Related papers: Exact results for the Barabasi queuing model
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting…
Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…
In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…
Designing distributed systems to have predictable performance under high load is difficult because of resource exhaustion, non-linearity, and stochastic behaviour. Timeliness, i.e., delivering results within defined time bounds, is a…
A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…
We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…
Following up on Barabasi's recent letter to Nature [435, 207--211 (2005)], we systematically investigate the time series of e-mail usage for 3,188 users at a university. We focus on two quantities for each user: the time interval between…
Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in…
This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to…
A recent paper "Emergence of scaling in random networks" (cond-mat/9910332) by Barabasi and Albert proposes a growth mechanism to produce a stationary scale free distribution of the number of edges per node in large networks such as the…