Simulation

1. 1 Simulation Fundamentals and Software

2. 2 Introduction to simulation What is simulation? Why do we use it? When do we use it? Simulation � very broad term � methods and applications to imitate or mimic real systems, usually via computer System � facility or process, actual or planned Manufacturing facility Bank or other personal-service operation Transportation/logistics/distribution operation Hospital facilities (emergency room, operating room, admissions) Computer network Freeway system Business process (insurance office) Criminal justice system Chemical plant Fast-food restaurant Supermarket Theme park Emergency-response system Why? Study the system � measure, improve, design, control When? Could just play with the actual system; then we know we are looking at the right thing But it�s often impossible to do so in reality with the actual system System doesn�t exist Would be disruptive, expensive, or dangerous Simulation � very broad term � methods and applications to imitate or mimic real systems, usually via computer System � facility or process, actual or planned Manufacturing facility Bank or other personal-service operation Transportation/logistics/distribution operation Hospital facilities (emergency room, operating room, admissions) Computer network Freeway system Business process (insurance office) Criminal justice system Chemical plant Fast-food restaurant Supermarket Theme park Emergency-response system Why? Study the system � measure, improve, design, control When? Could just play with the actual system; then we know we are looking at the right thing But it�s often impossible to do so in reality with the actual system System doesn�t exist Would be disruptive, expensive, or dangerous

3. 3 Introduction to simulation In this course, Understand stochastic (probabilistic) systems Performance over time Mostly event based (vs continuous) Some systems where time is not a factor Complex quality acceptance plan Gamblers� betting strategies (Monte Carlo sim)

4. 4 Simulation languages In this class, we will use Arena (based on SIMAN) Arena is on the computers in the public lab on the 4th floor Other discrete event simulation languages GPSS SLAM SIMSCRIPT

5. 5 Random numbers Stochastic systems can have more than one outcome Random numbers select one possible outcome Serve as a �seed� to set initial conditions Computers generate �pseudorandom� numbers

6. 6 Introduction to simulation Simulation deals with systems Types of systems Discrete (focus of this course) State of system changes at specific points in time (events)

7. 7 Introduction to simulation (2) Types of systems (cont) Continuous State of system changes continuously over time Maybe at some level everything is discrete � water is made up of moleculesMaybe at some level everything is discrete � water is made up of molecules

8. 8 Models Simulation attempts to model the �real world� But what is a model? Model � set of assumptions/approximations about how the system works Study the model instead of the real system � usually much easier, faster, cheaper, safer Can try wide-ranging ideas with the model Make your mistakes on the computer where they don�t count, rather than for real where they do count Model is a representation of the system that we use as a surrogate (substitute) for the actual systemModel is a representation of the system that we use as a surrogate (substitute) for the actual system

9. 9 Models (2) Often, just building the model is instructive � regardless of results Model validity (any kind of model � not just simulation) Care in building to mimic reality faithfully Level of detail Get same conclusions from the model as you would from system

10. 10 Models(3) Types of models Iconic (physical) Model airplane in a wind tunnel Symbolic (mathematical) Represents system in terms of logical/quantitative relationships

11. 11 Models (4) Two types of symbolic models: Analytical Equations give exact results Linear programming Inventory model (optimal order quantity) Queuing theory (statistical) *If possible, use analytical model Queuing � expected wait time; expected number in queue and associated varianceQueuing � expected wait time; expected number in queue and associated variance

12. 12 Models (5) Symbolic models (cont) Simulation Use only if analytical model is not possible or practical Imitates operations of real world Similar to observing operations of real systems Results are estimates of system - NOT EXACT

13. 13 Characteristics of simulation models Time is dynamic Outcomes Stochastic Based on random variable inputs State variables are discrete

14. 14 Advantages of simulation Can estimate Expected value (mean/average outcome) Most likely (mode outcome) Dispersion/shape (statistical distribution of all outcomes) Tool for controlled statistical experiments Allows statistical evaluation (comparison) of alternate strategies

15. 15 Advantages of simulation (2) Provides insight into complex interactions Compresses or expands time Can identify bottlenecks Can model uncertainty, nonstationarity

16. 16 Disadvantages of simulation Provides estimates only Analysis of results may be difficult Decision maker may not believe results Sometimes used when not appropriate Estimates � most important Results � more later Decision � graphics may help Not appropriate � analytical solution may be betterEstimates � most important Results � more later Decision � graphics may help Not appropriate � analytical solution may be better

17. 17 Definitions Entity Person, object, or thing whose movement through the system changes the state of the system. Attribute Property or characteristic of an entity or other object. A variable associated with an entity.

