Modeling 6: Deterministic Vs Probalistic Models

There are two categories of mathematical models used to describe security and loss prevention systems and environments – deterministic and probabilistic (also known as stochastic). The gravitational formula described in the last posting is an example of a deterministic model. This relationship between falling bodies and gravitational pull never varies regardless of circumstance – it is always the same. The size of a parachute adequate to reduce the velocity of a falling parachutist to acceptable limits can be determined using the deterministic gravitational formula, and the analysis of this phenomenon is called parametric analysis. The model is completely predictable.

Unpredictable systems have an element of uncertainty (risk) associated with them. That “normal (20,5)” access control point makes an excellent example. If the loss prevention or security practitioner were to make random, one-minute counts of traffic through that point, the individual counts would not likely consist of all 20’s (always counting 20 people per minute in each and every count). Using stochastic modeling, however, we can make intelligent and accurate predictions about the most likely capacity range of the access control point based on the known distribution information. By combining this information with the facility population, we can make very dependable decisions regarding the access control point (is it adequate, or does it pose a potentially hazardous bottleneck, etc.).

For solving problems in which we are certain of the relationships that are present within a system or process that is important to our operations, we can use linear and nonlinear programming, goal programming, network analysis and deterministic dynamic programming techniques. These are very useful tools for measuring stochastic systems because deterministic models are normally more simple and easier to manipulate than probabilistic models.

By judiciously assuming away the uncertainties in a system, we can usually identify the parts (attributes) of the system that have the greatest influence over its operation. This process focuses a problem and allows for more effective analysis of a stochastic system.