Transient Analysis of Fluid Models via Elementary Level-Crossing Arguments

An analysis of the time-dependent evolution of the canonical Markov modulated fluid flow model is presented using elementary level-crossing arguments.

[1]  Vaidyanathan Ramaswami,et al.  Steady State Analysis of Finite Fluid Flow Models Using Finite QBDs , 2005, Queueing Syst. Theory Appl..

[2]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[3]  V. Ramaswami,et al.  Efficient algorithms for transient analysis of stochastic fluid flow models , 2005, Journal of Applied Probability.

[4]  The Radon-Nikodym Theorem as a Theorem in Probability , 1978 .

[5]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[6]  L. Rogers.  Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains , 1994 .

[7]  K. Athreya,et al.  A New Approach to the Limit Theory of Recurrent Markov Chains , 1978 .

[8]  Vaidyanathan Ramaswami,et al.  Transient Analysis of Fluid Flow Models via Stochastic Coupling to a Queue , 2004 .

[9]  L. Breuer.  Introduction to Stochastic Processes , 2022, Statistical Methods for Climate Scientists.

[10]  W. R. Scheinhardt,et al.  Markov-modulated and feedback fluid queues , 1998 .

[11]  Ivo J. B. F. Adan,et al.  A two-level traffic shaper for an on-off source , 2000, Perform. Evaluation.

[12]  Vaidyanathan Ramaswami,et al.  Passage Times in Fluid Models with Application to Risk Processes , 2006 .

[13]  Vaidyanathan Ramaswami,et al.  Fluid Flow Models and Queues—A Connection by Stochastic Coupling , 2003 .

[14]  Vaidyanathan Ramaswami,et al.  A logarithmic reduction algorithm for quasi-birth-death processes , 1993, Journal of Applied Probability.

[15]  Vaidyanathan Ramaswami,et al.  Matrix analytic methods for stochastic fluid flows , 1999 .

[16]  S. Asmussen.  BUSY PERIOD ANALYSIS, RARE EVENTS AND TRANSIENT BEHAVIOR IN FLUID FLOW MODELS , 1994 .

[17]  S. Asmussen.  Stationary distributions for fluid flow models with or without Brownian noise , 1995 .

[18]  Tom Burr,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 2001, Technometrics.

[19]  Guy Latouche,et al.  Matrix-analytic methods for fluid queues with finite buffers , 2006, Perform. Evaluation.

[20]  S. Karlin,et al.  A second course in stochastic processes , 1981 .

[21]  Bruno Sericola,et al.  Transient Analysis of Stochastic Fluid Models , 1998, Perform. Evaluation.