Resilience of Locally Routed Network Flows: More Capacity is Not Always Better

In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed locally such that none of the outgoing links are overloaded unless the node receives an inflow greater than its total outgoing capacity. A link irreversibly fails if it is overloaded or if there is no operational link in its immediate downstream to carry its flow. For such systems, resilience is defined as the minimum amount of reduction in the link capacities that would result in the failure of all the outgoing links of an origin node. We show that such networks do not necessarily become more resilient as additional capacity is built in the network. Moreover, when the external inflow does not exceed the network capacity, selective reductions of capacity at certain links can actually help averting the cascading failures, without requiring any change in the local routing policies. This is an attractive feature as it is often easier in practice to reduce the available capacity of some critical links than to add physical capacity or to alter routing policies, e.g., when such policies are determined by social behavior, as in the case of road traffic networks. The results can thus be used for real-time monitoring of distance-to-failure in such networks and devising a feasible course of actions to avert systemic failures.Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 201

Algorithms for Replica Placement in High-Availability Storage

A new model of causal failure is presented and used to solve a novel replica placement problem in data centers. The model describes dependencies among system components as a directed graph. A replica placement is defined as a subset of vertices in such a graph. A criterion for optimizing replica placements is formalized and explained. In this work, the optimization goal is to avoid choosing placements in which a single failure event is likely to wipe out multiple replicas. Using this criterion, a fast algorithm is given for the scenario in which the dependency model is a tree. The main contribution of the paper is an $O(n + \rho \log \rho)$ dynamic programming algorithm for placing $\rho$ replicas on a tree with $n$ vertices. This algorithm exhibits the interesting property that only two subproblems need to be recursively considered at each stage. An $O(n^2 \rho)$ greedy algorithm is also briefly reported.Comment: 22 pages, 7 figures, 4 algorithm listing

On the behavior of threshold models over finite networks

We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise interaction with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynamics with heterogeneous thresholds over the agents. While the previous literature has studied such linear threshold models under the assumption that each agent may change actions at most once, a study of best response dynamics in such networked games necessitates an analysis that allows for multiple switches in actions. In this paper, we develop such an analysis. We establish that agent behavior cycles among different actions in the limit, we characterize the length of such limit cycles, and reveal bounds on the time steps required to reach them. We finally propose a measure of network resilience that captures the nature of the involved dynamics. We prove bounds and investigate the resilience of different network structures under this measure.Irwin Mark Jacobs and Joan Klein Jacobs Presidential FellowshipSiebel ScholarshipUnited States. Air Force Office of Scientific Research (Grant FA9550-09-1-0420)United States. Army Research Office (Grant W911NF-09-1-0556