General Concepts in Simulation

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General Concepts in Simulation

• Jerry Banks

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Definition of Simulation

• Simulation is the operation of a real-world
  process or system over time.
• Simulation involves the generation of an
  artificial history of the system, and the
  observation of that artificial history to draw
  inferences concerning the operating
  characteristics of the real system that is
  represented.

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Definition of Simulation

• One of the top 3 technologies
• Simulation is no longer the technique of last
  resort
• It is an indispensable problem-solving methodology

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Definition of Simulation

• We use simulation to
• Describe and analyze the behavior of a system
• Ask what if questions about the real system
• Aid in the design of real systems
• Existing and conceptual systems
• We model both kinds

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Ad Hoc Simulation

• Mechanics arrive for service at a tool crib
  between one and ten minutes apart in time
• Mechanics are served in a time between one and
  six minutes
• Integer values
• Simulate for twenty mechanics

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Ad Hoc Simulation Table
Mechanic Time Arrival Service Service Time Time I
dle Time between Time Time begins Service in Time
in Arrivals Ends System Queue ______________
__________________________________________________
__________________________________________________
_________1 - 0 2 0 2 2 0 0 2 5 5 2 5 7 2 3 0 3 1 6
6 7 13 7 0 1 20 7 98 1 98 99 1 4 0 72
34 7
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Performance Measures

• Avg time in system 72/20 3.6 minutes
• idle time (34/99)100 34
• Avg waiting time/mechanic 7/20 0.35 minutes
• Fraction having to wait 3/20 0.15
• Avg waiting time of those that waited 7/3
  2.33 minutes

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Model

• Representation of an actual system
• Model should be complex to answer the questions
  asked, but not too complex

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Event

• An occurrence that changes the state of the
  system
• Beginning of service for a mechanic, completion
  of a service

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Endogenous Event

• Happens within the system
• Beginning of service of the mechanic

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Exogenous Event

• Occurrence is outside of the simulation
• Arrival of a mechanic for service

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Discrete-Event Simulation Models

• Contrast with other types of models
• Mathematical models
• Descriptive models
• Statistical models
• Input-output models

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Discrete-Event Simulation Models

• Represent the components of a system and their
  interactions to such an extent that the
  objectives of the study are met
• Mathematical, statistical and input-output models
  represent a systems inputs and outputs
  explicitly, but represent the internals of the
  model with mathematical or statistical
  relationships
• Discrete-event simulation models include a
  detailed representation of the actual internals

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Dynamic

• Passage of time plays a crucial role
• Mathematical and statistical models are static in
  that they represent a system at a fixed point in
  time

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System State Variables

• Collection of all information needed to define
  what is happening within the system to a
  sufficient level at a given point in time
• Fcn. of the purposes of the investigation
• What may be the system state variables in one
  case may not be the same in another case even
  though the physical system is the same

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Discrete vs. Continuous

• System state variables in a discrete-event model
  remain constant over intervals of time and change
  value only at certain well-defined points called
  event times
• Continuous models have system state variables
  defined by differential or difference equations
  giving rise to variables that change continuously
  over time

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Others

• Mixed discrete-event and continuous
• Continuous models that are treated as
  discrete-event models after some reinterpretation
  of system state variables, and vice versa

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Entity

• An object that requires explicit definition
• Can be dynamic in that it moves through the
  system
• Can be static in that it serves other entities
• Mechanic is a dynamic entity
• Tool crib attendant is a static entity

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Attributes

• Local values
• Many entities can have the same attributes
• Color could be an attribute
• Time production began could be an attribute

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Variables

• Global values
• Available to all entities
• Clock

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Resource

• Static entity that provides service to dynamic
  entities
• Resource can serve one or more than one dynamic
  entity at the same time, (i.e., operate as a
  parallel server)

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Resource

• Dynamic entity can request one or more units of a
  resource
• If denied, the requesting entity joins a queue,
  or takes some other action (i.e., diverted to
  another resource, ejected from the system)

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Resource

• Other terms for queues include files, chains,
  buffers, and waiting lines
• If permitted to capture the resource, the entity
  remains for a time, then releases the resource

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Resource States

• Minimally, these states are idle and busy
• Other possibilities exist such as failed, blocked
  or starved, etc.

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List Processing

• Entities are managed
• by allocating them to resources that provide
  service
• by attaching them to event notices thereby
  suspending their activity into the future
• or by placing them into an ordered list
• Lists are used to represent queues

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Rule Processing

• Lists are usually processed according to FIFO
• LIFO
• SPT
• RAN
• PR
• HVA(), LVA()

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Activity

• Duration of time that is known prior to
  commencement of the activity
• When the duration begins its end can be scheduled
• Constant, random value from a statistical
  distribution, result of an equation, come from an
  input file, or computed based on the event state

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Activity Examples

• Service time may be constant 10 minutes for each
  entity
• Random values from an exponential distribution
  with a mean of 10 minutes

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Activity Examples

• 0.9 times a standard value from time 0 to 4
  hours, and 1.1 times the standard value after
  time 4 hours
• 10 minutes when the preceding queue contains less
  than or equal to four entities and 8 minutes when
  there are five or more in the preceding queue

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Delay

• Indefinite duration that is caused by some
  combination of system conditions
• Time that an entity will remain in the queue may
  be unknown since that time may depend on other
  events that may occur
• Arrival of a rush order that preempts a resource
• Failure necessitating repair of the resource

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Time Advance

• Discrete-event simulation contains activities
  that cause time to advance
• Most discrete-event simulations also contain
  delays as entities wait
• Beginning and ending of an activity or delay is
  an event

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Discrete-Event Simulation Model

• State variables change only at those discrete
  points in time at which events occur
• Events occur as a consequence of activity times
  and delays
• Entities may compete for system resources,
  possibly joining queues while waiting for an
  available resource
• Activity and delay times may hold entities for
  periods of time

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Running of Models

• Discrete-event simulation model is conducted over
  time (run) by a mechanism that moves simulated
  time forward
• System state is updated at each event along with
  capturing and freeing of resources that may or
  may not occur at that time

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Process-Interaction World View

• Entities move forward until they are
• Delayed
• Enter an activity
• Are terminated
• At which time another entity begins to move
  forward

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Some Questions

• How is the form of the input data determined?
• What if the input data follows some other
  statistical distribution?
• How does the user know when the simulation
  imitates reality?
• What other kinds of problems can be solved by
  simulation?

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Some Questions

• How long does the simulation need to run?
• How many different simulation runs should be
  conducted?
• What statistical techniques should be used to
  analyze the output?

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In-class exercise
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End