Estimating eddy diffusivities from noisy Lagrangian observations

The problem of estimating the eddy diffusivity from Lagrangian observations in the presence of measurement error is studied in this paper. We consider a class of incompressible velocity fields for which is can be rigorously proved that the small scale dynamics can be parameterised in terms of an eddy diffusivity tensor. We show, by means of analysis and numerical experiments, that subsampling of the data is necessary for the accurate estimation of the eddy diffusivity. The optimal sampling rate depends on the detailed properties of the velocity field. Furthermore, we show that averaging over the data only marginally reduces the bias of the estimator due to the multiscale structure of the problem, but that it does significantly reduce the effect of observation error

Efficient Non-parametric Bayesian Hawkes Processes

In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the stationarity of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on expectation maximization -- and we show that our methods have a linear time complexity, both theoretically and empirically. On synthetic data, we show our methods to be able to infer flexible Hawkes triggering kernels. On two large-scale Twitter diffusion datasets, we show that our methods outperform the current state-of-the-art in goodness-of-fit and that the time complexity is linear in the size of the dataset. We also observe that on diffusions related to online videos, the learned kernels reflect the perceived longevity for different content types such as music or pets videos

Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement. Implementation difficulties are also addressed with a focus on dealing with large data sets, where latent models are especially advantageous due the large number of observations facilitating identification of hidden factors. Namely, computational issues such as numerical underflow and high processing cost arise in this context and in this paper, we produce procedures to overcome these problems. This modelling framework is demonstrated using a large insurance data set to illustrate theoretical, practical and computational contributions and an empirical comparison to other count models highlight the advantages of the proposed approach.Comment: For simulated data sets and code, please go to https://github.com/agi-lab/reserving-MMNP

Stochastic Packet Loss Model to Evaluate QoE Impairments

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The estimation of quality for real-time services over telecommunication netb4works requires realistic models for impairments and failures during transmission. We focus on the classical Gilbert-Elliott model whose second-order statistics is derived over arbitrary time-scales. The model is used to fit packet loss processes of backbone and DVB-H traffic traces. The results show that simple Markov models are appropriate to capture the observed loss pattern and to discuss how such models can be used to examine the quality degradations caused by packet losses

Traffic Modeling in Industrial Ethernet Networks

This article discusses the traffic types typically used in industrial networks. The authors propose a number of methods of generating traffic that can be used in modeling traffic sources in the networks under consideration. The proposed traffic models have been developed on the basis of the ON/OFF model. The proposed solutions can be applied to model typical traffic types that are used in industrial systems, such as Time-Triggered (TT) traffic, Audio-Video Bridging (AVB) traffic or Best Effort traffic. The article discusses four traffic models with modifications and shows how the proposed models can be used in modeling different traffic types used in industrial networks

Wavelength converter sharing in asynchronous optical packet/burst switching: An exact blocking analysis for markovian arrivals

Cataloged from PDF version of article.In this paper, we study the blocking probabilities in a wavelength division multiplexing-based asynchronous bufferless optical packet/burst switch equipped with a bank of tuneable wavelength converters dedicated to each output fiber line. Wavelength converter sharing, also referred to as partial wavelength conversion, corresponds to the case of a number of converters shared amongst a larger number of wavelength channels. In this study, we present a probabilistic framework for exactly calculating the packet blocking probabilities for optical packet/burst switching systems utilizing wavelength converter sharing. In our model, packet arrivals at the optical switch are first assumed to be Poisson and later generalized to the more general Markovian arrival process to cope with very general traffic patterns whereas packet lengths are assumed to be exponentially distributed. As opposed to the existing literature based on approximations and/or simulations, we formulate the problem as one of finding the steady-state solution of a continuous-time Markov chain with a block tridiagonal infinitesimal generator. To find such solutions, we propose a numerically efficient and stable algorithm based on block tridiagonal LU factorizations. We show that exact blocking probabilities can be efficiently calculated even for very large systems and rare blocking probabilities, e.g., systems with 256 wavelengths per fiber and blocking probabilities in the order of 10−40. Relying on the stability and speed of the proposed algorithm, we also provide a means of provisioning wavelength channels and converters in optical packet/burst switching systems

Workload characterization, modeling, and prediction in grid Computing

Workloads play an important role in experimental performance studies of computer systems. This thesis presents a comprehensive characterization of real workloads on production clusters and Grids. A variety of correlation structures and rich scaling behavior are identified in workload attributes such as job arrivals and run times, including pseudo-periodicity, long range dependence, and strong temporal locality. Based on the analytic results workload models are developed to fit the real data. For job arrivals three different kinds of autocorrelations are investigated. For short to middle range dependent data, Markov modulated Poisson processes (MMPP) are good models because they can capture correlations between interarrival times while remaining analytically tractable. For long range dependent and multifractal processes, the multifractal wavelet model (MWM) is able to reconstruct the scaling behavior and it provides a coherent wavelet framework for analysis and synthesis. Pseudo-periodicity is a special kind of autocorrelation and it can be modeled by a matching pursuit approach. For workload attributes such as run time a new model is proposed that can fit not only the marginal distribution but also the second order statistics such as the autocorrelation function (ACF). The development of workload models enable the simulation studies of Grid scheduling strategies. By using the synthetic traces, the performance impacts of workload correlations in Grid scheduling is quantitatively evaluated. The results indicate that autocorrelations in workload attributes can cause performance degradation, in some situations the difference can be up to several orders of magnitude. The larger the autocorrelation, the worse the performance, it is proved both at the cluster and Grid level. This study shows the importance of realistic workload models in performance evaluation studies. Regarding performance predictions, this thesis treats the targeted resources as a ``black box'' and takes a statistical approach. It is shown that statistical learning based methods, after a well-thought and fine-tuned design, are able to deliver good accuracy and performance.UBL - phd migration 201

A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model

We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in the sense that they can be expressed as integrals. Difficulties associated with the numerical evaluation of these integrals are discussed, and techniques for avoiding these difficulties are provided. Overall, it is shown that computational complexity for our model is comparable to the case of a pure Heston model, but our correction brings significant flexibility in terms of fitting to the implied volatility surface. This is illustrated numerically and with option data

Control-theoretic Analysis of Admission Control Mechanisms for Web Server Systems

Web sites are exposed to high rates of incoming requests. The servers may become overloaded during temporary traffic peaks when more requests arrive than the server is designed for. An admission control mechanism rejects some requests whenever the arriving traffic is too high and thereby maintains an acceptable load in the system. This paper presents how admission control mechanisms can be designed with a combination of queueing theory and control theory. In this paper we model an Apache web server as a GI/G/1-system and then design a PI-controller, commonly used in automatic control, for the server. The controller has been implemented as a module inside the Apache source code. Measurements from the laboratory setup show how robust the implemented controller is, and how it corresponds to the results from the theoretical analysis