General Simulation Principles

1. General Simulation Principles • Refer to Chapter 3 • Very Important Chapter • Section 3.1 • Memorize all basic definitions & be able to discuss thoroughly • Also includes additional material not in book

2. Discrete Event Systems • Discrete systems – focus of course • Framework for modeling systems • General Terminology • General Purpose Languages vs. Simulation Packages • Dynamic (over time) • Stochastic (randomness)

3. System Model System State Entity Attributes List Event Event notice Event list (FEL) Activity Delay Clock *Terminology (pg. 89)

4. Terminology System Model Abstract representation of a system, in form other than the system itself Includes relationships that describe system (state, entities, activities, events, processes, delays, etc.) Mathematical, physical, computer program, etc. Collection of one or more entities interacting together over time to accomplish some goal or goals • School • Airport • Gas Station • Human Body

5. Terminology System State Entity Object or component of system that requires representation in the model; an object of interest Customer Server Queue Collection of variables necessary to fully describe the system at a point in time • Number-in-queue • Number-of-servers • Status-of-servers

6. Terminology Attributes Attribute Values Actual values assigned to an attribute at a particular point in time 0 to Capacity 1, 2, 3, … Busy, Idle, On-Break Num. Services/Time Business, Personal Properties of an entity that describe it • Length (of queue) • Capacity (of queue) • Status (of server) • Speed (of server) • Type (of customer

7. Terminology List Event Instantaneous occurrence that changes the state of system Arrival of customer Completion of service Breakdown of machine Collection of associated entities, ordered in some manner • FIFO queue of customers • Priority queue of customers • Available servers

8. Terminology Event Notice Event List (FEL) Future Event List List of Event Notices ordered by time Typically a linked list Is the “driver” for a simulation program Record of event to occur at current or future time + data necessary to execute it; event type & time • Arrival, 10 • End-service, 30

9. Terminology: ACTIVITY • Duration of time of specified length known when begins; scheduled & desired; • Unconditional wait • Duration determination • Deterministic: always 10 minutes • Statistical: Uniform (1,10) • Functional: based on attribute (age, capacity) • Begins & Ends with an Event • Service time: Begin Service, End Service

10. Terminology: DELAY • Duration of time of unspecified, indefinite length not known until it ends; duration determined by system conditions; i.e. by other events or activities; not scheduled or desired • Conditional wait • Time waiting in queue • Time waiting on any other event

11. Terminology: CLOCK • Variable representing simulated time • Elapsed time in smallest time unit necessary • Updated with each new event time as the event is executed

12. Primary vs. Secondary Events • Primary Event • Occurrence is scheduled • Placed on FEL • Arrival, Complete Service • Secondary Event • Occurrence due to some other event or condition • Not on FEL • Enter or Leave queue, Begin service

13. Waits Conditional vs. Unconditional • Conditional Wait = Delay • Caused by some other condition • In Queue • Unconditional Wait = Activity • Scheduled • Service time

14. Example 2.6 – page 51 Computer technical support center is staffed by 2 people, Able & Baker, who take calls & answer questions to solve computer problems. Able is more experienced & faster. If both are idle, Able takes call. If both busy, caller placed on hold & calls are answered in the order received.

15. System Model System State Entity Attributes List Event Event notice Event list (FEL) Activity Delay Clock State components from Example 2.6

16. Dynamic Relationships & Interactions Between Components • Consider the questions on page 91. • Answers are necessary to determine correct model.

17. Time Management Methods • Determines how CLOCK is managed (updated) Time Slice Approach • Continuous Systems vs. Critical Event Approach • Discrete Event Approach

18. Time Slice Approach • Simulation is controlled by time • Clock is incremented by fixed number of time units (N) each time • State of system is based on everything that occurred in past N time units • Typical for simulating continuous systems • Able to easily compress or expand time by varying N

19. Critical Event Approach • Simulation is controlled by occurrence of “critical events” • Clock is incremented (updated) by variable amounts as determined by occurrence of next critical event • Critical events cause specific changes in state of the system • Used for discrete systems

20. Time Slice vs. Discrete Event:Examples Discuss clock management & system updates… • Continuous • Release of pollutants into a river • Flood of city due to rain storm • Discrete • Use of student computer lab • Baggage check-in counter at airport

21. Future Events List (FEL) • A set of all events that have been scheduled to occur at a future time • Arrange in chronological order • Linked List • t<= t1<= t2 <= t3<=…tn • t is value of clock • t1 is the imminent event

22. Future Events List • What are implementation options? Pros & Cons? • Array • Ordered, Unordered • Linked List • Ordered

23. Event Scheduling – Time Advance Algorithm (main) 1. Remove imminent event 2. Advance Clock 3. Execute imminent event: update state 4. Generate future events (as necessary) & Place on FEL 5. Update Cumulative Statistics & counters 6. Repeat (1-5) until simulation ends

24. Stop Event • An event whose occurrence causes termination of the simulation EXAMPLES: 1. Clock time exceeds value N 2. Number of events exceeds value N 3. Queue reaches length L ~~~ Others ???

