Robotic Surveillance and Markov Chains With Minimal Weighted Kemeny Constant


This article provides analysis and optimization results for the mean first passage time, also called the Kemeny constant, of a Markov chain. Initial, we generalize the notion of the Kemeny constant to environments with heterogeneous travel and service times, denote this generalization because the weighted Kemeny constant, and we characterize its properties. Second, for reversible Markov chains, we show that the minimization of the Kemeny constant and its weighted counterpart will be formulated as convex optimization problems and, moreover, as semidefinite programs. Third, we apply these results to the design of stochastic surveillance strategies for quickest detection of anomalies in network environments. We have a tendency to numerically illustrate the proposed design: compared with alternative well-known Markov chains, the performance of our Kemeny-based mostly strategies are continually better and in several cases substantially thus.

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