Fluid approximation and its convergence rate for GI/G/1 queue with vacations
type: Item
instance of: scholarly article
title: Fluid approximation and its convergence rate for GI/G/1 queue with vacations
zbMATH Open document ID: 1220.60052
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2011-03-14T00:00:00Z
review text: The author considers a GI/G/1 queue with vacations, where vacations take place after completing the service of all customers in the buffer. If during a vacation new customers enter, they are served after the end of vacation, if not, another vacation begins. In order to establish the fluid approximation and exponential convergence rate, the approach is to identify a simple lower bound and a simple upper bound and show that both bounds converge to the same limit after fluid scaling under some assumptions. A fluid model is developed for the queue length, the busy time and the workload process. The fluid approximation turns out to be the same as that for the GI/G/1 queue. Different from the rate of convergence for the GI/G/1 queue, the exponential rate of convergence for the GI/G/1 queue with vacations holds only for large \(N\).
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5865239
zbMATH Keywords: GI/G/1 queue with vacation
zbMATH Keywords: fluid approximation
zbMATH Keywords: exponential rate of convergence
author: Yong-Jiang Guo
reviewed by: László Lakatos
MaRDI profile type: Publication
full work available at URL: s10255-011-0038-1
OpenAlex ID: W2146687993
cites work: Analysis of multi-server queues with station and server vacations
cites work: Fluid approximations and stability of multiclass queueing networks: Work-conserving disciplines
cites work: Rate of convergence of the fluid approximation for generalized Jackson networks
cites work: Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic
cites work: Q2730382
cites work: On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
cites work: Q4239313
cites work: Queueing systems with vacations - a survey
cites work: Q3640400
cites work: Q3806523
cites work: Reflected Brownian motion on an orthant
cites work: Q3969670
cites work: Diffusion approximations for queues with server vacations
cites work: Open Queueing Networks in Heavy Traffic
cites work: Q3999697
cites work: Preservation of rates of convergence under mappings
cites work: On the three threshold policy in the multi-server queueing system with vacations
DOI: 10.1007/S10255-011-0038-1
description: scientific article; zbMATH DE number 5865239