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Markov Chains: Reintroducing Lost Knowledge Back into a Modeling and Simulation Course

Kathleen M. Kaplan, D.Sc., Lt Col John J. Kaplan (Ph.D., J.D.) USAF

Howard University/USAF

Abstract

“Over 500 educational institutions are using Arena today!” states the popular textbook site. Many of these educational institutions use the Arena textbook in their Modeling and Simulation (M&S) courses. Yet, out of this six hundred sixty eight page M&S book, only one sentence mentions “Markovian.” Compare this to a textbook used by the authors in their college years, an entire section is dedicated to “Markov Chains and Their Properties” and Markovian techniques are seen throughout this earlier textbook. While the authors may be dinosaurs clinging to the past, the importance of integrating Markov Chains into an M&S course cannot be overlooked. In fact, there are at least nine simulation programs in use that are based on Markov principles: CARE III (Computer Aided Reliability Estimation), CARE RBD Markov Model, CARMS (Computer-Aided Rate Modeling and Simulation), CARSA (Computer Aided Redundant System Reliability Analysis), MARKOV1 (Decision Systems Associates), MKV, PC Availability (Markov), RAP (Reliability and Availability Program), and SURE (Semi-Markov Unreliability Range Evaluator). While the programmers of these simulation tools understand Markov principles, they did not receive that information from the popular Arena textbook! Instruction based solely upon the Arena text has lost the knowledge of Markov. Obviously there is interest in the use of Markov principles, so why aren’t these principles included in engineering instruction? The popular textbook uses application software, which is a favorable teaching tool, but cannot be relied upon fully as the programs do not allow students to completely understand and appreciate this important underlying concept of M&S. M&S educators should ensure this lost knowledge of Markov principles is reintroduced back into the M&S classroom.

This paper will discuss the current educational trend in M&S and provide ways to incorporate Markov Chains and principles into the curriculum. In combining both a computer application program and Markovian techniques, the student will be able to fully appreciate the connection of mathematics and engineering, required in all ABET accredited programs.

“Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright ©2005, American Society for Engineering Education”

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Kaplan, J., & Kaplan, K. (2005, June), Markov Chains: Reintroducing Lost Knowledge Back Into A Modeling And Simulation Course Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14922