Optimal Rate for a Queueing System in Heavy Traffic with Superimposed On-Off Arrivals

A rate control problem is addressed for a queueing system in heavy traffic. The arrival process is a stationary heavy-tailed On-Off process and service is done at a constant rate (controlled). With an infinite horizon discounted cost function, the main result shows the existence of an optimal rate a...

Full description

Saved in:
Bibliographic Details
Published inStochastic models Vol. 29; no. 4; pp. 497 - 517
Main Author Ghosh, Arka P.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 02.10.2013
Taylor & Francis Ltd
Subjects
Controlled queueing networks
Fractional Brownian control problem
Fractional Brownian motion
Heavy traffic analysis
On-Off process
Primary 60K25, 68M20, 90B22
Queuing theory
Secondary 60G22, 90B18
Self-similarity
Stochastic control
Stochastic models
Online AccessGet full text

Cover

More Information
Summary:A rate control problem is addressed for a queueing system in heavy traffic. The arrival process is a stationary heavy-tailed On-Off process and service is done at a constant rate (controlled). With an infinite horizon discounted cost function, the main result shows the existence of an optimal rate and specifies a bound on this optimal rate. As a part of the analysis, we solve an approximating control problem driven by fractional Brownian motion. We also derive an asymptotic maximal bound on the second moment of the centered On-Off process, which is a key ingredient of the proof and is of independent interest.
ISSN:1532-6349
1532-4214
DOI:10.1080/15326349.2013.840144