Matrix-Analytic Methods – An Algorithmic Approach to Stochastic Modelling and Analysis

The field of matrix analytic methods (MAM) was pioneered by Dr. Marcel F. Neuts in the middle of the 1970s for the study of queueing models. In the past 40 years, the theory on MAM has been advanced in parallel with its applications significantly.

[1]  M. Neuts.  A Versatile Markovian Point Process , 1979 .

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[3]  W. Whitt,et al.  The transient BMAP/G/l queue , 1994 .

[4]  Qi-Ming He,et al.  Fundamentals of Matrix-Analytic Methods , 2013, Springer New York.

[5]  Tetsuya Takine,et al.  Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions , 2001, Queueing Syst. Theory Appl..

[6]  D. P. Kroese,et al.  Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process , 2003 .

[7]  Mogens Bladt,et al.  Renewal Theory and Queueing Algorithms for Matrix-Exponential Distributions , 1996 .

[8]  B. Sengupta.  Markov processes whose steady state distribution is matrix-exponential with an application to the GI/PH/1 queue , 1989, Advances in Applied Probability.

[9]  Li Xia,et al.  Optimal Control of State-Dependent Service Rates in a MAP/M/1 Queue , 2017, IEEE Transactions on Automatic Control.

[10]  Vaidyanathan Ramaswami,et al.  Introduction to Matrix Analytic Methods in Stochastic Modeling , 1999, ASA-SIAM Series on Statistics and Applied Mathematics.

[11]  V. Ramaswami.  The N/G/1 queue and its detailed analysis , 1980, Advances in Applied Probability.

[12]  Jing-Sheng Song,et al.  Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand , 2001, Oper. Res..

[13]  Peter Buchholz,et al.  Input Modeling with Phase-Type Distributions and Markov Models: Theory and Applications , 2014 .

[14]  Yiqiang Q. Zhao,et al.  The stationary tail asymptotics in the GI/G/1-type queue with countably many background states , 2004, Advances in Applied Probability.

[15]  G. Latouche,et al.  Analysis of fluid flow models. , 2018, 1802.04355.

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

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

[18]  Qi-Ming He,et al.  Queues with marked customers , 1996, Advances in Applied Probability.

[19]  Marcel F. Neuts,et al.  Markov chains with marked transitions , 1998 .

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

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

[22]  C. O'Cinneide.  Characterization of phase-type distributions , 1990 .

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

[24]  Latouche Guy,et al.  A note on two matrices occurring in the solution of quasi-birth-and-death processes , 1987 .

[25]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[26]  S. Asmussen,et al.  Marked point processes as limits of Markovian arrival streams , 1993 .

[27]  Ren Asmussen,et al.  Fitting Phase-type Distributions via the EM Algorithm , 1996 .