Interacting queues in heavy traffic
type: Item
instance of: scholarly article
title: Interacting queues in heavy traffic
zbMATH Open document ID: 1203.90053
author: John A. Morrison
author: Sem Borst
published in: Queueing Systems
publication date: 2010-06-11T00:00:00Z
review text: The authors consider a system of parallel queues with Poisson arrivals and exponentially distributed service requirements. The various queues are coupled through their service rates, causing a complex dynamic interaction. Specifically, the system consists of one primary queue and several secondary queues whose service rates depend on whether the primary queue is empty or not. Conversely, the service rate of the primary queue depends on which of the secondary queues are empty. An important special case arises when the service rates satisfy a specific relationship so that the various queues form a work-conserving system. This case is, in fact, equivalent to a so-called Generalized Processor Sharing (GPS) system. GPS-based scheduling algorithms have emerged as popular mechanisms for achieving service differentiation while providing statistical multiplexing gains. They consider a heavy-traffic scenario, and assume that each of the secondary queues is underloaded when the primary queue is busy. Using a perturbation procedure, they derive the lowest-order asymptotic approximation to the joint stationary distribution of the queue lengths, in terms of a small positive parameter measuring the closeness of the system to instability. Heuristic derivations of these results are presented. They also treat two extensions: (i) the more general work-conserving case where the service rate of a secondary queue may depend on its own length, and is a slowly varying function of the length of the primary queue; and (ii) the non-work-conserving case where the service rate of a secondary queue may depend on its own length, but not on the length of the primary queue. In my opinion it is a high quality paper.
reviewed by: János Sztrik
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5719906
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: bandwidth sharing
zbMATH Keywords: coupled processors
zbMATH Keywords: first-order approximation
zbMATH Keywords: heavy traffic
zbMATH Keywords: generalized processor sharing
zbMATH Keywords: perturbation
zbMATH Keywords: state-dependent service rates
zbMATH Keywords: time scale decomposition
MaRDI profile type: Publication
full work available at URL: s11134-010-9174-1
OpenAlex ID: W2126260018
cites work: Large deviations analysis of the generalized processor sharing policy
cites work: Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows
cites work: The asymptotic workload behavior of two coupled queues
cites work: Generalized processor sharing queues with heterogeneous traffic classes
cites work: Q3662408
cites work: On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
cites work: Two coupled processors: The reduction to a Riemann-Hilbert problem
cites work: Analysis of the fluid weighted fair queueing system
cites work: Analysis of generalized processor-sharing systems with two classes of customers and exponential services
cites work: Heavy traffic analysis of two coupled processors
cites work: Processor-sharing of two parallel lines
cites work: Diffusion Approximation for Head-of-the-Line Processor Sharing for Two Parallel Queues
cites work: Fluid and heavy traffic diffusion limits for a generalized processor sharing model
cites work: The heavy traffic limit of an unbalanced generalized processor sharing model
cites work: Large deviations and the generalized processor sharing scheduling for a multiple-queue system
DOI: 10.1007/S11134-010-9174-1
description: scientific article; zbMATH DE number 5719906