Discrete Event Simulation

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Discrete Event Simulation

• Dr. Frank H. Li
• USC Upstate
• 8/24/05

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Ways To Study A System
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Characterizing a Model

• Deterministic or Stochastic
• Does the model contain stochastic components?
• Randomness is easy to add to a DES
• Static or Dynamic
• Is time a significant variable?
• Continuous or Discrete
• Does the system state evolve continuously or only
  at discrete points in time?
• Continuous classical mechanics
• Discrete queuing, inventory, machine shop models

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Model Taxonomy
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DES Model Development

• Algorithm How to develop a model
• Determine the goals and objectives
• Build a conceptual model
• Convert into a specification model
• Convert into a computational model
• Verify (Did we build the model right?)
• Validate (Did we build the right model?)
• (Typically an iterative process)

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Discrete Event Simulation (1)

• A discrete event is something that occurs at an
  instant of time.
• Pushing an elevator button
• Starting/stopping of a motor
• Turning on a light
• Activities such as moving a train from point A to
  point B are NOT discrete events. Why?

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Discrete Event Simulation (2)

• However, we can model moving a train from point
  A to point B as
• The event of the train leaving point A at 7am
• The event of the train arriving at point B at
  11am
• A discrete event simulation is to study a complex
  system by computing the times that would be
  associated with real event in a real-life
  situation.

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Discrete Event Simulation (3)

• How to model moving a train from point
• A to point B?
• Initially, generate an event (E1) with an
  attribute occure_time 7am
• Do we need to generate another event with an
  attribute occure_time 11am ? NO!
• When E1 is handle, E1 will trigger (generate) an
  event E2 scheduled at 4 hours later.

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Discrete Event Simulation (4)

• A simulation could use the real-time clock.
  However this would take unnecessarily long time.
• Waiting 4 hours to see train arrival at point B
• A discrete event simulation is to compute, as
  quickly as possible, the physical time that
  would occur in real time in a physical system,
  but without actually waiting for the delays
  between events to occur in real time.

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Discrete Event Simulation (5)

• Four components
• Simulation time
• Events
• An Event list
• Event handler (can be the main program)
• Simulation time
• Begins at 0
• e.g., the train leaves from A at 0 simulation
  time
• it arrives B at 4 hour simulation time

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Discrete Event Simulation (6)

• Events
• Object C/Java
• Structure C
• Number Matlab
• Having an attribute occur_time
• Events can be scheduled and handled
• When scheduled, an event will be put into the
  event list, which is sorted by occur_time
  (ascending)
• When handled, do something and may trigger other
  events (schedule events)

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Discrete Event Simulation (7)

• Event handler (main program)
• While( Event list is not empty)
• get the first event
• handle the event
• Advance the simulation time by the occur_time
  of the current event
• Run the event (do something about it)
• May schedule new events
• generate new events (occur_time)
• put into ordered event list
• Remove the current event from the event list

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Discrete Event Simulation (8)

• main()
• schedule E1,0
• schedule E2,0
• while( Event list is not empty)
• E getEvent()
• Handler( E )
• RemoveEvent( E )

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Discrete Event Simulation (9)

• Handler( Event E )
• Switch( E )
• case e1
• xxx
• schedule Ea,t
• break
• case e2
• yyy
• schedule Eb,t
• break

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Discrete Event Simulation (10)

• Random number generator
• Why random numbers?
• e.g.,
• Inter-arrival time exponential distribution
• Arrival time Poisson distribution
• Service time exponential distribution
• Function/method generates random number in
  C/Java

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Discrete Event Simulation (11)

• Distribution -1 mean log(1.0 -
  randomNumber)
• mean is the mean of this exponential
  distribution
• log() is a base e log function
• randomNumber is a random number between 0 to 1
• Feed a series of randomNumbers to this formula,
  get a series of values for this distribution.

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Quality of Service (QoS) in Cellular Networks

• Calls
• New calls
• Handoff calls
• QoS
• (New) call blocking probability (CBP)
• Handoff dropping probability (HDP)
• HDP is more important than CBP (Why?)
• There are N channels in a base station. We
  simulate several channel allocation algorithms
  and compare the performance.

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Traffic Model (1)

• The average new calls arrival rate ?_new
  (requests/sec)
• The average handoff calls arrival rate ?_handoff
  (requests/sec)
• Total average call arrival rate (?_new
  ?_handoff)
• Note When arrival rate is ?, the inter-arrival
  time is 1/ ?

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Traffic Model (2)

• The average call time 1/µ (second/call)
• Since there are N channels, if all channels are
  occupied all the time, on average, N calls will
  finish in 1/µ second.
• Therefore, Nµ calls will finish in each second.
  (Nµ calls/sec service rate)
• In summary
• Arrival rate (?_new ?_handoff) calls/sec
• Service rate Nµ calls/sec
• Mean Traffic load
• ?_mean (?_new ?_handoff) / (Nµ)
• Traffic load in a measurement interval
• ? (total channel busy time) / (total channel
  time)
• How to choose ?_new and ?_handoff ?

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Performance Metrics

• During a time period
• Utilization (U) the average percentage of
  channels occupied
• CBP
• HDP
• Comparing several schemes
• Complete sharing (CS) scheme
• Complete partition (CP) scheme
• Some other schemes you propose to improve system
  performance

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About the Programming Project

• Work in groups of 3 or 4 for this project. Hand
  in a single set of report for the entire group.
  Each group will make an up to 10 minute
  demonstration.
• Your programming project report must contain the
  following sections
• Introduction an brief overview of your project
• Specification what this program suppose to do
• Implementation program structure, core algorithm
  pseudo code, etc.
• Test cases and results
• Discussion issues and challenges
• Appendix the hardcopy of your source code. A
  softcopy of the program should be emailed to me
  in the zipped folder on the same day.