity) Entity Type Entity Picture User Defined Other J (Only Arena Integer) M (Station)

62. Default Arena Entity Attributes Entity.HoldCostRate Entity.JobStep Entity.Picture Entity.Sequence Entity.Station Entity.Type

63. Entity Icon or Picture Exhibit 6-51 p. 180 Entity Pictures Dialog Window Exhibit 6-52 p. 180 Arena Picture Editor

64. Comparison.doe @ 60 Minutes Exhibit 6-53 p. 181 Comparison.doe at TNOW = 60 Minutes

65. Comparison.doe Report Exhibit 6-54 p. 181 Comparison.doe Number in Queues Report

66. MV1.doe Exhibit 6-55 p. 182 MV1.doe Network Logic Flow

67. Branch Block Exhibit 6-56 p. 182 MV1.doe Branch Block

68. MV1.doe @ 60 Minutes Exhibit 6-57 p. 182 MV1.doe at TNOW = 60 Minutes

69. MV1.doe Report Exhibit 6-58 p. 183 MV1.doe Number in Queues Report

70. Arena Stand Alone Programs Exhibit 6-59 p. 183 Sheet: Arena Components

71. Arena Examples Exhibit 6-60 p. 184 Sheet: Examples

72. Arena Smart Files Exhibit 6-61 p. 184 Sheet: Smarts

73. Summary Process Simulation Using Arena Analysis and Simulation of Queuing Processes Arena Simulation Environment Other Queueing Process Models Other Arena Programs and Examples Next: Arena Applications