18. 18 Examples Entity Attribute Customer arrival time departure time Machine status (idle, busy, down) Airliner type capacity airspeed

19. 19 Definitions (cont) Global variables Characteristic of the system, rather than an entity Resource An object which acts upon an entity. Queues Places where entities wait for resources. Examples: drill, lathe in a machine shop server at a restaurant In Siman, an entity �seizes� and �releases� an entity. Examples: drill, lathe in a machine shop server at a restaurant In Siman, an entity �seizes� and �releases� an entity.

20. 20 Definitions (cont) State of system Values of a set of variables describing a system Event Instantaneous occurrence that causes a change in state. Activity Time consuming element in a system In Siman, queues may be given names, capacities, ordering schemes (FIFO, sort), etc. Most queue operations are handled automatically. E.g.machine shop � running status; number of jobs in queue; number of jobs in process; next arrival time Activity � machine process time; aircraft boarding time Event time � job arrival, job completion In Siman, queues may be given names, capacities, ordering schemes (FIFO, sort), etc. Most queue operations are handled automatically. E.g.machine shop � running status; number of jobs in queue; number of jobs in process; next arrival time Activity � machine process time; aircraft boarding time Event time � job arrival, job completion

21. 21 The simulation clock Represents real system time (called TNOW in Arena) Updating the simulation clock Fixed increment time advance method Increment clock by fixed amount If an event is scheduled to occur during increment, follow appropriate actions Very inefficient (why?)

22. 22 The simulation clock (2) Next event time advance method Advance clock to time of next event Requires list of scheduled events sorted by time Most efficient (why?)

23. 23 Simple service model example System has two major events One major activity Events � arrival departure Activity � service; departure comes at end of service �activity�Events � arrival departure Activity � service; departure comes at end of service �activity�

24. 24 Simple service model example We could enumerate all arrival times and all process times in advance Usual practice is to determine them when they are needed

25. 25 Event-oriented simulation of a single server system

26. 26 If next event is a departure

27. 27 Single server systemmanual simulation example

28. 28 Single server systemmanual simulation example

29. 29 Arrivals and departures

30. 30 State diagram

31. 31 Recapping the simulation Data collected during simulations Observational Time-dependent Know the difference!

32. 32 Recapping the simulation (2) Observational data Sequence of equally weighted observations Observations are mostly times� Time in queue Time in system But the time the observation occurs � or sequence- is generally meaningless or irrelevant

33. 33 Calculating observational data Arena uses TALLY to collect observational data Example Customer Time in Queue Time in System 1 0 3 2 1 4 3 2 4 4 1 2 5 0 1 Average = 4/5=0.8 14/5=2.8

34. 34 Calculating time-dependent data Arena uses DSTAT to collect time dependent data Also known as time-persistent data Sequence of values weighted by the length of time the value persists Normally not times (queue length, customers in system) Duration of value is important

35. 35 Calculating time-dependent data Example of DSTAT Deposit $300.00 on 1st day of a 30-day month Draw it out on the second day What is the average balance in the account for the month?

36. 36 Calculating time-dependent data Values must be time-weighted Thus, Average = The values (300, 0) are weighted by the length of time (1, 29) they exist What if we left the money in for two days?

37. 37 Calculating time-dependent data What if we put $300 in on the first day $300 on the second day And took it all out on the fifth day?

