Classification of Simulation Models

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Classification of Simulation Models

• Static vs. Dynamic Simulation Model
• Static Simulation Model is a representation of a
  system at a particular point in time (i.e., time
  plays no role)
• Examples Monte Carlo Simulation (will discuss
  later)
• Estimating the probability of winning a game in a
  casino machine.
• Estimating the value of p.

• Dynamic Simulation Model is a representation of
  a system as it evolves over time
• Examples include models of a bank, a processor

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• Deterministic vs. Stochastic Simulation Models

• Deterministic Simulation Model does not
  contain any probabilistic components.
• Example a system of differential equations
  representing a chemical reaction.
• Output are also deterministic
• Stochastic Simulation models those having at
  least some random input components.
• Examples include Queuing models (Interarrival
  times between two consecutive customers and
  service times are usually random)
• They produce output that are also random.

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1. Continuous vs. Discrete Simulation Models.

• Discrete Simulation models those representing
  systems whose state changes at discrete points of
  time.
• Changes of the system occur continuously as the
  time evolves

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Discrete-event Simulation Model

• Simulation models we consider in this course are
  discrete, dynamic, and stochastic. Such models
  are called Discrete-Event Simulation Models
• Changes occur at a separate points of time
• i.e., The system can change only at a countable
  number of points in time.
• What does it change the system state? Events
• Event is an instantaneous occurrence that
  changes the state of the system Examples Arrival
  of a new customer, a Departure of a customer from
  a queuing model

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Time-Advance Mechanism

• Simulation Clock is a variable in the simulation
  model that keeps track of the current simulation
  time (does not depend on the computer time)

0
Simulation clock

• There are 2 approaches for advancing the
  simulation clock
• Next-event time advance
• Fixed-increment time advance

0
Dt
2 Dt
3 Dt
4 Dt
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Next-Event Time Advance

• The most common used approach
• The simulation clock is initialized to zero.
• Time of occurrence of future events are
  determined.
• The simulation clock is then advanced to the time
  of the occurrence of the next event (the event
  that is scheduled to occur first).
• The system is updated taking in account that the
  event has occurred.
• Update the time of the occurrence of the next
  events.
• Go to step 3.
• Repeat until a stopping criterion is satisfied.

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Example A single server Queuing system

• e.g., one-operator barbershop, a cashier in a
  supermarket, etc.
• Define
• ti time of arrival of the ith customer.
• Ai ti ti-1 the interarrival time between
  the (i-1)st and the ith customer.
• Si the service time of the ith customer
• Di the delay time in queue of the ith
  customer.
• ci ti Di Si departure time of the ith
  customer.
• ei The time of the occurrence of the ith event.
  

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The next-event time-advance approach illustrated
for the single-server queuing system.