COMP 155 Computer Simulation September 10 2008 LECTURE

COMP 155 Computer Simulation September 10, 2008 LECTURE 5: DISCRETE EVENT SIMULATION

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 Drill Press Blank Part Arrives 7 6 5 Queue � Finished Part Departs 4 Part in Service 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)

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 ○ People, Equipment, Space entities compete for � 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