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Fluid limits of string valued Markov processes. (English) Zbl 1015.60088
Authors’ abstract: The stability properties of the bandwidth allocation algorithm first fit are analyzed for the distributions concentrated on three sizes for the request. We give the explicit expression of the ergodicity condition of this model; it involves a quadratic functional of the input parameters. The stochastic processes describing these systems are string valued Markov processes. The notion of a smooth random state is introduced. Starting from a smooth random state the fluid limits of the process can be investigated. The fluid limits of interest are random dynamical systems in \(\mathbb{R}^2\) which are products of random \(2\times 2\) matrices.

60K25 Queueing theory (aspects of probability theory)
60J27 Continuous-time Markov processes on discrete state spaces
90B22 Queues and service in operations research
60J75 Jump processes (MSC2010)
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