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Asymptotic Behavior of a M/G/1 Queueing Model with a Single Vacation and Finite Number of Customers

Volume 3, Number 2 (2012), 45 - 59

Asymptotic Behavior of a M/G/1 Queueing Model with a Single Vacation and Finite Number of Customers

Communicated By: 
Enrique Zuazua
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Abstract

Our aim is the study of the asymptotic behavior of a time-dependent M/G/1 queueing model with a single vacation and finite number of customers. For this purpose we prove first that its well posedness can be characterized via an operator being the generator of an irreducible C0- semigroup. We investigate the long term behavior of the system via the spectrum of this generator using techniques from irreducible matrices and spectral theory of positive semigroups.