Modeling and decision making in communication networks

The central theme of this thesis is probability modeling and methodology for faults and related issues of probing, availability, reliability, performability, and worm propagation. As part of a cost minimization approach to faults, several notions new to fault management are developed. These include optimal determination of threshold (for network metrics) through sensitivity and specificity considerations, and measures of reliability of a diagnosis. The approach requires modeling the probability distribution of a network metric and, toward this end, an excesses over threshold approach based on the generalized Pareto distribution (GPD) is proposed and applied to port 80 data. The methodology of binary probing and follow-up testing is studied. A sharp upper bound on the probability of correctness of the most probable explanation is obtained. Measures of reliability of the probe results are proposed and studied. Availability in a Markovian model is represented as a random order statistic of random rank from a uniform distribution. The notion of 'shocks' is introduced to study reliability of computer systems and a compound Poisson process model is developed. Frequently, it is not just the drop in average performance level but the increased variability in performance which causes deterioration in QoS. To address this issue, a performability model is developed for degradable systems and the mean and variance of a cumulative performance function are studied. Performability indices are introduced and the proposed model is illustrated through the behavior of packet loss in the Access Grid (AG). Finally, this thesis makes a number of contributions to modeling worm propagation on the Internet. A Nonhomogeneous Random Scanning (NHRS) model is derived to allow time-dependent variation in a worm's contact rate forced by network congestion and routing instabilities arising from worm propagation itself. It generalizes the Random Constant Spread (RCS) model. Procedures for fitting NHRS and RCS models are given. In response to the possibility of failure of measures to prevent or treat Internet worms, an Imperfect Prevention-Imperfect Recovery (IMP-IMR) model is developed. The decision-theoretic approach to corrective action is again demonstrated in the context of choosing between two worm containment strategies.