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Fluid Limit for Closed Queueing Network with Several Multi-servers

  • Svetlana AnulovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10684)

Abstract

A closed network consists of several multi-servers with n customers. Service requirements of customers at a multi-server have a common cdf. State parameters of the network: for each multi-server empirical measure of the age of customers being serviced and for the queues the numbers of customers in them, all multiplied by \(n^{-1}\).

Our objective: asymptotics of dynamics as \(n\rightarrow \infty \). The asymptotics of dynamics of a single multi-server and its queue with an arrival process as the number of servers \(n\rightarrow \infty \) is currently studied by famous scientists K. Ramanan, W. Whitt et al. Presently there are no universal results for general distributions of service requirements — the results are either for continuous or for discrete time ones; the same for the arrival process. We establish the asymptotics for a network in discrete time, find its equilibrium and prove convergence as \(t\rightarrow \infty \).

Motivation for studying such models: they represent call/contact centers and help to construct them effectively.

Keywords

Call/contact centers Queueing network Multi-server queues Measure-valued processes Fluid limit approximation Fluid limit equilibrium and convergence 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IPU RANMoscowRussian Federation

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