樹狀網路之控制與統計反向問題

The Control and Statistical Inverse Problem for Tree Types of Queueing Networks

詹政霖(Jheng-Lin Jhan)

指導教授 ： 洪英超

國立中央大學/理學院/統計研究所/碩士(2008年)

摘要

本文考慮一樹狀網路模型(Tree-type network model)，此網路模型在現實生活中有廣泛的應用(如無線網路(wireless network)，電話交換中心(call centers)等)。我們所關心的是此樹狀網路中每個佇列的服務品質(Quality of Service; QoS)。但是受限於網路權限(authorization)，通訊法規(protocol)等限制，系統管理者往往無法得到完整的佇列資訊。所以本篇論文主旨在於如何透過可觀測的佇列來估計其他無法觀測的佇列資訊，這一類的問題被稱為網路診斷
(Network Tomography)。本文的方法是藉由建立一統計模型來推估感興趣的參數值，而這種利用可觀測到的有限資訊來推測無法觀測的佇列資訊的統計問題，我們稱之為Statistical Inverse Problem。最後我們透過電腦模擬來評估所提方法對佇列工作遺失率的估計準確性，並提出改善系統表現值的方法。

關鍵字

網路診斷 ； 樹狀網路模型 ； 服務品質

並列摘要

Assessing and monitoring the performance of computer and communi-
cations networks is an important problem for network engineers. We con-
sider a tree-type network model, and it has a broad application in real life(
wireless network, call centers, etc.). Our focus here is on estimating and monitoring network Quality-of-Service (QoS) parameters. But constrain-
ed by authorization or protocol, network engineers usually can’t get queues information completely. We discuss methods for estimating edge- level parameters from end-to-end path-level measurements, an important engineering problem that raises interesting statistical modeling issues. This kind of question is called “Network Tomography”. The method of this paper is to estimate interested parameters by constructing a statistical model, and we call this statistical issue “Statistical Inverse Problem”. In the end we will show a simulation result and advance a method to improve model performance.

並列關鍵字

Statistical Inverse Problem ； Network tomography

參考文獻

[1] George Michailidis, Bowel Xi, Vijayan N.Nair.

“Statistical aspects of the analysis of data

networks”, Technometrics , 49, pp.318-334, 2007.

[3] Geo5204 “Minimum norm solutions” Inverse theory lecture 6.

[4] Zellner. A. (1986) “On assessing prior distributions and Bayesian regression analysis with g-prior distribution”, In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp233-243.Amsterdam:North-holland.