以群聚計算法求解叉狀型等候系統之穩態機率(I)

Abstract

這是一個為期兩年的研究計畫，於計畫中進行調查一個新的計算方式於求解叉狀等候系統的穩態機率。我們初步證明此推導計算方式，縮減了以往複雜的矩陣計算。我們希望在這個研究計畫中可以演繹和推導此方法於一般服務時間的系統中。在第一年，我們希望將此結果運用於phase-type 的服務系統中。在第二年，則可以將第一年的結果應用於叉狀等候系統。這種計算法的好處是在大型的矩陣計算時可以顯著地減少計算量，提供使用者快速而且正確的解。

Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death (QBD) type Markov Chain normally are dependent on the structure of the queueing network. In this two-year project, a new computing scheme is developed for attaining stationary probabilities in queueing networks of the fork-type. This scheme provides a general approach to reducing the complexity of computing algorithm. The result becomes more significant when a large buffer size is involved but it cannot be ignorant. The preliminary result of this approach is proved and provided with an illustrated example in this proposal. In the first year, it is supposed to apply the approach to a more general case where the service time is of the phase-type. Based on the result in the first year, a similar approach is used to study a folk-type queueing model during the second year.