38. 38 Calculating time-dependent data

39. 39 Calculating time-dependent data To determine �average� Queue length Number of customers in system Weight number of customers by the length of time In general, for time persistent data: Average = ti = length of ith period qi = quantity in ith period

40. 40 Back to manual example Recall the state diagram (number of customers in system) Calculate the average in system

41. 41 Calculating average in system Numerator 1*2 + 2*1 + 1*1 + 2*2 + 1*1 + 2*1 + 1*1 + 0*2 + 1*1 =14 Denominator 2 + 1 + 1 + 2 + 1 + 1 + 1 + 2 + 1 = 12 Average = 14/12 = 1.167 What is the average time in queue?

42. 42 Simulation Modeling Perspectives- continued

43. 43 Discrete and Continuous Simulation Discrete Simulation Dependent variables (system responses) change only at discrete time points (event times) Ex: Number of customers in the bank will be changed by: A customer arrives at bank (+1 arrival event) A customer departs bank (-1 departure event)

44. 44 Discrete and Continuous Simulation Continuous Simulation Dependent variables change continuously Ex: A water faucet filling water tanks at a certain rate (maybe constant)

45. 45 Discrete and Continuous Simulation Combined Simulation Some continuous variables - values may cause discrete event Ex: Filled water tanks should be shipped away if a truck is available and the filling continued after a short stop, otherwise stop water until filled tanks are moved

46. 46 The World Views of Discrete (Event) Simulation Modeling

47. 47 The World Views of Discrete (Event) Simulation Modeling Event Takes places at an �isolated� point in time to start or finish an activity No duration Ex: �take-off� as an event to the entire flight process Process A time-ordered sequence of events that may encompass several activities Activity Has beginning (an event) and ending (an event) The entire duration is in between the two Lead to the three world views in discrete simulation modeling: event, activity scanning, and process orientations

48. 48 The World Views of Discrete (Event) Simulation Modeling Event Orientation Systems modeled only by changes that occur at discrete event times, e.g., arrival, departure Events may change system�s state (an attribute or attributes that describe the system�s status), e.g., busy ? idle Actions may be taken as a result of events, according a decision logic associated with the specific combination of system�s current state and events that are occurring, e.g., if teller is idle and customer arrives and the transaction is a deposit, initiate a service activity of �deposit� (which may take a prescribed duration with a probability distribution)

49. 49 The World Views of Discrete (Event) Simulation Modeling Activity = f {Current State(s), Event(s)} From an entity�s perspective, an activity may also have to concern current current state of other entities Ex: System: A robot-machine mini cell Entity: Robot Current state: Idle Event: Arrival of a part Activities: If machine idle (available) Then pick up part and put on machine, otherwise wait

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51. 51 The World Views of Discrete (Event) Simulation Modeling Relation to Statistics Ex: Bank-Teller System Customer: arrival ? (wait if teller busy) ? service ? departure System state: NIS=NIS+1 NIS=NIS-1 Queue state: NIQ=NIQ+1 NIQ=NIQ-1 Teller state: idle ? busy busy ? idle Cus�s TIS: Tci=TNOW TISci=TNOW-Tci Cus�s TIQ: TQi=TNOW TIQci=TNOW-TQi Note: (1) Statistics for time-persistent variables (2) Statistics based on observations

52. 52 The World Views of Discrete (Event) Simulation Modeling Activity Scanning Orientation Model activities and prescribed conditions that cause an activity to start and end Events that start or end the activity not scheduled by the model, but are initiated from the prescribed condition Conditions are scanned as simulated time advances Necessary to scan the entire set of activities to ensure the activity�s accountability (compare: entity state checking in event orientation) Scanning process slow - system inefficient Not widely used in discrete simulation

53. 53 The World Views of Discrete (Event) Simulation Modeling Process Orientation Model sequences of elements that occur in defined patterns, e.g., waiting in queue for a busy server Logic of the sequence of events generalized and defined in a single statement A high-level simulation language with graph network symbols, e.g., SLAM II, SIMAN, SIMNET User-friendly interface - but still have to program Higher-level - discrete use of symbols without programming, e.g., SLAMSYSTEMS

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