4,470 research outputs found

    Some Asymptotic Results for the Transient Distribution of the Halfin-Whitt Diffusion Process

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    We consider the Halfin-Whitt diffusion process Xd(t)X_d(t), which is used, for example, as an approximation to the mm-server M/M/mM/M/m queue. We use recently obtained integral representations for the transient density p(x,t)p(x,t) of this diffusion process, and obtain various asymptotic results for the density. The asymptotic limit assumes that a drift parameter β\beta in the model is large, and the state variable xx and the initial condition x0x_0 (with Xd(0)=x0>0X_d(0)=x_0>0) are also large. We obtain some alternate representations for the density, which involve sums and/or contour integrals, and expand these using a combination of the saddle point method, Laplace method and singularity analysis. The results give some insight into how steady state is achieved, and how if x0>0x_0>0 the probability mass migrates from Xd(t)>0X_d(t)>0 to the range Xd(t)<0X_d(t)<0, which is where it concentrates as tt\to\infty, in the limit we consider. We also discuss an alternate approach to the asymptotics, based on geometrical optics and singular perturbation techniques.Comment: 43 pages and 8 figure

    An Explicit Solution to the Chessboard Pebbling Problem

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    We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations G(k)G(k) and a related double sequence G(k,m)G(k,m). Exact expressions for these are derived, and we then consider various asymptotic limits.Comment: 12 pages, 7 reference

    On Spectral Properties of Finite Population Processor Shared Queues

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    We consider sojourn or response times in processor-shared queues that have a finite population of potential users. Computing the response time of a tagged customer involves solving a finite system of linear ODEs. Writing the system in matrix form, we study the eigenvectors and eigenvalues in the limit as the size of the matrix becomes large. This corresponds to finite population models where the total population is N1N\gg 1. Using asymptotic methods we reduce the eigenvalue problem to that of a standard differential equation, such as the Hermite equation. The dominant eigenvalue leads to the tail of a customer's sojourn time distribution.Comment: 28 pages, 7 figures and 5 table

    On the Sojourn Time Distribution in a Finite Population Markovian Processor Sharing Queue

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    We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing unit (CPU). For systems with a large population NN and a commensurately rapid service rate, or infrequent arrivals, we obtain various asymptotic results. We analyze the conditional sojourn time distribution of a tagged customer, conditioned on the number nn of others in the system at the tagged customer's arrival instant, and also the unconditional distribution. The asymptotics are obtained by a combination of singular perturbation methods and spectral methods. We consider several space/time scales and parameter ranges, which lead to different asymptotic behaviors. We also identify precisely when the finite population model can be approximated by the standard infinite population M/M/1M/M/1-PS queue.Comment: 60 pages and 3 figure

    Learning a Dilated Residual Network for SAR Image Despeckling

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    In this paper, to break the limit of the traditional linear models for synthetic aperture radar (SAR) image despeckling, we propose a novel deep learning approach by learning a non-linear end-to-end mapping between the noisy and clean SAR images with a dilated residual network (SAR-DRN). SAR-DRN is based on dilated convolutions, which can both enlarge the receptive field and maintain the filter size and layer depth with a lightweight structure. In addition, skip connections and residual learning strategy are added to the despeckling model to maintain the image details and reduce the vanishing gradient problem. Compared with the traditional despeckling methods, the proposed method shows superior performance over the state-of-the-art methods on both quantitative and visual assessments, especially for strong speckle noise.Comment: 18 pages, 13 figures, 7 table
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