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We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…

Probability · Mathematics 2020-09-01 Martin Zubeldia , Michel Mandjes

We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…

Probability · Mathematics 2026-03-20 Nicos Georgiou , Enrico Scalas , Vladislav Vysotsky

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…

Probability · Mathematics 2025-12-09 A. V. Logachov , O. M. Logachova , A. A. Yambartsev , K. A. Zaykov

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

Probability · Mathematics 2022-10-19 Christian Hirsch , Takashi Owada

In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of $D$ queues, in a system of $N$ queues; after completion of service at its queue, a job leaves the network. We also…

Probability · Mathematics 2013-09-10 Maury Bramson , Yi Lu , Balaji Prabhakar

We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…

Probability · Mathematics 2014-12-09 Harsha Honnappa , Rahul Jain , Amy R. Ward

We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…

Probability · Mathematics 2017-01-19 Patrick Eschenfeldt , David Gamarnik

This paper studies a single server queue in heavy traffic, with general inter-arrival and service time distributions, where arrival and service rates vary discontinuously as a function of the (diffusively scaled) queue length. It is proved…

Probability · Mathematics 2025-12-18 Rami Atar , Masakiyo Miyazawa

This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process,…

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

In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and…

Probability · Mathematics 2009-02-27 Vijay G. Subramanian , Tara Javidi , Somsak Kittipiyakul

It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such…

Probability · Mathematics 2017-01-30 Harald Bernhard , Bikramjit Das

Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…

Probability · Mathematics 2008-08-22 Rami Atar

A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…

Statistics Theory · Mathematics 2010-02-24 Amarjit Budhiraja , Paul Dupuis , Vasileios Maroulas

The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…

Probability · Mathematics 2025-02-05 Henrik Hult , Adam Lindhe , Pierre Nyquist , Guo-Jhen Wu

We study a double-ended queue which consists of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system immediately. The matching follows first-come-first-serve principle. If…

Probability · Mathematics 2016-07-18 Xin Liu

A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…

Probability · Mathematics 2012-04-30 Weining Kang , Kavita Ramanan

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2022-11-03 Zachary Bezemek , Konstantinos Spiliopoulos

This paper considers the Cram\'er-Lundberg model, with the additional feature that the number of clients can fluctuate over time. Clients arrive according to a Poisson process, where the times they spend in the system form a sequence of…

Probability · Mathematics 2023-05-25 Peter Braunsteins , Michel Mandjes

We derive a large deviation principle for the space-time evolution of users in a relay network that are unable to connect due to capacity constraints. The users are distributed according to a Poisson point process with increasing intensity…

Probability · Mathematics 2017-12-12 Christian Hirsch , Benedikt Jahnel

We consider real-valued branching random walks and prove a large deviation result for the position of the rightmost particle. The position of the rightmost particle is the maximum of a collection of a random number of dependent random…

Probability · Mathematics 2019-06-27 Nina Gantert , Thomas Höfelsauer