Fundamental Simulation Concepts, Esquemas y mapas conceptuales de Origen del Lenguaje

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Fundamental Simulation Concepts

SIE 431/

Young-Jun Son, PhD

Systems and Industrial Engineering

[email protected]

Steps in Simulation Study

Model Specifics

• Initially (time 0) empty and idle
• Base time units: minutes
• Input data (assume given for now), in minutes:
• Stop when 20 minutes of (simulated) time have passed

Sample Path

• Sample path
  • Realization of system behavior
  • Stochastic realization; trajectory

Goals of Study (Performance Metrics) (2)

• Average number of parts in queue:
• Maximum number of parts in queue:

Q ( t ) = number of parts in queue at time t

20

( )

 0 Q t dt

max ( ) 0 20

Q t  t 

Goals of Study (Performance Metrics) (3)

• Average and maximum total time in system of parts (cycle time):
• Utilization of machine (proportion of time busy)
• And, more

TSi = time in system of part i

i i P

P

i

i

TS P

TS

max 1 ,...,

, 



20

0

( ) 1 if machine is busy at time , ( ) 20 0 if machine is idle at time

B t dt t B t t



Spreadsheet based Simulation

• Logic: recursive equation

Spreadsheet based Simulation (2)

Components (terminologies) of Simulation Model

• Entities
  • Dynamic objects in the simulation
  • Something moving throughout the system
  • Examples: ( )
• It may not be tangible, such as order for the company, requests,

etc

Components (terminologies) of Simulation Model (2)

• Attributes
  • Local variable (tag) characterizing entities
  • Each entity can have same or different values
  • Most important thing is that their values are tied to specific entities
  • Examples:
  • Values can be real number, integer number, texts, or some other object types: different software supports different data types

Components (terminologies) of Simulation Model (4)

• Resources
  • Entities compete with each other for service from resources such as personnel, equipment, or space in storage area of limited size
  • Example:
  • Seizing and releasing. Capturing and freeing. Changing of system variables
  • Capacity or units of a resource: a resource can represent a group of several individual and identical servers. If you want to differentiate them, you need to define another resource
  • Definition differs in different simulation packages (for now, we stick to the Arena’s definition)

Components (terminologies) of Simulation Model (5)

• Queues
  • A place where entities can wait when no resource is available
  • Queue also has a capacity
  • Example:
  • You must model how to handle an entity arriving at a queue that’s already full
  • Should we allow this happen and do something? Balking!!
  • Should we model so that this does not occur?
  • This could be a logical queue or physical queue. This differs depending on different simulation packages

Components (terminologies) of Simulation Model (7)

• Events
  • An event is something that happens at an instant of (simulated) time that might change a system state (such as attributes, variables, or statistical accumulators)
  • There are four kinds of events in our example:
    • Initialization to set things up: making all zeroes or initialization values
    • Arrival: A new part enters the system
    • Departure: A part finishes its service at the machine and leaves the system
    • The End: The simulation is stopped at time 15 minutes
  • Question: why not the following is not included to the event:
    • “parts leave the queue and begin service at the machine, which changes the system”?

Components (terminologies) of Simulation Model (8)

• Event calendar
  • Event calendar is the place where future events are stored
  • Event calendar has a set of records, where each record is associated with
    1. id of an entity, 2) event time, and 3) the kind of event (init, arrive, depart, or end)
  • When it’s time to execute the next event, the top record is removed from the calendar and the information in this record is used to execute the appropriate logic, such as changing variables, showing message boxes, or placing new records to the event calendar
  • Arena (or other commercial simulation packages) places newly scheduled events to the event calendar in increasing order of event times) => the top one is always the next event to occur
  • The variables that describe the system don’t change between successive events - Example: machine start processing, machine end processing: no change of system states