COMP155 Computer Simulation September 10, 2008

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

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

Example System  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) Blank Part Arrives Finished Part Departs Drill Press Part in Service 4 Queue 567

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 maximum total time in system for parts? What is the utilization ratio of the drill press?

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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