不完全連接感測拓譜的隨機接取系統之穩定性分析

Abstract

傳統對於隨機接取系統的分析與設計並不考慮連結拓譜，隱然假設所有的使用者可以彼此感測。而相應的終端機隱匿問題只能用些工程技巧彌補，但卻未曾以網路的角度徹底了解。這篇論文使用了隨機圖學的概念於不完全連接的感測拓譜，研究了阿羅哈 (ALOHA) 、無限感知網路 (cognitive radio networks) 與載波偵聽多路存取 (CSMA) 系統。為了避免穩態分析造成的錯誤結論，我們用動態分析的方法將系統描述成馬可夫鏈，利用佛斯特-李雅普諾夫條件 (Foster-Lyapunov criteria) 研究系統的穩定性。我們提出了清晰簡潔的隨機接取系統穩定性條件，並用模擬證實它們的正確性。

Traditional analysis and design on random access systems do not take sensing topology into consideration, which implicitly assumes that one user can sense all other users. The corresponding hidden terminal problem is only mitigated by some engineering techniques but never completely understood from a network view. This work applies random graph on imperfect sensing topology to study three random access systems: ALOHA, cognitive radio networks and CSMA. To avoiding misleading conclusion from equilibrium analysis, we take a dynamic approach by modeling the systems as Markov chains, and investigate the system stabiliby from the recurrence of Markov chains with the aid of Foster-Lyapunov criteria. Elegant stability conditions are derived in this work, together with the verification from simulation result.