Simulation and modeling - Old Questions
1. What is model? What are the different types of models? Give example for each.
Model
- Model is a computerized program that defines the mechanics of the considered system.
- During system modeling, the focus is on the system components, system structure, relationships among the components of the system and the behavior of the modeled system.
- Model must have state which may change on each time step.
- Model represents the system for the purpose of studying the system.
Types of Model
1. Physical Model
Physical model is the smaller or larger physical copy of an object being modeled. The physical model helps in visualization of the object taken into consideration in an effective way. It is also used to solve equations with the particular boundary conditions.
Two types of physical model:
i) Static Physical Model:
- Static physical model is the physical model which describes relationships that do not change with respect to time.
- Such models only depict the object’s characteristics at any instance of time, considering that the object’s property will not change over time.
- E.g. An architectural model of a house, scale model of a ship and so on.
ii) Dynamic Physical Model:
- Dynamic physical model is the physical model which describes the time varying relationships of the object properties.
- Such models describes the characteristics of the object that changes over time.
- It rely upon the analogy between the system being studied and some other system of a different nature, but have similarity on forces that directs the behavior of the both systems.
- E.g. A model of wind tunnel, a model of automobile suspension and so on.
2. Mathematical Model
Mathematical model is the model which is composed of a symbols and logic. It describes the system using mathematical concepts. The mathematical model is used to explain the system and to study the effects of different components, and to make predictions about the behavior of the system.
Two types of mathematical model:
i) Static Mathematical Model:
- Static mathematical model is the mathematical model that represents the logical view of the system in equilibrium state.
- Such models are time-invariant.
- It is generally represented by the basic algebraic equations.
- E.g. An equation relating the length and weight on each side of a playground variation, supply and demand relationship model of a market and so on.
ii) Dynamic Mathematical Model:
- Dynamic mathematical model is the mathematical model that accounts for the time dependent changes in the logical state of the system.
- Such models are time-variant.
- It is generally represented by differential equations or difference equations.
- E.g. The equation of motion of planets around the sun in the solar system.
3. Deterministic Model
It contains no random variables. They have a known set of inputs which will result in a unique set of outputs. E.g. Arrival of patients to the Dentist at the scheduled appointment time.
4. Stochastic Model
It has one or more random variable as inputs. Random inputs leads to random outputs. E.g. Simulation of a bank involves random inter-arrival and service times.