Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices $W_k$ are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products $W_kW_{k-1}... W_1$. In this paper, we find the exact exponential rate $I$ for the convergence in probability of the product of such matrices when time $k$ grows large, under the assumption that the $W_k$'s are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate $I$ is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection

Resource Allocation in Networking and Computing Systems: A Security and Dependability Perspective

In recent years, there has been a trend to integrate networking and computing systems, whose management is getting increasingly complex. Resource allocation is one of the crucial aspects of managing such systems and is affected by this increased complexity. Resource allocation strategies aim to effectively maximize performance, system utilization, and profit by considering virtualization technologies, heterogeneous resources, context awareness, and other features. In such complex scenario, security and dependability are vital concerns that need to be considered in future computing and networking systems in order to provide the future advanced services, such as mission-critical applications. This paper provides a comprehensive survey of existing literature that considers security and dependability for resource allocation in computing and networking systems. The current research works are categorized by considering the allocated type of resources for different technologies, scenarios, issues, attributes, and solutions. The paper presents the research works on resource allocation that includes security and dependability, both singularly and jointly. The future research directions on resource allocation are also discussed. The paper shows how there are only a few works that, even singularly, consider security and dependability in resource allocation in the future computing and networking systems and highlights the importance of jointly considering security and dependability and the need for intelligent, adaptive and robust solutions. This paper aims to help the researchers effectively consider security and dependability in future networking and computing systems.publishedVersio

On the Power of the Adversary to Solve the Node Sampling Problem

International audienceWe study the problem of achieving uniform and fresh peer sampling in large scale dynamic systems under adversarial behaviors. Briefly, uniform and fresh peer sampling guarantees that any node in the system is equally likely to appear as a sample at any non malicious node in the system and that infinitely often any node has a non-null probability to appear as a sample of honest nodes. This sample is built locally out of a stream of node identifiers received at each node. An important issue that seriously hampers the feasibility of node sampling in open and large scale systems is the unavoidable presence of malicious nodes. The objective of malicious nodes mainly consists in continuously and largely biasing the input data stream out of which samples are obtained, to prevent (honest) nodes from being selected as samples. First we demonstrate that restricting the number of requests that malicious nodes can issue and providing a full knowledge of the composition of the system is a necessary and sufficient condition to guarantee uniform and fresh sampling. We also define and study two types of adversary models: an omniscient adversary that has the capacity to eavesdrop on all the messages that are exchanged within the system, and a blind adversary that can only observe messages that have been sent or received by nodes it controls. The former model allows us to derive lower bounds on the impact that the adversary has on the sampling functionality while the latter one corresponds to a more realistic setting. Given any sampling strategy, we quantify the minimum effort exerted by both types of adversary on any input stream to prevent this sampling strategy from outputting a uniform and fresh sample