Related papers: Tail Bounds for Queues with Abandonment: Constant,…
An information measure based on fractional partitions of a set is used to derive a general dependence balance inequality for communication. This inequality is used to obtain new upper bounds on reliable and secret rates for multiterminal…
Rare events, and more general risk-sensitive quantities-of-interest (QoIs), are significantly impacted by uncertainty in the tail behavior of a distribution. Uncertainty in the tail can take many different forms, each of which leads to a…
We use an Ornstein--Uhlenbeck (OU) process to approximate the queue length process in a $GI/GI/n+M$ queue. This one-dimensional diffusion model is able to produce accurate performance estimates in two overloaded regimes: In the first…
In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…
This paper studies the interpretability of neural network features from a Bayesian Gaussian view, where optimizing a cost is reaching a probabilistic bound; learning a model approximates a density that makes the bound tight and the cost…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
We investigate the tail behaviour of the steady state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queuing systems with dependent interarrival and service times, and includes…
Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…
A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival and service time distributions. We address this extremal queue problem by…
We consider the problem of high-dimensional heavy-tailed statistical estimation in the streaming setting, which is much harder than the traditional batch setting due to memory constraints. We cast this problem as stochastic convex…
We address the problem of finite-horizon control of a discrete-time linear system, where the initial state distribution follows a Gaussian mixture model, the terminal state must follow a specified Gaussian distribution, and the state and…
This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…
We simulate queues of activity in a directed sandpile automaton in 1+1 dimensions by adding grains at the top row with driving rate $0 < r \leq 1$. The duration of elementary avalanches is exactly described by the distribution $P_1(t) \sim…
We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions charac- terizing the stochastic properties of the passenger queue length,…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
Metro systems in megacities such as Beijing, Shenzhen and Guangzhou are under great passenger demand pressure. During peak hours, it is common to see oversaturated conditions (i.e., passenger demand exceeds network capacity), which bring…
This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergence rate are developed in both total variation and Wasserstein…