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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.

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.
其他識別: U0005-2001201109402600
Appears in Collections:通訊工程研究所

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