A healthy and considerable debate is taking place in scientific circles about whether science has sprouted a third leg to complement the more traditional legs of theory and experimentation. That third leg is computation.
The debate is complicated by the fact that computation can itself be used for experimentation in a wide variety of application areas. (Computer Science departments at a university, for example, can be housed within an engineering program or a science program.) Our purpose here is not to resolve this debate, but rather to focus on one of the core methodologies within computation, which is simulation.
The number of possible application areas for simulation experiments is great. Simulation experiments can be conducted on mathematical models for things such as queueing systems, financial instruments, supply chains, or surgical procedures. As a simple example, consider weather prediction. A computer is required to crunch all the data needed to evaluate the total number of possible storm tracks for a hurricane with anticipated landfall. But simulation can be used to analyze systems that don’t even exist. “What if” questions concerning the system can be posed to assess the impact of various alterations to the system. In this way, simulation can be used for modeling systems that are too expensive to build or too dangerous to experiment with in practice.
One important question that arises with simulation experiments is whether a Monte Carlo simulation or a discrete-event simulation is appropriate. A Monte Carlo simulation is appropriate when the passage of time does not play a significant role in the events being simulated. Estimating probabilities, expected values, etc., in problems associated with dealing playing cards, rolling dice, and flipping coins, for example, can be addressed by a Monte Carlo simulation. In order to estimate the probability of a specific event, a Monte Carlo experiment is conducted repeatedly, often several million times, and then the number of times that the event of interest arises is identified. This serves as an estimate of the true probability of the event of interest.
Although the concept is simple, the real-world implications are profound. Monte Carlo simulations are used in varied contexts, such as stock-price predictions, sports outcome predictions, and even to explore various molecular conformations of antibiotics.
In contrast, the passage of time plays an integral role in a discrete-event simulation model. Discrete-event simulations have been applied to business areas including inventory, queueing, and reliability.
As an example of an industrial simulation, consider a machine that operates on parts that arrive to the machine in a fashion that can be approximated by a probability model. A mathematical model of the interaction between the machine and the parts would involve the following:
- a data-based probability model for the time between arrivals of parts to the queue
- a probability distribution for the machine service time
- and an algorithm for placing parts in the queue (first come, first served is a common default, but other queueing disciplines are possible).
In addition, if another probability model indicates that the machine might fail, this probability can be incorporated into the simulation model. A typical “what if” question that could be posed concerning this machine simulation could measure the benefit of adding a second machine in terms of throughput and machine utilization.
Discrete-event simulations can be coded using almost any high-level programming language, although coding is streamlined by using one of the dozens of packages that are specifically designed for discrete-event simulation.
Dr. Larry Leemis, a Professor in the Department of Mathematics at The College of William & Mary, and Dr. Barry Lawson, an Associate Professor of Computer Science in the Department of Mathematics and Computer Science at the University of Richmond, will conduct Introduction to Monte Carlo and Discrete-Event Simulation, a continuing-education course offered by INFORMS, October 16-17 in Chicago. Click here to register.
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