Related papers: Tail Probabilities in Queueing Processes

Stochastic network calculus is a tool for computing error bounds on the performance of queueing systems. However, deriving accurate bounds for networks consisting of several queues or subject to non-independent traffic inputs is…

Use-case-specific network slicing in decentralized multi-tenancy cloud environments is a promising approach to bridge the gap between the demand and supply of resources in next-generation communication networks. Our findings associate…

In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…

Large language models (LLMs) propel the prosperity of interactive AI applications showcased by ChatGPT that demand timely response of inference services. However, LLM inference is computation intensive and memory intensive, and improper…

To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

Low-latency communication has recently attracted considerable attention owing to its potential of enabling delay-sensitive services in next-generation industrial cyber-physical systems. To achieve target average or maximum delay given…

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…

In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly…

Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…

In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of…

Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the…

Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models. The Markovian models include M/M/$\infty$, M/M/r and M/M/1+M queues with random resetting, in which a continuous-time Markov…

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and…

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…

A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…

The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…

Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…