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Matrix-analytic methods for fluid queues with finite buffers
Performance Evaluation, 2006 The application of matrix-analytic methods to the resolution of fluid queues has shown a close connection to discrete-state quasi-birth-and-death (QBD) processes. We further explore this similarity and analyze a fluid queue with finite buffer. We show, using a renewal approach, that the stationary distribution is expressed as a linear combination of ...
Guy Latouche
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SpringerBriefs in Mathematics, 2012
Matrix-analytic methods are geared toward MCs having state spaces that can be partitioned into subsets called levels. The transition matrices of such MCs, when symmetrically permuted according to increasing level number, should also have a particular nonzero structure, such as block tridiagonal or block Hessenberg.
Tugrul Dayar, Dayar Tugrul
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Matrix-analytic methods are geared toward MCs having state spaces that can be partitioned into subsets called levels. The transition matrices of such MCs, when symmetrically permuted according to increasing level number, should also have a particular nonzero structure, such as block tridiagonal or block Hessenberg.
Tugrul Dayar, Dayar Tugrul
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Matrix-Analytic Methods in Stochastic Models
Springer Proceedings in Mathematics and Statistics, 2013Factorization properties for a MAP-modulated fluid flow model under server vacation policies.- A compressed cyclic reduction for QBDs with low rank upper and lower transitions.- Bilateral matrix-exponential distribution.- AutoCAT: Automated Product-Form Solution of Stochastic Models.- Markovian trees subject to catastrophes: Would they survive forever?.
Latouche, Guy +5 more
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Discrete time queues and matrix-analytic methods
Top, 2002This is an expository paper dealing with discrete time analysis of queues using matrix-analytic methods (MAM). Discrete time analysis queues has always been popular with engineers who are very keen on obtaining numerical values out of their analyses for the sake of experimentation and design.
Attahiru S Alfa, Alfa Attahiru Sule
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Introduction to Matrix‐Analytic Methods in Queues 1
, 2022 Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since.In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and
Chakravarthy, Srinivas
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2000
This chapter shows how to find the equilibrium probabilities in processes of GI/M/1 type, and M/G/1 type, and GI/G/1 type by matrix analytic methods. GI/M/1-type processes are Markov chains with transition matrices having the same structure as the imbedded Markov chain of a GI/M/1 queue, except that the entries are matrices rather than scalars ...
Winfried K. Grassmann, David A. Stanford
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This chapter shows how to find the equilibrium probabilities in processes of GI/M/1 type, and M/G/1 type, and GI/G/1 type by matrix analytic methods. GI/M/1-type processes are Markov chains with transition matrices having the same structure as the imbedded Markov chain of a GI/M/1 queue, except that the entries are matrices rather than scalars ...
Winfried K. Grassmann, David A. Stanford
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The use of non-linear programming in matrix analytic methods
Communications in Statistics. Stochastic Models, 1998Summary: We present new methods for finding the \(R\) and \(G\) matrices which play a crucial role in determining the steady-state distribution of Markov chains of the GI/M/1 and M/C/1 type respectively. The methods involve finding solutions to some nonlinear programming problems.
Alfa, Attahiru Sule +2 more
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Matrix elements in the analytic tetrahedron method
International Journal of Quantum Chemistry, 2009The analytic tetrahedron method for evaluating various principal value integrals over a Brillouin zone is generalized to allow for variation of matrix elements or other functions in the numerator of the integrand throughout each tetrahedron. A three-dimensional Taylor series expansion retaining terms involving the gradient is made for the matrix ...
N. E. Brener, J. L. Fry, R. A. Johnson
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