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Abstract:
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The objective of this work is to model the costs of diverse threats arriving to a computer network during an interval of time. We assume that the arrival is modeled by a nonhomogenous Poisson process and that each arrival is accompanied by a number of attributes which enter the model as marks on the arrival time. These marks or attributes are random variables which may depend on the time of arrival and other covariates. Subsetting or thinning the original Poisson point process produces Poisson point processes for specific families of threats and/or sub nets of the original network and for costs of the arriving threats. Explicit formulation is obtained for the intensities (mean, variance, probability distribution) of all point processes, and an application of Campbell's theorem produces the mean and variance of the sum of costs. The formulations are well suited for modeling.
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