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About the cumulative idle time in multiphase queues

Published online by Cambridge University Press:  15 October 2005

Saulius Minkevičius  and
Stasys Steišūnas
Saulius Minkevičius
Affiliation:
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. [email protected]
Stasys Steišūnas
Affiliation:
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. [email protected]
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Abstract

The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). Also we note that multiphase queueing systems can be useful for modelling practical multi-stage service systems in a variety of disciplines, especially on manufacturing (assembly lines), computer networking (packet switch structures), and in telecommunications (e.g. cellular mobile networks), etc. This research presents heavy traffic limit theorems for the cumulative idle time in multiphase queues. In this work, functional limit theorems are proved for the values of important probability characteristics of the queueing system (a cumulative idle time of a customer).

Keywords

Queueing systemsmultiphase queuesfunctional limit theoremsheavy traffica cumulative idle time of a customer.
Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 2 , April 2005 , pp. 75 - 85
Copyright
© EDP Sciences, 2005

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