In this paper, we consider the problem of distributed linear parameter estimation in static and dynamic sensor networks. We propose iterative averaging algorithms based on Laplacian dynamics which converge to the centralized least squares solution asymptotically. In the first part of this paper, we consider the case of unclustered (flat architecture) sensor networks and analyze convergence of the iterative algorithm, for both static and dynamic topologies. Subsequently, we extend our analysis to static but clustered sensor networks with pulsed inter-cluster updates. In this scheme, we assume that all inter-cluster communications occur every H time steps, H > 1, and the corresponding updates are held till the next update instant. Depending on the sensor locations and the topology formation algorithm used, it may be the case that inter-cluster communications require higher transmitter power support than intra-cluster communications. From a power efficiency (or alternately, network lifetime) point of view, it may therefore be beneficial to limit the extent of inter-cluster communication, without significantly enhancing the convergence time of the distributed estimation algorithm. We anticipate that a pulsed inter-cluster update scheme will also be beneficial for applications such as military sensor networks, where low probability of detection and interception is essential. Our analysis provides sufficient conditions under which the distributed algorithm operating on a pulsed inter-cluster update scheme converges. Simulation results are provided which illustrate the dependence of the convergence rate of the algorithm on H.
Abstruct-We consider the problem of power controlled minimum frame length scheduling for TbMA wireless networks, Given a set of one-hop transmission requests, our objective is to schedule them in a minimum number of time slots, so that each slot schedule is free of' self-interferences and meets desired SINR constraints. Additionally, the transmit power vector corresponding to each slot schedule should be minimal. We consider two different versions of the problem, a per-slot version and a per-frame version, and develop mixed integer linear programming models which can be used for solving the problems optimally. In addition, vie propose a heuristic algorithm for the per-slot version. I. INTRODUCTlONIn this paper, we consider the problem of power controlled adaptive frame length scheduling in TDMA wireless networks. To the best of our knowledge, the issue of joint scheduling and power control was first addressed by Tamer and Ephremides in 11, 21. Given a set of one-hop transmission requests constituting a request list, they suggest a two-phase algorithm which essentially decouples the scheduling and power control objectives. The scheduling objective, which is used to remove "selfinterferences" from the request list, is achieved by executing a centralized algorithm at the scheduler. After successful execution of this phase, the authors show that the power control problem in TDMA or hybrid TDMMCDMA ad hoc networks is similar to the power control problem in cellular systems. Consequently. algorithms developed for the latter can be used for ad hoc networks.In [ l , 21, the authors assume that the frame length comprises a fixed number of time slots, which is determined heuristically. Our work! on the other hand, focusses on the adaptive frame length case wherein, given a request list, the objective is to schedule them in a minimum number of time slots, so that each slot schedule is free of self-interferences and meets desired SINR constraints. Additionally, the transmit power vector corresponding to each slot schedule should be minimal, Ideally. the optimization should be carried out on a per-frame basis. However, this approach requires an excessive number of variables prohibiting optimal offline analysis even for moderately sized request lists. Consequently, for the most part, we focus on a (suboptimal) per-slot optimization approach which is much more lractable than a per-frame approach. Another aspect of our work. which differs from [ 1-21, is our consideration of sectored anlennas as opposed to omnidirectional antennas.The minimum frame length scheduling objective in our work has also been researched in the context of link scheduling in spatial-TDMA (STDMA) networks 13. 43. The work in 131 provides a comparison of graph-based versus SINR based link scheduling policies while [41 proposes optimal link and node scheduling algorithms using mixed integer linear programming (MILP) techniques. However, transmitter power is assumed to be fixed in these papers. Our work can therefore he seen as an extension of the link schedu...
We examine the stability of distributed simulations of electric circuits via their representation as distributed discrete-time dynamical systems. Our framework leads to necessary and sufficient stability conditions for distributed circuit solvers, even when the inter-processor communication pattern changes dynamically. The proposed framework is not only suitable for analyzing the co-simulation of large-scale power systems but also for analyzing a variety of dynamical systems that operate over a network. Stability analysis for a distributed simulation model of coupled nonlinear oscillation-known as the Kuramoto model-is also examined.
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