25. Critical Events • In a basic queuing system, there are 2 critical events. • What are they? • 1. ????? • 2. ????? • These are events in FEL

26. Arrival Event Processing ARRIVAL* No Yes ServerBUSY? ENTER QUEUE BEGIN SERVICE*

27. Complete Service Event Processing Complete Service Remove from Q Server Idle NO YES AnotherIN Q? Begin Service*

28. Generating Events • Initialize • Stop event (if stopping on TIME) • First Arrival (of each type) • Next Arrival • As an Arrival is removed • Complete Service • As an arrival Begins Service Note * on flowcharts  new event generated

29. Queuing System Components • Queue • Calling population • Discipline • Capacity • Arrivals • Times, rates • Nature of

30. Queuing System Components • Services • Times • Nature of • System • Number of queues • Number of servers • State variables • Capacity • Nature of Arrivals/ Departures

31. Characteristics • Key elements: Customers and Servers • Calling Population: set of potential customers - finite vs. infinite • System Capacity: the total number which may wait and be served at any given time • Finite vs. infinite • Arrival rate vs. effective arrival rate

32. Characteristics (cont.) • Arrival Process • Characterized by inter-arrival times of successive customers • Scheduled vs. random • 1 at a time or batches • Poisson Arrivals – independence • Examples

33. Introduction to Queuing Models • Queue = Waiting line • Customer = any entity that may request “service” from a system • Typical Measures of System Performance • Server utilization • Length of waiting lines • Delays of customers

34. Queuing Models (cont.) • Input Parameters • Arrival rates • Service demand • Service rate • Number & arrangements of servers

35. Start-up vs. Wind-down Conditions • Start-up • What is state of system when simulation starts? Empty? Full? • Initialization? • Wind-down • How is simulation stopped? • Are customers left in system? What do you do with them?

36. Queuing Models • Mathematical Analysis vs. Simulation Analysis • Topics to be addressed • Dynamic behavior • General characteristics • Meaning and relationships of the important performance measures • Estimation of performance measures • Effect of varying input parameters • Mathematical solutions to basic models

37. Queue Attributes • # of Phases or Stations (sequential) • # of Channels (parallel) • # of Servers • Blockers-non blocking stations • Capacity • Discipline (FIFO, LIFO, Priority, etc.)

38. Queue Behavior • Balk: upon arrival, customer decides not to enter the system • Renege: after being in queue for some period of time, customer leaves system • Jockey: to change queues after entering one queue

39. Queue Behavior • Priority: a number affecting the processing of customers • Preempt: to stop serving one customer before completion in order to begin serving another customer

40. Single Server-Single Queue Queue Arrive Server Depart

41. Parallel Servers – Same Type Single Queue S Arrive  Q Depart S

42. Parallel Servers & QueuesDifferent Servers A1 Q1 S1 D A2 Q2 S2 D A1 & A2 have different arrival rates. S1 & S2 are different types w/ different rates.

43. Parallel Servers S1 Arrive Depart Q S2 S1 & S2 provide same service but may have different service rates. Choice between S1 & S2 may be rule-based or random.

44. Sequential Servers A D Q1 S1 Q2 S2 Each customer must receive both services.

45. Goals of Simulation • Common Questions 1. Average Queue Length? 2. Amount (%) of server Idle Time? (Utilization) 3. Mean Waiting time of Customers? 4. Others? Consider Information Cost Value

46. Simulation Methodology • Plan • Model • Validate & Verify • Simulate • Apply

47. Simulation Methodology 1. Plan • Define problem & factors that affect the system • Estimate resources needed to observe system and collect data • Determine feasibility of continuing • Consider reduction • Collect info.- interviews, literature search, observation

48. Methodology (cont.) • Model • Construct a REPRESENTATION consisting of the minimal set possible

49. Methodology (cont.) • Validate and Verify • Validate: to ensure that the model accurately represents the system • Verify: to ensure that the program accurately represents the model • How? – historical data & predictions • Statistical tests • Sensitivity Analysis • Reasons for Failure to validate or verify

50. Methodology (cont.) • Apply • What is output? • How should the results be interpreted? • How can we use the results? • How can we communicate the results to others?