Fluid and heavy traffic diffusion limits for a generalized processor sharing model
type: Item
instance of: scholarly article
title: Fluid and heavy traffic diffusion limits for a generalized processor sharing model
zbMATH Open document ID: 1016.60083
author: Kavita Ramanan
author: Martin I. Reiman
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: The paper considers a single server queueing system with several customer classes. Each customer arriving into the system brings in a certain amount of work. The server processes the incoming work using a generalized processor sharing discipline. According to this discipline, any excess capacity is split among remaining customer classes in proportion to components of some weight vector. The paper contains fluid and heavy traffic limit theorems for unfinished work, queue length, sojourn time and waiting time processes.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1906141
zbMATH Keywords: single server queueing system
zbMATH Keywords: customer classes
zbMATH Keywords: generalized processor sharing discipline
zbMATH Keywords: unfinished work
zbMATH Keywords: queue length
zbMATH Keywords: sojourn time
zbMATH Keywords: waiting time processes
reviewed by: Oleg K. Zakusilo
MaRDI profile type: Publication
OpenAlex ID: W2101049248
cites work: Regulations dÉterminates et stochastiques dans le premier “orthant” de RN
cites work: Large deviations analysis of the generalized processor sharing policy
cites work: Stability of two families of queueing networks and a discussion of fluid limits
cites work: State space collapse with application to heavy traffic limits for multiclass queueing networks
cites work: Simple Necessary and Sufficient Conditions for the Stability of Constrained Processes
cites work: Stochastic discrete flow networks: Diffusion approximations and bottlenecks
cites work: On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
cites work: A Skorokhod problem formulation and large deviation analysis of a processor sharing model
cites work: Convex duality and the Skorokhod problem. I
cites work: Convex duality and the Skorokhod problem. II
cites work: A multiclass feedback queueing network with a regular Skorokhod problem
cites work: A time-reversed representation for the tail probabilities of stationary reflected Brownian motion.
cites work: A limit theorem for priority queues in heavy traffic
cites work: Reflected Brownian motion on an orthant
cites work: On the Invariance Principle for the First Passage Time
cites work: Reflected diffusions defined via the extended Skorokhod map
cites work: Open Queueing Networks in Heavy Traffic
cites work: A boundary property of semimartingale reflecting Brownian motions
cites work: Q5618806
cites work: Weak convergence theorems for priority queues: preemptive-resume discipline
cites work: Some Useful Functions for Functional Limit Theorems
cites work: Reflected brownian motion in a wedge: Semimartingale property
cites work: Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse
DOI: 10.1214/AOAP/1042765664
Recommended article: Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates
Recommended article: Diffusion limits of limited processor sharing queues
Recommended article: The heavy traffic limit of an unbalanced generalized processor sharing model
Recommended article: Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic
Recommended article: Heavy-traffic limits for discriminatory processor sharing models with joint batch arrivals
Recommended article: The fluid limit of a heavily loaded processor sharing queue
Recommended article: Steady state approximations of limited processor sharing queues in heavy traffic
description: scientific article; zbMATH DE number 1906141