Computer Modeling and Simulation

1
Computer Modeling and Simulation

• An Introduction

2
Simulation

• is a tool to evaluate the performance of a
  system, existing or proposed, under different
  configurations of interest and over long period
  of real time.

3
Simulation

• is to pretend that one deals with a real thing
  while really working with an imitation
• in operations research, the imitation is a
  computer model of the simulated reality
• example
• flight simulator in a PC

4
Model

• is a representation of the construction and
  working of some system
• similar to but simpler than the system it
  represents.
• for a simulation study, a model is a
  mathematical model developed with the help of a
  simulation software.

5
Why use a model?

• cheaper
• safer
• saves time than real system

6
When to use simulation?

• systems that changes with time
• systems that involves randomness

7
Modeling

• is the process of producing a model

8
Model Classifications

• deterministic (input and output variables are
  fixed)
• stochastic (at least one of the input or output
  variables is probabilistic)
• static (time is not taken into account)
• dynamic (time-varying interactions among
  variables are taken into account).

9
System Terminology

• State
• A variable characterizing an attribute in the
  system such as level of stock in inventory or
  number of jobs waiting for processing
• Event
• An occurrence at a point in time which may
  change the state of the system, such as arrival
  of a customer or start of work on a job.

10
System Terminology

• Entity
• An object that passes through the system, such
  as cars in an intersection or orders in a
  factory. Often an event (e.g., arrival) is
  associated with an entity (e.g., customer).
• Queue
• A queue is not only a physical queue of people,
  it can also be a task list, a buffer of finished
  goods waiting for transportation or any place
  where entities are waiting for something to
  happen for any reason.

11
System Terminology

• Creating
• Creating is causing an arrival of a new entity
  to the system at some point in time.
• Scheduling
• Scheduling is the act of assigning a new future
  event to an existing entity.

12
System Terminology

• Random Variable
• is a quantity that is uncertain, such as
  interarrival time between two incoming flights or
  number of defective parts in a shipment.
• Random Variate
• is an artificially generated random variable.

13
System Terminology

• Distribution
• is the mathematical law which governs the
  probabilistic features of a random variable.

14
Example

• Building a simulation gas station with a single
  pump served by a single service man
• assume that the arrival of cars as well as their
  service times are random

15
Solution (1)

• At first identify the
• states
• events
• entities
• queue
• random realizations
• distributions

16
Solution (1)

• after identification of the different system
  requirements, you will come up with the different
  values
• states
• Number of cars waiting for service, number of
  cars served at any moment
• events
• Number of cars, start of service, end of service
• entities
• cars

17
Solution (1)

• queue
• The queue of cars in front of the pump, waiting
  for services
• random realizations
• inter-arrival times, service times
• distributions
• assume exponential distribution for both
  inter-arrival time and service time

18
Solution (2)
Arrival Routine
19
Solution (2)
Departure Routine
20
Advantages of Simulation

• to reduce the chances of failure to meet
  specifications
• to eliminate bottlenecks
• to prevent under or over-utilization of
  resources and
• to optimize system performance.