Matrix-analytic methods for fluid queues with finite buffers
Performance Evaluation
Matrix-geometric algorithms for stochastic fluid flows
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Matrix-geometric algorithms for stochastic fluid flows
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier
Queueing Systems: Theory and Applications
Hitting probabilities and hitting times for stochastic fluid flows: The bounded model
Probability in the Engineering and Informational Sciences
Short communication: Uniqueness of asymptotic solution for general Markov fluid models
Performance Evaluation
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The Markov modulated fluid model with finite buffer of size β is analyzed using a stochastic discretization yielding a sequence of finite waiting room queueing models with iid amounts of work distributed as exp (n驴). The n-th approximating queue's system size is bounded at a value qn such that the corresponding expected amount of work qn/(n驴) 驴 β as n 驴 驴. We demonstrate that as n 驴 驴, 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.