Model: A model is defined as a representation of a system for the purpose of studying the system. It is necessary to consider only those aspects of a system that affect the plan under investigation for studying them.
Mathematical Model: It uses symbolic notation and mathematical equation to represent a system. It represents a system in terms of logical and quantitative relationships.
Example: Area of circle = $\pi r^2$
Physical Model: It is based on some analogy between systems such as mechanical and electrical, electrical and hydraulic systems attributes are represented by measurements such as voltage or the position of a motor shaft. E.g. Scale models, prototype plants.
Static model: It sometimes called as Monte Carlo simulation model, that represents a system at ta particular point in time. E.g. Map, photo
Dynamic model: It represents systems as they change over time e.g. simulation of cafeteria from 2 pm to 4 pm.
Deterministic model: It is one which contains no random variables. it has a known set of i/p's which will result in a unique set of o/p's. e.g. Arrival of patient as per appointment time.
Stochestic model: It is one which contains one or more random variables as i/p's. Random o/p's are generated which can be considered only as estimates of the true characteristics of a model. e.g. Simulation of a bank
Discrete model: It is one in which the state variables change only at a discrete set of points in time. e.g. no. of customers waiting in line in bank.
Continuous model: It is one in which the state variables change continuous over time e.g. Head of water behind the dam.