## Use of Simulation Modeling

Modeling is a method of solving problems, in which the system under study is replaced by a simple object that describes the real system and/or its behavior and is called a model.

Simulation is used when conducting experiments on a real system would be impossible or impractical: for example, because of the high cost of prototyping and testing, or because the fragility of the system will not support extensive tests, or because of the duration of the experiment in real time is impractical.

Bits, not atoms. We need to distinguish between physical and mathematical modeling. An example of a physical model is a scale copy of an airplane in a wind tunnel. Simulations are a special class of computer-based mathematical models whose behavior is dictated by equations and algorithms, typically based on data, and represented by some type of computer user interface. These models mimic the behavior of some real-world system and develop theoretical outputs based on varying input data. This allows the simulation user to examine complex behavior and scenarios on a wide range of conditions far more quickly and inexpensively than with physical systems.

### Example of a Simulation Model

How to apply simulation can be illustrated by looking at an example based on a bank’s customer service department. Let’s assume that we’re trying to determine the minimum staffing level needed to reach some established service level.

We develop a Quality of Service measure; average queue size customers cannot exceed N people. In order to solve this problem you need to have some basic knowledge about the system such as how many customers visit the bank, at what frequency, and how long it takes a teller to service an individual customer. And, since we’re trying to model a real world situation, we have to vary the customer arrival time (lunch hour rush) and length of service to account for simple and complex transactions.

This task only seems specialized; it is a one of a general case of similar queuing problems which arise in many fields involving human and technical resource utilization. Companies are always seeking to lower the cost of underutilized resources, whether technical experts or capital equipment. Determining optimal resource schedules and balancing systems costs to its workload reduces costs and increases profits.

The first step in solving this problem is to create a model that corresponds to the structure and business processes of the bank. The model only needs to consider those factors that impact the problem being analyzed. For example, the availability of office services for corporate accounts or credit department has no effect on services to individuals, because they are physically and functionally separate. Schematically, this model can be represented as a sequence of these actions.

Run the model…

The second step is to feed our model some raw data: the variability and peaks of customer arrivals, average customer service length, the amount of available tellers and service personnel. Based on this data, the model simulates or reproduces the work of the bank within a specified period of time.

The next step is to analyze the statistics collected and provided by the model. If the average queue size exceeds the specified N limit, the number of available staff should be increased and a new experiment should be done.

After several experiments the user will have determined optimal staffing for the expected customer profiles. Naturally, this type of experimentation has been automated and the user can quickly vary a wide range of parameter values or optimize for the best solutions rather than conduct multiple repetitive tests.