Abstract-We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate largescale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

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Abstract-We consider first and second order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an H2 norm of the stochastic system. We use the setting of fractal networks to investigate the question of whether a purely topological measure, such as the fractal dimension, can capture the asymptotics of coherence in the large system size limit. Our analysis for first-order systems is facilitated by connections between first-order stochastic consensus and the global mean first passage time of random walks. We then show how to apply similar techniques to analyze second-order stochastic consensus systems. Our analysis reveals that two networks with the same fractal dimension can exhibit different asymptotic scalings for network coherence. Thus, this topological characterization of the network does not uniquely determine coherence behavior. The question of whether the performance of stochastic consensus algorithms in large networks can be captured by purely topological measures, such as the spatial dimension, remains open.

Abstract-We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute in-network computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with timevarying topologies. The network dynamics necessarily introduce inaccuracies to our in-network computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for time-varying networks. Evaluations show that our distributed algorithms for both static and time-varying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.

We consider a distributed average consensus algorithm over a network in which communication links fail with independent probability. In such stochastic networks, convergence is defined in terms of the variance of deviation from average. We first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures. We then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise. We give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks. We also present simulation-free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability.Index Terms-Distributed systems, gossip protocols, multiplicative noise, packet loss, randomized consensus. W E study the distributed average consensus problem over a network with stochastic link failures. Each node has some initial value and the goal is for all nodes to reach consensus at the average of all values using only communication between neighbors in the network graph. Distributed average consensus is an important problem that has been studied in contexts such as vehicle formations [1]-[3], aggregation in sensor networks and peer-to-peer networks [4], load balancing in parallel processors [5], [6], and gossip algorithms [7], [8].Distributed consensus algorithms have been widely investigated in networks with static topologies, where it has been shown that the convergence rate depends on the second smallest eigenvalue of the Laplacian of the communication graph [9], [10]. However, the assumption that a network topology is static, i.e. that communication links are fixed and reliable throughout the execution of the algorithm, is not always realistic. In mobile networks, the network topology changes as the agents change position, and therefore the set of nodes with which each node can communicate may be time-varying. In sensor networks and mobile ad-hoc networks, messages may be lost due to interference, and in wired networks, networks may suffer from packet loss and buffer overflow. In scenarios such as these, it is desirable to quantify the effects that topology changes and communication failures have upon the performance of the averaging algorithm.In this work, we consider a network with an underlying topology that is an arbitrary, connected, undirected graph where links fails with independent but not necessarily identical probability. In such stochastic networks, we define convergence in terms of the variance of deviation from average. We show that the averaging problem can be formulated as a linear system with multiplicative noise and use our formulation to derive a recursion equation for the second order statistics of the deviation from average. We also give expressions for the mean square convergence rate in the asymptotic limits of small failure prob...

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We consider a distributed average consensus algorithm over a network in which communication links fail with independent probability. Convergence in such stochastic networks is defined in terms of the variance of deviation from average. We characterize the decay factor of the variance in terms of the eigenvalues of a Lyapunov-like matrix recursion. We give expressions for the decay factors in the asymptotic limits of small failure probability and large networks. We also present a simulation-free method for computing the decay factor for any particular graph instance and use this method to study the behavior of various network examples as a function of link failure probability.

The emerging trend of edge computing has led several cloud providers to release their own platforms for performing computation at the 'edge' of the network. We compare two such platforms, Amazon AWS Greengrass and Microsoft Azure IoT Edge, using a new benchmark comprising a suite of performance metrics. We also compare the performance of the edge frameworks to cloud-only implementations available in their respective cloud ecosystems. Amazon AWS Greengrass and Azure IoT Edge use different underlying technologies, edge Lambda functions vs. containers, and so we also elaborate on platform features available to developers. Our study shows that both of these edge platforms provide comparable performance, which nevertheless differs in important ways for key types of workloads used in edge applications. Finally, we discuss several current issues and challenges we faced in deploying these platforms.