We give an improved algorithm for drawing a random sample from a large data stream when the input elements are distributed across multiple sites which communicate via a central coordinator. At any point in time the set of elements held by the coordinator represent a uniform random sample from the set of all the elements observed so far. When compared with prior work, our algorithms asymptotically improve the total number of messages sent in the system as well as the computation required of the coordinator. We also present a matching lower bound, showing that our protocol sends the optimal number of messages up to a constant factor with large probability. As a byproduct, we obtain an improved algorithm for finding the heavy hitters across multiple distributed sites.
A related model of distributed streams was considered in @cite_3 @cite_15 . In this model, the coordinator was not required to continuously maintain an estimate of the required aggregate, but when the query was posed to the coordinator, the sites would be contacted and the query result would be constructed. In their model, the coordinator could be said to be reactive'', whereas in the model considered in this paper, the coordinator is pro-active''.
@cite_15 @cite_3
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Due to the potentially large number of Distributed Energy Resources (DERs) - demand response, distributed generation, distributed storage - that are expected to be deployed, it is impractical to use detailed models of these resources when integrated with the transmission system. Being able to accurately estimate the transients caused by demand response is especially important to analyze the stability of the system under different demand response strategies, where dynamics on time scales of seconds to minutes are important. On the other hand, a less complex model is more amenable to study stability of a large power system, and to design feedback control strategies for the population of devices to provide ancillary services. The main contribution of this paper is to develop an aggregated model for a heterogeneous population of Thermostatic Controlled Loads (TCLs) to accurately capture their collective behavior under demand response. The aggregated model efficiently includes statistical information of the population, systematically deals with heterogeneity, and accounts for a second-order effect necessary to accurately capture the transient dynamics in the collective response. The developed aggregated model is validated against simulations of thousands of detailed building models using GridLAB-D (an open source distribution simulation software) under both steady state and severe dynamic conditions. This paper presents a novel economic model to regulate capacity sharing in a federation of hybrid cloud providers (CPs). The proposed work models the interactions among the CPs as a repeated game among selfish players that aim at maximizing their profit by selling their unused capacity in the spot market but are uncertain of future workload fluctuations. The proposed work first establishes that the uncertainty in future revenue can act as a participation incentive to sharing in the repeated game. We, then, demonstrate how an efficient sharing strategy can be obtained via solving a simple dynamic programming problem. The obtained strategy is a simple update rule that depends only on the current workloads and a single variable summarizing past interactions. In contrast to existing approaches, the model incorporates historical and expected future revenue as part of the virtual machine (VM) sharing decision. Moreover, these decisions are not enforced neither by a centralized broker nor by predefined agreements. Rather, the proposed model employs a simple grim trigger strategy where a CP is threatened by the elimination of future VM hosting by other CPs. Simulation results demonstrate the performance of the proposed model in terms of the increased profit and the reduction in the variance in the spot market VM availability and prices. Received 28 May 2002; revised 18 September 2002; accepted 24 September 2002; published 14 February 2003. [1] When an inverse problem is solved to estimate an unknown function such as the hydraulic conductivity in an aquifer or the contamination history at a site, one constraint is that the unknown function is known to be everywhere nonnegative. In this work, we develop a statistically rigorous method for enforcing function nonnegativity in Bayesian inverse problems. The proposed method behaves similarly to a Gaussian process with a linear variogram (i.e., unrestricted Brownian motion) for parameter values significantly greater than zero. The method uses the method of images to define a prior probability density function based on reflected Brownian motion that implicitly enforces nonnegativity. This work focuses on problems where the unknown is a function of a single variable (e.g., time). A Markov chain Monte Carlo (MCMC) method, specifically, a highly efficient Gibbs sampler, is implemented to generate conditional realizations of the unknown function. The new method is applied to the estimation of the trichloroethylene (TCE) and perchloroethylene (PCE) contamination history in an aquifer at Dover Air Force Base, Delaware, based on concentration profiles obtained from an underlying aquitard. INDEX TERMS: 1831 Hydrology: Groundwater quality; 1869 Hydrology: Stochastic processes; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: stochastic inverse modeling, contaminant source identification, inference under constraints, Markov chain Monte Carlo (MCMC), Gibbs sampling, Bayesian inference Many people share their activities with others through online communities. These shared activities have an impact on other users' activities. For example, users are likely to become interested in items that are adopted (e.g. liked, bought and shared) by their friends. In this paper, we propose a probabilistic model for discovering latent influence from sequences of item adoption events. An inhomogeneous Poisson process is used for modeling a sequence, in which adoption by a user triggers the subsequent adoption of the same item by other users. For modeling adoption of multiple items, we employ multiple inhomogeneous Poisson processes, which share parameters, such as influence for each user and relations between users. The proposed model can be used for finding influential users, discovering relations between users and predicting item popularity in the future. We present an efficient Bayesian inference procedure of the proposed model based on the stochastic EM algorithm. The effectiveness of the proposed model is demonstrated by using real data sets in a social bookmark sharing service.