@article{Qu2025, 
author = {Jiaqi Qu and Yunlan Wei and Yanpeng Zheng and Zhaolin Jiang},
title = {Fast algorithms for a linear system with infinitesimal generator structure of a Markovian queueing model},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6546-6559},
keywords = {band LU decomposition, infinitesimal generator structure, Markovian queueing model, perturbed four-banded matrix, spectral decomposition, Toeplitz solver},
url = {https://www.sciopen.com/article/10.3934/math.2025299},
doi = {10.3934/math.2025299},
abstract = {In this paper, we focused on solving the perturbed four-banded linear system derived from the traffic process associated with a Markovian queueing model. Utilizing the spectral decomposition of circulant and skew circulant matrices, we computed the product of Toeplitz inversion and a vector, leading to a decomposition algorithm for perturbed four-banded linear systems. This decomposed Toeplitz system features multiple right-hand terms, significantly reducing computational complexity through Toeplitz inversion. Additionally, we introduced an algorithm based on banded LU decomposition, resulting in a banded linear system with multiple right-hand terms, where the sparsity of the banded LU decomposition is pivotal. To evaluate the algorithm's performance, we presented two examples in numerical simulations.}
}