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We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or points) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.)…

Probability · Mathematics 2017-05-24 Harsha Honnappa

In this paper we present results for bivariate exponential distributions which are represented by phase type distributions. The paper extends results from previous publications [5, 14] on this topic by introducing new representations that…

Performance · Computer Science 2021-08-30 Peter Buchholz

When an explicit expression for a probability distribution function $F(x)$ can not be found, asymptotic properties of the tail probability function $\bar{F}(x)=1-F(x)$ are very valuable, since they provide approximations or bounds for…

Probability · Mathematics 2019-04-16 Bin Liu , Yiqiang Q. Zhao

A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…

Probability · Mathematics 2014-01-17 Yunan Liu , Ward Whitt

We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…

Probability · Mathematics 2018-10-01 H. Christian Gromoll , Bryce Terwilliger , Bert Zwart

In this paper, we present a kernel-based, multi-task Gaussian Process (GP) model for approximating the underlying function of an individual's mobility state using a time-inhomogeneous Markov Process with two states: moves and pauses. Our…

Machine Learning · Statistics 2023-06-22 Ekin Ugurel

Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the busy period of an M/M/1 queue of a small perturbation in the…

Networking and Internet Architecture · Computer Science 2007-08-13 Nelson Antunes , Christine Fricker , Fabrice Guillemin , Philippe Robert

We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…

Computation · Statistics 2020-07-31 Mauricio Nascimento , Benjamin A. Shaby

We study the power spectral density of continuous time Markov chains and explicit its relationship with the eigenstructure of the infinitesimal generator. This result helps us understand the dynamics of the number of customers for a M/M/1…

Probability · Mathematics 2023-10-24 Thomas Vanderbruggen

In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…

Probability · Mathematics 2016-09-08 Young Myoung Ko , Natarajan Gautam

Multi-server queueing systems describe situations in which users require service from multiple parallel servers. Examples include check-in lines at airports, waiting rooms in hospitals, queues in contact centers, data buffers in wireless…

Probability · Mathematics 2019-07-30 Johan S. H. van Leeuwaarden , Britt W. J. Mathijsen , Bert Zwart

The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…

Probability · Mathematics 2010-06-15 Jose Blanchet , Jingchen Liu

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

Statistics Theory · Mathematics 2023-05-24 Kangqiang Li , Yuxuan Wang

Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing…

Probability · Mathematics 2023-01-13 U. C. Gupta , Nitin Kumar , S. Pradhan , F. P. Barbhuiya

We study the so-called pinning model, which describes the behavior of a Markov chain interacting with a distinguished state. The interaction depends on an external source of randomness, called disorder, which can attract or repel the Markov…

Probability · Mathematics 2023-02-27 Niccolo Torri

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…

Data Analysis, Statistics and Probability · Physics 2015-06-11 E. L de Santa Helena , C. M. Nascimento , G. J. L. Gerhardt

This work studies the problem of constructing a representative workload from a given input analytical query workload where the former serves as an approximation with guarantees of the latter. We discuss our work in the context of workload…

Databases · Computer Science 2021-02-04 Shaleen Deep , Anja Gruenheid , Paraschos Koutris , Jeffrey Naughton , Stratis Viglas

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of…

Statistical Mechanics · Physics 2013-05-29 Ph. Blanchard , M. -O. Hongler

We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators…

Statistics Theory · Mathematics 2018-09-25 Rafal Kulik , Philippe Soulier , Olivier Wintenberger , Rafa Kulik

We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…

Probability · Mathematics 2026-05-21 Shubhada Agrawal , Siva Theja Maguluri , Martin Zubeldia