Browsing by Author "Yao, Frances"

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Asymptotic Critical Transmission Radii for Greedy Forward Routing in Wireless Ad Hoc Networks
(2009-05-01)
Wan, Peng-Jun
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Yi, Chih-Wei
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Wang, Lixin
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Yao, Frances
;
Jia, Xiaohua
In wireless ad hoe networks, greedy forward routing is a localized geographic routing algorithm in which one node discards a packet if none of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination. If all nodes have the same transmission radii, the critical transmission radius for greedy forward routing is the smallest transmission radius which ensures packets can be delivered by greedy forward routing through any source-destination pair. In this paper, we study asymptotic critical transmission radii of randomly deployed wireless ad hoc networks. Assume network nodes are represented by a Poisson point process of density n over a unit-area convex compact region whose boundary curvature is bounded. We show that the ratio of critical transmission radii to root ln n/pi n is asymptotically almost surely equal to root 1/(2/3 - root 3/2 pi) approximate to 1.6.
Improved Asymptotic Bounds on Critical Transmission Radius for Greedy Forward Routing in Wireless Ad Hoc Networks
(2008)
Wang, Lixin
;
Yi, Chih Wei
;
Yao, Frances
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資訊工程學系
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Department of Computer Science
Consider a random wireless ad hoc network represented by a Poisson point process over a unit-area disk with mean n. Let sigma(n) denote its critical transmission radius for greedy forward routing, and beta(0) = 1/(2/3 - root 3/2 pi) approximate to 1.6(2). It was recently proved that for any constant epsilon > 0, it is asymptotically almost sure that (1 - epsilon) root beta(0) 1n n/pi n <= sigma(n) <= (1 + epsilon) root beta(0) 1n n/pi n. In this paper, we obtain tighter asymptotic bounds on sigma(n). Specifically, we prove that for any constant c, the asymptotic probability of sigma(n) <= root beta(0) ln n+c/pi n is at least 1-(1/1/beta(0)-1/3-beta(0)/2)e(-c) and at most e(-beta 0/2e-c) Consequently, for any positive sequence (xi(n) : n >= 1) with xi(n) = o(ln n) and xi(n) -> proportional to, it is asymptotically almost sure that root beta(0) ln n-xi(n)/pi n <= sigma(n) <= root beta(0) ln n+xi(n)/pi n We also conjecture that for any constant c, the asymptotic probability of sigma(n) <= root beta(0) ln n+c/pi n is exactly exp (-(1/1/beta(0)-1/3 - beta(0)/2)e(-c)).
On The Longest RNG Edge of Wireless Ad Hoc Networks
(2008)
Wan, Peng-Jun
;
Wang, Lixin
;
Yao, Frances
;
Yi, Chih-Wei
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資訊工程學系
Relative neighborhood graph (RNG) has been widely used in topology control and geographic routing in wireless ad hoc networks. Its maximum edge length is the minimum requirement on the maximum transmission radius by those applications of RNG. In this paper, we derive the precise asymptotic probability distribution of the maximum edge length of the RNG on a Poisson point process over a unit-area disk. Since the maximum RNG edge length is a lower bound on the critical transmission radius for greedy forward routing, our result also leads to an improved asymptotic almost sure lower bound on the critical transmission radius for greedy forward routing.