Multiple-Input Heavy-Traffic Real-Time Queues

A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered-earliest deadline first and first-...

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Bibliographic Details
Published in:The Annals of applied probability 2003, Vol.13 (1), p.54-99
Main Authors: Kruk, Lukasz, Lehoczky, John, Shreve, Steven, Yeung, Shu-Ngai
Format: Article
Language:English
Subjects:
60G57
60J65
60K25
Brownian motion
Cumulative distribution functions
Deadlines
diffusion limits
Due dates
heavy traffic
Idleness
Perceptron convergence procedure
queueing
Queueing networks
random measures
Scheduling
Topological theorems
Traffic
Workloads
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Summary:A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered-earliest deadline first and first-in, first-out. The set of current lead times of the K streams is modeled as a K-dimensional vector of random counting measures on R, and the limit of this vector of measure-valued processes is obtained under heavy traffic conditions.
ISSN:1050-5164
2168-8737
DOI:10.1214/aoap/1042765663