Fluid Flow Models and Queues—A Connection by Stochastic Coupling

Abstract

Abstract We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death processes in the matrix-geometric approach of Ramaswami and subsequent results based on them obtained by Soares and Latouche. Keywords: Fluid flowsQueuesStochastic couplingMatrix geometric method Acknowledgment The authors thank Ward Whitt for many helpful discussions, and Benny VanHoudt for identifying several typos in an earlier version. Soohan Ahn was supported (partially) by the Post-Doctoral Fellowship Program of Korea Science & Engineering Foundation (KOSEF).