相关论文: Diffusion approximation for a processor sharing qu…

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…

We study Batch Processor-Sharing (BPS) queuing model with hyper-exponential service time distribution and Poisson batch arrival process. One of the main goals to study BPS is the possibility of its application in size-based scheduling,…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

In this paper we propose a highly accurate approximate performance analysis of a heterogeneous server system with a processor sharing service discipline and a general job-size distribution under a generalized join the shortest queue (GJSQ)…

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random…

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…

We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$, while jobs arrive to a dispatcher at rate $n^2-(a-b)\sqrt{n}$, with fixed $a>b>0$. Arrivals are routed by a marginal join-the-shortest-queue…

Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…

Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

We consider a connection-level model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here,…

Allocation of (redundant) file chunks throughout a distributed storage system affects important performance metrics such as the probability of file recovery, data download time, or the service rate of the system under a given data access…

We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…

We investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering…

We consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the…

We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After…

Till today we dreamt of imperceptible delay in a network. The computer science research grows today faster than ever offering more and more services (computational representational, graphical, intelligent implication etc) to its user. But…

Future Internet will be composed by a tremendous number of potentially interconnected people and devices, offering a variety of services, applications and communication opportunities. In particular, short-range wireless communications,…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…