Lecture 5: Discrete Event Simulation

1. COMP155Computer Simulation September 10, 2008 Lecture 5:Discrete Event Simulation

2. Discrete Event Simulation • discrete event simulation:state variable change only at a discrete set of points in time • events:the set of points in time at which state changes occur

3. Steps in a SimulationStudy from Discrete-Event Simulation 4th ed. Banks et.al. Prentice Hall 2005

4. Example System DrillPress • One type of entities: parts to be drilled • multiple entities over time • One process: drilling a part • One resource: drill press • required to complete drilling process • one the drill press is in use for a part, it is not released until that part is finished • (this is the example system in chapters 2 and 3) 7 6 5 Blank PartArrives Finished PartDeparts 4 Queue Part in Service

5. Goals of Drill Press Study • What do we want to discover? • How many parts can be processed in some time frame? • What is average and maximum waiting time for parts in the queue? • What is the maximum size of the queue? • What are the average and maximumtotal time in system for parts? • What is the utilization ratio of the drill press?

6. Components of a Simulation/Model • Entities • Attributes • Resources • Queues • Global Variables • Statistical Accumulators • Events • Simulation Clock

7. Entities • Things that move around, change status, and interact with other entities • Entities are dynamic objects: arrive, move around, leave • Usually represent “real” things • DP system: entities are the parts • May have “fake” entities for modeling “tricks” • Breakdown demon, break angel • May have multiple realizations(instances) in system concurrently • May have multiple types of entities concurrently

8. Attributes • Characteristic of all entities: describe, differentiate • All entities of same type have same attribute “slots” but different values • Possible Attributes: • Time of arrival, due date, priority, color • Notion of an attribute is same as in other CS contexts (OO, UML, ER …) • Arena defines certain automatic attributes, developer adds application specific attributes

9. Resources • Resources are things that entities compete for • People, Equipment, Space • Entities seize a resource, use it, release it • Better to think “resource is assigned to an entity”, rather than an “entity belonging to a resource” • Resources may have several units of capacity • examples • seats at a table in a restaurant • identical ticketing agents at an airline counter • Number of units of resource may change during a simulation run

10. Queues • A queue is a place for entities to wait when they can’t move forward • example: need to seize an unavailable resource • Queues have names • name often tied to a corresponding resource • Queues generally have finite capacity • need to model what happens if an entity arrives at a full queue

11. Global Variables • Global Variables reflect characteristics of whole system, not of specific entities • Examples: • Travel time between all station pairs • Number of parts in system • Simulation clock (built-in Arena variable) • Entities can access and change variables • Arena defines certain global variable, developer adds application GVs

12. Statistical Accumulators • Used to record information needed for output performance measures • passive variables: used for recording, but not for processing in simulation • Arena automatically handles most statistical accumulators • invisible to simulation logic

13. Variables vs. Accumulators • Global Variables: • simulation clock • number of parts in queue (now) • Statistical Accumulators: • number of parts drilled (so far) • total of queue waiting times (so far) • max time in queue (so far) • max time in system (so far)

14. Events • Something that happens at an instant of time • May change attributes, variables or statistical accumulators • System maintains an event calendar • used to determine next interesting instance in time • Discrete-event simulation • by definition, nothing in system changes between events

15. System Clock • Global variable maintained by Arena to track simulation time • Clock advances as events are processed

16. Experiment Design • A run or execution of a simulation gives information about one set of conditions with one set of random inputs • Multiple runs are needed to deal with: • randomness • configuration changes

17. Randomness in Simulation • A single simulation run is not sufficient for non-deterministic systems • Drill press simulation: five replications: Note substantial variability across replications

18. Comparing Alternatives • Goals may require comparison of different system configurations • particularly when simulation is used for design • what is the fastest, cheapest or “best” design • Drill press system: What would happen if the arrival rate were to double? • Cut interarrival times in half • Rerun the model for double-time arrivals • Make five replications

19. Drill Press Simulation Results • Circles:original arrival times • Triangles:arrival rate doubled • solid: replication 1 • hollow:replications 2-5

20. Assignment 3 • Teams of 4 • Develop a simulation study using Arena • Problems from IIE/RA annual contest • IIE: Institute of Industrial Engineers • RA: Rockwell Automation • Finished reports due September 29

21. Assignment 3: First Task • Goals of study • informal list • Informal model of system • block/flow diagram • identify entities, resources, processes, queues