System Behavior: Deterministic and Probabilistic Models

General Concept of the System

The word 'system' describes many things: objects, methods, groups. The focus of a significant system implies knowing the structure and components of each one of them.

Classification of Systems

Classification involves levels of predictability and levels of complexity.

1. Level of predictability
2. Level of complexity

Deterministic and Probabilistic Approaches

The first approach is based on deterministic and probabilistic models. The approach is divided into three categories:

• Simple (sencillos)
• Complex
• Very complex

When it is possible to determine for sure how a system works, the system is said to be deterministic (i.e., containing few subsystems and interrelationships).

Conversely, when it is not possible to determine for sure how it works, it is called a probabilistic system.

Analysis of Cause and Effect

Systems can be analyzed in terms of inputs and outputs: the elements that enter are considered the causes that interact to produce an output. The output is the effect. The system acts like a box of functions that change inputs into results or output elements.

Effect and Delay Analysis

In the agricultural system example, the input does not lead to an immediate effect (i.e., immediate crop growth).

The time interval after the input supply until the crop is grown and ready for harvest is called a delayed effect. These circumstances are clearer when given a representative system, such as the aircraft throttle system, as shown in the following chart.

Aircraft Throttle Example

In this graph we see that the plane's speed (effect or output) remains substantially the same after the throttle (cause or input) has been closed. We note also that the speed decreases for quite a while after the throttle was moved into the closed position.

With a more complex system, more information is required to determine, predict, or simulate what the output level will be at a given time based on some input.

Optimization Analysis

In any system there is the possibility of achieving an optimal mix of inputs that will produce the desired results while optimizing the whole system.

A concrete example is a pool-painting project, where we are in charge and responsible for hiring the ^Number of painters to perform the work. The question before us is: what works best — four or two? Is eight better than four? Eight or twelve? It may seem that the larger the number of painters for the project, the greater the efficiency, but generally it is not.

Here we consider a graph which indicates the optimal number of painters needed to carry out the project in the shortest time.