Nonlinear Matrix Equations in Applied Probability—Solution Techniques and Open Problems

DOI10.1137/1030046zbMath0642.65033OpenAlexW2031720945WikidataQ111593343 ScholiaQ111593343MaRDI QIDQ3783425

Publication date: 1988

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1030046

zbMATH Keywords

queueing inventory minimal nonnegative solutions stochastic models applied probability nonlinear matrix equations communications error analyses dam theories

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Queueing theory (aspects of probability theory) (60K25) Probabilistic methods, stochastic differential equations (65C99)

Related Items (25)

A comparative numerical study of the spectral theory approach of Nishimura and the roots method based on the analysis of \(\mathrm{BDMMAP}/\mathrm{G}/1\) queue ⋮ ON LATOUCHE–RAMASWAMI'S LOGARITHMIC REDUCTION ALGORITHM FOR QUASI-BIRTH-AND-DEATH PROCESSES ⋮ An integrated production and inventory model to dampen upstream demand variability in the supply chain ⋮ A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains ⋮ A probabilistic algorithm for determining the fundamental matrix of a block M/G/1 Markov chain ⋮ A numerically efficient method for the \(MAP/D/1/K\) queue via rational approximations ⋮ Exploiting the Toeplitz structure in certain queueing problems ⋮ A simple and efficient computing procedure of the stationary system-length distributions for \(G I^X / D / c\) and \(B M a P / D / c\) queues ⋮ From the matrix-geometric to the matrix-exponential ⋮ The waiting-time distribution and its moments of the PH/PH/1 queue ⋮ Computational methods in risk theory: a matrix-algorithmic approach ⋮ A fast Newton-Shamanskii iteration for a matrix equation arising from M/G/1-type Markov chains ⋮ Coordinating lead times and safety stocks under autocorrelated demand ⋮ A matrix-geometric solution of the jockeying problem ⋮ Solving matrix polynomial equations arising in queueing problems ⋮ AMAP/G/1 Queue with an Underlying Birth–Death Process ⋮ Queues with Correlated Service and Inter-Arrival Times and Their Application to Optical Buffers ⋮ Relaxed functional iteration techniques for the numerical solution of \(M/G/1\) type Markov chains ⋮ A simple analysis of system characteristics in the batch service queue with infinite-buffer and Markovian service process using the roots method:GI/C-MSP^(a,b)/1/∞ ⋮ Queue-length, waiting-time and service batch size analysis for the discrete-time \(GI/D-MSP^{\text{(a,b)}}/1/\infty\) queueing system ⋮ On the numerical solution of a nonlinear matrix equation in Markov chains ⋮ Cost optimization of an unreliable server queue with two stage service process under hybrid vacation policy ⋮ Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process ⋮ Ladder heights and the Markov-modulated M/G/1 queue ⋮ A Fast Newton's Iteration for M/G/1-Type and GI/M/1-Type Markov Chains

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