6,766 research outputs found

    Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

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    Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

    Estimating Dynamic Traffic Matrices by using Viable Routing Changes

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    Abstract: In this paper we propose a new approach for dealing with the ill-posed nature of traffic matrix estimation. We present three solution enhancers: an algorithm for deliberately changing link weights to obtain additional information that can make the underlying linear system full rank; a cyclo-stationary model to capture both long-term and short-term traffic variability, and a method for estimating the variance of origin-destination (OD) flows. We show how these three elements can be combined into a comprehensive traffic matrix estimation procedure that dramatically reduces the errors compared to existing methods. We demonstrate that our variance estimates can be used to identify the elephant OD flows, and we thus propose a variant of our algorithm that addresses the problem of estimating only the heavy flows in a traffic matrix. One of our key findings is that by focusing only on heavy flows, we can simplify the measurement and estimation procedure so as to render it more practical. Although there is a tradeoff between practicality and accuracy, we find that increasing the rank is so helpful that we can nevertheless keep the average errors consistently below the 10% carrier target error rate. We validate the effectiveness of our methodology and the intuition behind it using commercial traffic matrix data from Sprint's Tier-1 backbon

    Sample-path large deviations for tandem and priority queues with Gaussian inputs

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    This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Techniques to Improve Stable Distribution Modeling of Network Traffic

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    The stable distribution has been shown to more accurately model some aspects of network traffic than alternative distributions. In this work, we quantitatively examine aspects of the modeling performance of the stable distribution as envisioned in a statistical network cyber event detection system. We examine the flexibility and robustness of the stable distribution, extending previous work by comparing the performance of the stable distribution against alternatives using three different, public network traffic data sets with a mix of traffic rates and cyber events. After showing the stable distribution to be the overall most accurate for the examined scenarios, we use the Hellinger metric to investigate the ability of the stable distribution to reduce modeling error when using small data windows and counting periods. For the selected case and metric, the stable model is compared to a Gaussian model and is shown to produce the best overall fit as well as the best (or at worst, equivalent) fit for all counting periods. Additionally, the best stable fit occurs at a counting period that is five times shorter than the best Gaussian case. These results imply that the stable distribution can provide a more robust and accurate model than Gaussian-based alternatives in statistical network anomaly detection implementations while also facilitating faster system detection and response
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