Simulation and Modelling - Old Questions

3. What do you understand by static mathematical model? Explain with example. Differentiate between stochastic and deterministic activities.

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.