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Multi-channel Queueing Networks with Input Flow Controlled by Semi-Markov Process

Multi-channel Queueing Networks with Input Flow Controlled by Semi-Markov Process In this paper asymptotic behavior of the service process for the multi-channel network with input flow controlled by semi-Markov process is studied. Conditions in which a stationary regime exists are pointed out. Integral representation for generating function of the stationary distribution is constructed. In case of exponentially distributed service times limit Gaussian and diffusion Ornstein–Uhlenbeck processes for normalized service process of network processing under heavy traffic conditions are obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

Multi-channel Queueing Networks with Input Flow Controlled by Semi-Markov Process

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Mathematics, general; Computer Science, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-019-00398-4
Publisher site
See Article on Publisher Site

Abstract

In this paper asymptotic behavior of the service process for the multi-channel network with input flow controlled by semi-Markov process is studied. Conditions in which a stationary regime exists are pointed out. Integral representation for generating function of the stationary distribution is constructed. In case of exponentially distributed service times limit Gaussian and diffusion Ornstein–Uhlenbeck processes for normalized service process of network processing under heavy traffic conditions are obtained.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Jul 4, 2019

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