Simulation and Modelling - Old Questions

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.

For example:  Supply and demand relationship model of a market 

Consider a market model assuming the linear behavior of supply and demand with price.

• Demand for a product will be low when the price is high and will be high when the price is low.
• Supply for a product will be high when the price is high and will be low when the price is low.
• If conditions remain stable, the price will settle to the point at which demand equals supply.

The relations can be stated mathematically as:    

    Q = a – bP
    S = c + dP
    S = Q

where, S = supply, Q = demand and P = price

The linear market model is shown below:

Difference Between Stochastic and Deterministic Activities

• Stochastic model / activity 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.
• Deterministic model / activity 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.