Invariant subspaces of matrices with applications
Invariant subspaces of matrices with applications
Rational iterative methods for the matrix sign function
SIAM Journal on Matrix Analysis and Applications
On the asymptotic behavior of heterogeneous statistical multiplexer with applications
IEEE INFOCOM '92 Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 2)
Linear System Theory and Design
Linear System Theory and Design
The BMAP/G/1 QUEUE: A Tutorial
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
Finite and Infinite QBD Chains: A Simple and Unifying Algorithmic Approach
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
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A large class of teletraffic analysis problem encountered in communication networks are based on Markov chains of M/G/1 and G/M/1 type, the study of which require numerically eficient and reliable algorithms to solve the nonlinear matrix equations arising in such chains. The traditional transform approach to solve these chains which requires root finding is known to cause problems when some roots are close or identical. The alternative iterative schemes based on matrix analytic methods have in general low linear convergence rates yielding a computation time bottleneck an solving large-scale probability models. We develop a novel algebraic theory for the solution of these chains based on which we propose numerically efficient algorithms. The key to our approach is an invariant subspa. ce computation implemented using the matrix sign function iterations. These algorithms have high convergence rates unlike the linear convergence rates of existing algorithms, they are amenable to parallelization and can, easily be implemented using standard linear algebra software packages.