Abstract
A new queueing model is proposed, namely the \(MM\,\sum_{k=1}^{K}{CPP_k}/GE/c/L\,G\)-Queue, also known as the Sigma queue. A steady state solution for this queue in a computable form is presented, based on an analytic methodology applying certain non-trivial transformations on the balance equations, which turn out to be of the QBD-M (Quasi Simultaneous-Multiple-Bounded Births and Deaths) type. As a consequence, existing methods such as the spectral expansion method or the matrix-geometric method can be used to obtain the steady state probabilities. The utility of this queue is demonstrated through the performance analysis of an optical burst switching (OBS) node. Numerical results show the impact of the burstiness of arrival process on the performance of the OBS multiplexer.
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Chakka, R., Van Do, T. (2011). Some New Markovian Models for Traffic and Performance Evaluation of Telecommunication Networks. In: Kouvatsos, D.D. (eds) Network Performance Engineering. Lecture Notes in Computer Science, vol 5233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02742-0_27
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DOI: https://doi.org/10.1007/978-3-642-02742-0_27
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