Multiple-input heavy-traffic real-time queues.
type: Item
instance of: scholarly article
title: Multiple-input heavy-traffic real-time queues.
zbMATH Open document ID: 1046.60082
author: Steven Shreve
author: Shu-Ngai Yeung
author: Łukasz Kruk
author: John P. Lehoczky
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: Customers with random service times and random due dates from \(K\) renewal streams arrive at their own buffer at a single server. The server serves the buffers which are nonempty according to a generalized processor sharing discipline (head-of-the-line with weights). The buffers are either FIFO or EDF (earliest deadline first). Service times, interarrival times and due dates are stream specific characterized by two moments with the usual independence assumptions. To describe the detailed state of the system a lead time profile for the system is introduced which describes for all customers present their time until dead line. Constructing the usual processes to describe the queueing and workload behaviour over the streams a sequence of rescaled systems with their associated processes under diffusion scaling for heavy traffic is investigated. For this sequence the heavy traffic limit is determined.
reviewed by: Hans Daduna
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1906142
zbMATH Keywords: generalized processor sharing
zbMATH Keywords: heavy traffic
zbMATH Keywords: diffusion limit
zbMATH Keywords: random measures
zbMATH Keywords: due dates
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1042765663
OpenAlex ID: W2024292188
cites work: Q3794956
cites work: Q4269108
cites work: State space collapse with application to heavy traffic limits for multiclass queueing networks
cites work: Stability, queue length, and delay of deterministic and stochastic queueing networks
cites work: Polling systems with zero switchover times: A heavy-traffic averaging principle
cites work: A calculus for network delay. I. Network elements in isolation
cites work: Real-time queues in heavy traffic with earliest-deadline-first queue discipline
cites work: Multiple channel queues in heavy traffic. I
cites work: Q3240992
cites work: Q3334756
cites work: Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse
DOI: 10.1214/AOAP/1042765663
description: scientific article; zbMATH DE number 1906142