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Simulation Concepts 49
Other modeling approaches
you use any discrete event or discrete rate blocks in a model, the timing will change to event driven (time steps will not be periodic) and it will not be a continuous model.
Other modeling approaches
Although there are several other approaches to modeling, they usually fit within one of the three major categories (continuous, discrete event, or discrete rate) discussed above. For exam- ple, System Dynamics and Bond graphs are subsets of continuous modeling, and queueing the- ory models are subsets of discrete event modeling.
Because of their specialized use, three specific modeling approaches (Monte Carlo, State/ Action, and Agent Based) are described below.
Monte Carlo modeling
Widely used to solve certain problems in statistics, Monte Carlo simulations provide a range of results rather than a single value. This approach can be applied to any ExtendSim model and used wherever uncertainty is a factor.
Monte Carlo modeling uses random numbers to vary input parameters for a series of calcula- tions. These calculations are performed many times and the results from each individual calcu- lation are recorded as an observation. The individual observations are statistically summarized, giving an indication of the likely result and the range of possible results. This not only tells what could happen in a given situation, but how likely it is that it will happen.
You build a Monte Carlo simulation in ExtendSim by incorporating random elements in a model and obtaining multiple observations. There are two ways to do this:
• The classical Monte Carlo method is to take a single mathematical equation or set of equa- tions, then cause the equation to be calculated many times. In this type of simulation, time is not a factor. The entire model is run to completion and evaluated at each step; each subse- quent step performs a new calculation. An example is the Monte Carlo model, discussed later in this section.
• AnalternativeMonteCarloapproach,typicallyappliedinadiscreteeventmodel,istoeither divide a single simulation run into multiple sections (batch means) or run the simulation many times (multirun analysis). Monte Carlo is incorporated by adding randomness to the model, running it many times, and analyzing the results. This method can be applied to any continuous, discrete event, or discrete rate model. It is shown in the Queue Statistics model, described later in this section. For more information about using the Statistics block (Value library) for performing batch means or multirun analysis, see “Statistics” on page 642.
Monte Carlo model
An example of the classical method is the Monte Carlo model. This model determines the expected revenue from a new product. It runs for 10,000 steps, from time 0 to time 9999, and each step results in an observation. This cycle is repeated 24 times, once for each of the

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