相关论文: Doubly Exponential Solution for Randomized Load Ba…

This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on $\mathbb Z^d$ converges exponentially fast to its stationary distribution in $L^2$. Specifically, we provide general…

The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…

The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service…

We propose and compare new global solution algorithms for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the agent distribution so that equilibrium in the economy can be characterized by a high,…

For two-component load-sharing systems, a doubly-flexible model is developed where the generalized Fruend bivariate (GFB) distribution is used for the baseline of the component lifetimes, and the generalized gamma (GG) family of…

This paper studies the exponential stability of random matrix products driven by a general (possibly unbounded) state space Markov chain. It is a cornerstone in the analysis of stochastic algorithms in machine learning (e.g. for parameter…

In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\lambda n$, where $\lambda = \lambda (n) \in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers…

We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait…

In this work, we study a generalized Fisher market model that incorporates social influence. In this extended model, a buyer's utility depends not only on their own resource allocation but also on the allocations received by their…

We consider the supermarket model in the usual Markovian setting where jobs arrive at rate $n \lambda_n$ for some $\lambda_n > 0$, with $n$ parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest…

We consider two models of two-units repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using…

In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic…

We present a generalized hypercube queueing model extending Larson's (1974) framework to overlapping service regions such as police beats. Traditional hypercube models effectively capture light-traffic systems by tracking each server's busy…

We consider the Markovian supermarket model with growing choices, where jobs arrive at rate $n\lambda_n$ and each of $n$ parallel servers processes jobs in its queue at rate $1$. Each incoming job joins the shortest among $d_n \in…

The dynamic vehicle dispatching problem corresponds to deciding which vehicles to assign to requests that arise stochastically over time and space. It emerges in diverse areas, such as in the assignment of trucks to loads to be transported;…

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or…

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…

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…

Assortment optimization is an important problem that arises in many industries such as retailing and online advertising where the goal is to find a subset of products from a universe of substitutable products which maximize seller's…

Epoch-wise double descent is the phenomenon where generalisation performance improves beyond the point of overfitting, resulting in a generalisation curve exhibiting two descents under the course of learning. Understanding the mechanisms…