Open Access
August 2002 Fluid limits of string valued Markov processes
Jean-François Dantzer, Philippe Robert
Ann. Appl. Probab. 12(3): 860-889 (August 2002). DOI: 10.1214/aoap/1031863172


The stability properties of the bandwidth allocation algorithm first fit are analyzed for the distributions concentrated on three sizes for the requests. 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 $2\times2$ matrices.


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Jean-François Dantzer. Philippe Robert. "Fluid limits of string valued Markov processes." Ann. Appl. Probab. 12 (3) 860 - 889, August 2002.


Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1015.60088
MathSciNet: MR1925443
Digital Object Identifier: 10.1214/aoap/1031863172

Primary: 60K25 , 90B12
Secondary: 60J75 , 90B22

Keywords: bandwidth allocation , Bin packing algorithms , dynamic bin-packing , ergodicity , fluid limits , multiclass queuing systems

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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