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Investigations into the Application of Cumulant Functions in Operations Research and Stochastic Modeling

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This report is a chronological documentation of the research progress made by Martijn Kolloffel throughout the Fall Semester 2003. The research focuses on the use of cumulant functions in queueing theory and stochastic modeling. This report is a result of a DOD research grant proposed by Dr. Timothy. I. Matis, with the purpose to engage undergraduate students from New Mexico State University in research in stochastic models. My progress was monitored, evaluated, and documented through the participation in the undergraduate research course IE 400. The investigation into the application of cumulant functions in stochastic modeling is a continuation of research activities in the spring semester of 2003. The usefulness of cumulant based analysis methods is researched by the formulation of a suitable model. The first goal in this semesters research endeavor is the definition of a model that is relevant to military applications. After the model is completely defined, we use a cumulant derivation procedure to find an approximation to the measure of interest. We then validate our solution by comparing it to a model simulation. After validation we strive to expand the scale of the initial model, which can show the mathematical tractability of this procedure for large-scale systems. We also intend to expand the model by using phase type distributions, which allows us to model most probability distributions. During the summer of 2003 some ideas for formulating a model suitable for cumulant-based modeling had been generated in relation to a NASA research grant, that focused on the reliability of components that are used in space technology. We think that the stochastic analysis of component reliability in military applications can also be relevant and useful to the Department of Defense. Optimizing maintenance schedules of military equipment can prevent critical system failure and improve system availability.

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  • Statistics and Probability
  • Operations Research

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