Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/4881
標題: 無線隨意網路連接性分析
Analysis on the Connectivity in Wireless Ad Hoc Networks: New Results and Their Implications
作者: 莊旻翰
Chuang, Min-Han
關鍵字: Percolation;滲透理論;full connectivity;unreliable transmission;完全連接;不可靠的傳輸
出版社: 通訊工程研究所
引用: [1] O. Dousse, P. Thiran, and M. Hasler, Impact of interferences on connectivity in ad hoc networks," IEEE J. Sel. Areas Commun., vol. 13, no. 2, pp. 425 { 436, Apr. 2005. [2] M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti, Stochastic geometry and random graphs for the analysis and design of wire-less networks," IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp. 1029 { 1046, Sep. 2009. [3] R. Meester and R. Roy, Continuum Percolation. Cambridge, U.K.: Cambridge Univ. Press, 1996. [4] E. N. Gilbert, Random plane networks," Society for Industrial and Applied Mathematics, vol. 9, no. 4, pp. 533 { 543, Dec. 1961. [5] O. Dousse, P. Thiran, and M. Hasler, Connectivity in ad-hoc and hybrid net-works," in Proc. IEEE INFOCOM''02, Nov. 2002, pp. 1079 { 1088. [6] O. Dousse, F. Baccelli, and P. Thiran, Percolaion in the signal to interfernce ratio graph," J. Appl. Prob., vol. 43, no. 2, pp. 552{562, Jun. 2006. [7] G. Grimmett, Percolation, 2nd ed. John Wiley and Sons, 1999.
摘要: 
在本文中,我們探討的問題是,何時無線網路中的兩個節點有可能互相通訊?何時幾乎肯定是可以互相通訊?我們藉由找到讓網路節點圖滿足滲流理論的條件回答第一個問題。在這部分,我們採用二維晶格的邊界滲流理論來闡述這個條件。只要小正方形封閉的機率是小於0.5而且每一個小正方形內有至少4個節點,滲透理論就會發生。根據這點,我們建立了讓網路節點圖完全連接的條件。在這部分,兩個相鄰的小正方形只要有一條通訊路徑就是相連在一起,而不需要保證有直接的通訊連接。透過歸納,如果每一個小正方形內包含至少一個節點而且每一個小邊界可使用的機率大於等於0.3822,網路節點圖幾乎肯定會完全連接。模擬部分驗證了我們提出的條件。此外,我們把提出的條件應用到SINR模型[1]。根據我們提出的條件,每一個節點可以忍受比[1]呈現的結果還要更多的干擾。最後,我們延伸到不可靠的傳輸的情況而且分別提出了適合的條件去滿足滲透理論跟完全連結。我們發現當在不可靠傳輸的時候,增加每一個小正方形內的節點數或是維持成功傳送的機率在門檻值之上,這兩個方法可以達到滲透理論跟完全連接

In this work, we investigate the problems of when it is possible for two nodes in a wireless network to communicate with each other and when this communi- cation can be assured almost surely. We answer the first problem by finding the conditions for the occurrence of percolation in a network graph. In this part, we adopt the result from bond percolation in a two-dimensional lattice to develop the conditions for percolation. As long as the probability that a sub-square is close is less than 0.5 and the number of nodes in a sub-square is at least four, percolation occurs. Following that, we establish the conditions for full connectivity in a network graph. In this part, how two adjacent sub-squares are connected differentiates this works from others. In this work, two adjacent sub-squares are connected if there exists a communicating path between them whereas a direct communication link is needed to ensure the connectivity between two adjacent sub-squares. Through induction, the full connectivity occurs almost surely if each sub-square contains at least one node and the probability of having an open sub-edge is greater than or equal to 0.3822. Simulations are conducted to validate the proposed conditions for percolation and full connectivity. In addition, we apply the proposed conditions to SINR model [1]. Based on the proposed conditions, each node can tolerate more interference than that stated in [1]. Last, we extend the derived results to the case of unreliable transmission and propose suitable conditions for percolation and full connectivity, respectively. We find when the transmission is unreliable, increasing nodes per sub-square or maintaining the probability of successful transmission above a certain threshold seems to be two possible approaches to achieve percolation and full connectivity.
URI: http://hdl.handle.net/11455/4881
其他識別: U0005-2001201109402600
Appears in Collections:通訊工程研究所

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