Solving Quadratic Matrix Equations Arising in Random Walks in the Quarter Plane
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Publication:5113364
DOI10.1137/19M1276960zbMath1441.15010arXiv1907.09796OpenAlexW3022771954MaRDI QIDQ5113364
Dario Andrea Bini, Beatrice Meini, Jie Meng
Publication date: 4 June 2020
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1907.09796
Markov chainsrandom walksNewton iterationmatrix equationsToeplitz matricesfixed point iterationinfinite matrices
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Cites Work
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- Queues with boundary assistance: The effects of truncation
- Improved cyclic reduction for solving queueing problems
- New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains
- Truncation and augmentation of level-independent QBD processes.
- Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process
- Light tail asymptotics in multidimensional reflecting processes for queueing networks
- Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process
- Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox
- GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES
- Revisiting the Tail Asymptotics of the Double QBD Process: Refinement and Complete Solutions for the Coordinate and Diagonal Directions
- Random Walks in the Quarter Plane
- On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes
- Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes
- Two Parallel Queues Created by Arrivals with Two Demands I
- A Computational Framework for Two-Dimensional Random Walks With Restarts
- Introduction to Matrix Analytic Methods in Stochastic Modeling
- Newton's iteration for non-linear equations in Markov chains
- Numerical analysis of a quadratic matrix equation
- The stationary tail asymptotics in the GI/G/1-type queue with countably many background states
- SUFFICIENT CONDITIONS FOR A GEOMETRIC TAIL IN A QBD PROCESS WITH MANY COUNTABLE LEVELS AND PHASES
- On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
- On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- Tri-Layered QBD Processes with Boundary Assistance for Service Resources
- Numerical Methods for Structured Markov Chains
- Decay rates for quasi-birth-and-death processes with countably many phases and tridiagonal block generators