Large deviations rate function for polling systems
type: Item
instance of: scholarly article
title: Large deviations rate function for polling systems
zbMATH Open document ID: 1053.60096
DOI: 10.1023/A:1015781417451
author: Franck Delcoigne
author: Arnaud de La Fortelle
published in: Queueing Systems
publication date: 2002-07-11T00:00:00Z
review text: A polling system with one server, Markovian routing and exponential service times and walkover times is considered. Let \(Q_t\) be the state vector of the system at time \(t\). A sample path large deviations principle is established for \(\{Q_{nt}/n\}_{t\geq 0}\) as \(n\to\infty\) and certain information on the form of the rate function is given. Key tools in the analysis are a so-called local generator, obtained by considering only subsets of the states and neglecting the positivity restrictions on the process, and fluid limits. The example of cyclic polling is considered and the connection to large deviations theory for Jackson networks is discussed.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1766381
zbMATH Keywords: large deviations
zbMATH Keywords: local rate function
zbMATH Keywords: polling system
zbMATH Keywords: fluid limits
zbMATH Keywords: empirical generator
zbMATH Keywords: change of measure
zbMATH Keywords: contraction principle
zbMATH Keywords: entropy
zbMATH Keywords: convex program
reviewed by: Søren Asmussen
MaRDI profile type: Publication
full work available at URL: a:1015781417451
OpenAlex ID: W1509372771
description: scientific article; zbMATH DE number 1766381