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Steady state analysis of finite fluid flow models using finite QBDs. (English) Zbl 1080.90023
Summary: The Markov modulated fluid model with finite buffer of size \(\beta\) is analyzed using a stochastic discretization yielding a sequence of finite waiting room queueing models with iid amounts of work distributed as \(\exp(n \lambda)\). The \(n\)-th approximating queue’s system size is bounded at a value \(q_{n}\) such that the corresponding expected amount of work \(q_{n}/(n \lambda) \rightarrow \beta\) as \(n \rightarrow \infty\). We demonstrate that as \(n \rightarrow \infty\), we obtain the exact performance results for the finite buffer fluid model from the processes of work in the system for these queues. The necessary (strong) limit theorems are proven for both transient and steady state results. Algorithms for steady state results are developed fully and illustrated with numerical examples.

MSC:
90B22 Queues and service in operations research
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