Operations Research (In Mathematics in Cyber Research)
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Contributing USMA Research Unit(s)
Army Cyber Institute
In the last eighty years, the discipline of operations research has been used extensively to provide analytical evidence for research outcomes in the mathematical sciences. Problems of interest may involve variations of cost-benefit analyses, the measurement of attributes or features, differing levels of uncertainty, and constrained or unconstrained frameworks. The analyses are not always concerned with generating unique optimal solutions; often, an array of near-optimal solutions may be more appropriate depending on the assumptions, factors, and objectives of a particular study. Research work may also be more aligned toward investigating how complex processes behave either in a static or dynamic manner. Sensitivity analyses may accompany outcomes to provide an indication of the robustness of different solutions. In summary, the assortment of methods, tools, and analytics in operations research is vast and growing. Emerging fields such as data science and techniques such as machine learning will fuel continued growth in this mathematical discipline for many years to come.
Interestingly, the domain of cyber theory and applications is also growing, and the products and processes in this realm have qualities and characteristics that warrant using methods in operations research. Cyber attacks can be modeled using hierarchical threat structures and may involve competing decision strategies from both an organization or individual and the adversary. Network traffic flow, intrusion detection and prevention systems, interconnected human-machine interfaces, and automated systems all require higher levels of complexity in modeling and possess inherently random sub-processes. Attributes, such as cyber resiliency, network adaptability, security capability, and information technology flexibility require the measurement of multiple characteristics, many of which may involve both quantitative and qualitative interpretations. For nearly every organization that is invested in some cybersecurity practice, decisions must be made that involve the competing objectives of cost, risk, and performance.
This chapter will highlight only a small portion of the operations research space. The sub-discipline of decision analysis is first described, which may involve the modeling or measuring of actions, factors, or responses using mathematics to aid in decision making. The sub-discipline of mathematical optimization is then discussed, which may involve solving for the most desirable outcome or solutions given a constrained or unconstrained framework. The last broad topic, techniques in stochastic process modeling are provided to account for the random or uncertain behavior of cyber processes and where insight and greater forecasting power may be achieved. Along the way, the focus will be on the mathematics associated with these sub-disciplines of operations research. Finally, at the conclusion of this chapter, research implications and extensions are offered to the examiner that desires to carry these practices forward in cyber research.
Goethals, Paul; Scala, Natalie; and Bastian, Nathaniel D., "Operations Research (In Mathematics in Cyber Research)" (2022). ACI Books & Book Chapters. 17.
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