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題名:	具有特別排列的QBD 過程的解法 Solving Qbd Processes with Special Structures
作者:	陸行
貢獻者:	應數系
關鍵詞:	生死過程;矩陣幾何形式解;矩陣特徵值 Quasi-birth-death process;matrix-geometric solutions;eigenvalues
日期:	2019-10
上傳時間:	2025-03-31 11:55:27 (UTC+8)
摘要:	當平穩機率向量存在時，我們考慮排隊系統馬氏鏈矩陣的解具有矩陣幾何形式。其計算算法中的基本步驟通常求解矩陣R，矩陣R是二次方程矩陣的解。利用排隊系統的生成矩陣的特殊結構，我們開發一種比經典的速率矩陣迭代算法更高效的特徵值方法計算平穩機率分佈。我們將在提案中用數值例子說明新算法的優點。 We consider a class of Markov chains for which the stationary probability vector, when it exists, is of the matrix-geometric form. The essential step in the computational algorithm usually is the evaluation of a matrix R which is a solution of a matrix quadratic equation. The objective of this proposal is to find equilibrium probabilities of QBD processes with a special structure. In specific, only state transitions between neighboring levels are allowed, that is, no event can increase or decrease the level by more than 1. We construct a more efficient and innovative K-matrix based algorithm for computing the stationary probability distribution. Showing how this can be exploited in QBD, we use an eigenvalue approach to develop a more efficient algorithm for the improved accuracy and computational efficiency.
關聯:	科技部, MOST107-2221-E004-007, 107.08-108.07
資料類型:	report
顯示於類別:	[應用數學系] 國科會研究計畫

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