Related papers: Tail Asymptotics for Discrete Event Systems

This short communication considers an infinite-server system with overdispersed input. The objective is to identify the exact tail asymptotics of the number of customers present at a given point in time under a specific scaling of the model…

The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic…

One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…

In this paper, we consider a discrete-time preemptive priority queue with different service rates for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive…

We study the asymptotic response time tail in the M/G/n multi-server queue with heavy-tailed (regularly varying) job sizes, a setting representative of modern computing workloads. For single-server systems, tail optimization is well…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…

We provide the exact large-time behavior of the tail distribution of the extinction time of a self-similar fragmentation process with a negative index of self-similarity, improving thus a previous result on the logarithmic asymptotic…

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positive associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of…

Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…

Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions amongst nodes. We…

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single…

We study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless)…

Just like the degrees of human and animal interaction networks, the distribution of the times between interactions is known to often be right-skewed and fat-tailed. Both these distributions affect epidemic dynamics strongly, but, as we show…

Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…

We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial $M/G/1$-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and…

A telegraph process with an elastic barrier at the origin was studied in [5]; in particular the number of visits of the origin before the absorption is a geometric distributed random variable M. Some asymptotic results (large and moderate…

In the performance analyses of wireless networks, asymptotic quantities and properties often pro- vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance…