About the cumulative idle time in multiphase queues
RAIRO - Operations Research - Recherche Opérationnelle, Volume 39 (2005) no. 2, pp. 75-85.

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).

DOI: 10.1051/ro:2005008
Keywords: queueing systems, multiphase queues, functional limit theorems, heavy traffic, a cumulative idle time of a customer
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Minkevičius, Saulius; Steišūnas, Stasys. About the cumulative idle time in multiphase queues. RAIRO - Operations Research - Recherche Opérationnelle, Volume 39 (2005) no. 2, pp. 75-85. doi : 10.1051/ro:2005008. http://archive.numdam.org/articles/10.1051/ro:2005008/

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