Biblio

This paper considers a 2-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker) simultaneously disrupts one or more links to maximize her value of lost flow but also faces cost of disrupting links. This game is strategically equivalent to a zero-sum game. Linear programming duality and the max-flow min-cut theorem are applied to obtain properties that are satisfied in any mixed Nash equilibrium. In any equilibrium, both players achieve identical payoffs. While the defender's expected transportation cost decreases in attacker's marginal value of lost flow, the attacker's expected cost of attack increases in defender's marginal value of effective flow. Interestingly, the expected amount of effective flow decreases in both these parameters. These results can be viewed as a generalization of the classical max-flow with minimum transportation cost problem to adversarial environments.

The objective of this work is to develop an efficient and practical sensor placement method for the failure detection and localization in water networks. We formulate the problem as the minimum test cover problem (MTC) with the objective of selecting the minimum number of sensors required to uniquely identify and localize pipe failure events. First, we summarize a single-level sensing model and discuss an efficient fast greedy approach for solving the MTC problem. Simulation results on benchmark test networks demonstrate the efficacy of the fast greedy algorithm. Second, we develop a multi-level sensing model that captures additional physical features of the disturbance event, such as the time lapsed between the occurrence of disturbance and its detection by the sensor. Our sensor placement approach using MTC extends to the multi-level sensing model and an improved identification performance is obtained via reduced number of sensors (in comparison to single-level sensing model). In particular, we investigate the bi-level sensing model to illustrate the efficacy of employing multi-level sensors for the identification of failure events. Finally, we suggest extensions of our approach for the deployment of heterogeneous sensors in water networks by exploring the trade-off between cost and performance (measured in terms of the identification score of pipe/link failures).