Related papers: Exact tail asymptotics for fluid models driven by …
In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
The MGT fluid model has been used extensively to guide designs of AQM schemes aiming to alleviate adverse effects of Internet congestion. In this paper, we provide a new analysis of a TCP/AQM system that aims to improve the accuracy of the…
In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The…
Using a result of Blanchet and Wallwater (2015: Exact sampling of stationary and time-reversed queues. ACM TOMACS, 25, 26) for exactly simulating the maximum of a negative drift random walk queue endowed with independent and identically…
We determine the statistical properties of wave functions in disordered quantum systems by exact diagonalization of one-, two- and quasi-one dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we find that the tails of…
Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(\xi_n:n\geq 0)$ to produce the process $(S_n+\xi_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum…
The long-time behaviors of the velocity autocorrelation function $C(t)$ for sheared fluids ^M are investigated theoretically and numerically. It is found the existence of the cross-overs of^M $C(t)$ from $t^{-d/2}$ to $t^{-d}$ ^M in sheared…
Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes,…
A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), $\{{\boldsymbol{Y}}_n\}=\{(X_{1,n},X_{2,n},J_n)\}$, is a two-dimensional skip-free random walk $\{(X_{1,n},X_{2,n})\}$ on $\mathbb{Z}_+^2$ with a supplemental…
We study a heavily overloaded single-server queue with abandonment and derive bounds on stationary tail probabilities of the queue length. As the abandonment rate $\gamma \downarrow 0$, the centered-scaled queue length $\tilde{q}$ is known…
We investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct, where X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic processes. We assume that the process Y has subexponential characteristics and that the process…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage…
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
A fluid queue is a stochastic process which moves linearly with a rate that is determined by the state of a continuous-time Markov chain (CTMC). In this paper we construct an approximation to a fluid queue using a quasi birth-and-death…
We introduce the \textit{generalized join the shortest queue model with retrials} and two infinite capacity orbit queues. Three independent Poisson streams of jobs, namely a \textit{smart}, and two \textit{dedicated} streams, flow into a…
We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…
Self-similarity, a fractal characteristic of traffic flow dynamics, is widely recognized in transportation engineering and physics. However, its practical application in real-world traffic scenarios remains limited. Conversely, the traffic…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…