Return Probabilities for Stochastic Fluid Flows

[1]  Beatrice Meini,et al.  Solving matrix polynomial equations arising in queueing problems , 2002 .

[2]  Chun-Hua Guo,et al.  Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices , 2001, SIAM J. Matrix Anal. Appl..

[3]  Dario Bini,et al.  On Cyclic Reduction Applied to a Class of Toeplitz-Like Matrices Arising in Queueing Problems , 1995 .

[4]  Nigel G. Bean,et al.  Hitting probabilities and hitting times for stochastic fluid flows , 2005 .

[5]  David Williams,et al.  A ‘potential-theoretic’ note on the quadratic Wiener-Hopf equation for Q-matrices , 1982 .

[6]  Wen-Wei Lin,et al.  Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations , 2006, SIAM J. Matrix Anal. Appl..

[7]  Beatrice Meini,et al.  Numerical methods for structured Markov chains , 2005 .

[8]  Guy Latouche,et al.  Risk processes analyzed as fluid queues , 2005 .

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

[10]  P. Taylor,et al.  ALGORITHMS FOR RETURN PROBABILITIES FOR STOCHASTIC FLUID FLOWS , 2005 .

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

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

[13]  Peter G. Taylor,et al.  Further results on the similarity between fluid queues and QBDs , 2002 .

[14]  V. Mehrmann.  A STEP TOWARD A UNIFIED TREATMENT OF CONTINUOUS AND DISCRETE TIME CONTROL PROBLEMS , 1996 .

[15]  Chun-Hua Guo,et al.  Convergence of the solution of a nonsymmetric matrix Riccati differential equation to its stable equilibrium solution , 2006 .

[16]  Noah H. Rhee,et al.  A Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems , 2002, SIAM J. Matrix Anal. Appl..

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

[18]  Gene H. Golub,et al.  On direct methods for solving Poisson's equation , 1970, Milestones in Matrix Computation.

[19]  Bruno Sericola,et al.  Distribution of busy period in stochastic fluid models , 2001 .

[20]  Wen-Wei Lin,et al.  A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation , 2006, Numerische Mathematik.

[21]  Chun-Hua Guo,et al.  Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models , 2006 .

[22]  Chun-Hua Guo.  Comments on a Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems , 2003, SIAM J. Matrix Anal. Appl..

[23]  Vidyadhar G. Kulkarni,et al.  STOCHASTIC DISCRETIZATION FOR THE LONG-RUN AVERAGE REWARD IN FLUID MODELS , 2003, Probability in the Engineering and Informational Sciences.

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

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

[26]  Beatrice Meini,et al.  On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems , 1996, SIAM J. Matrix Anal. Appl..

[27]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[28]  Alan J. Laub,et al.  On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations , 2000, SIAM J. Matrix Anal. Appl..

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

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

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

[32]  Richard S. Varga,et al.  Matrix Iterative Analysis , 2000, The Mathematical Gazette.

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

[34]  Dario Bini,et al.  On the solution of algebraic Riccati equations arising in fluid queues , 2006 .

[35]  Chun-Hua Guo,et al.  Convergence Analysis of the Latouche-Ramaswami Algorithm for Null Recurrent Quasi-Birth-Death Processes , 2001, SIAM J. Matrix Anal. Appl..

[36]  Hung-Yuan Fan,et al.  A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations , 2005 .

[37]  Guy Latouche,et al.  Fluid queues to solve jump processes , 2005, Perform. Evaluation.

[38]  L Bright,et al.  Equilibrium Distributions for Level-Dependent Quasi-Birth-and-Death Processes , 1996 .

[39]  R. Bhatia,et al.  How and Why to Solve the Operator Equation AX−XB = Y , 1997 .

[40]  G. Golub,et al.  A Hessenberg-Schur method for the problem AX + XB= C , 1979 .