GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Asymptotically optimal geometric mobile ad-hoc routing
DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
On greedy geographic routing algorithms in sensing-covered networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Asymptotic critical transmission radius for greedy forward routing in wireless ad hoc networks
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
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Consider a random wireless ad hoc network represented by a Poisson point process over a unit-area disk with mean n. Let σn denote its critical transmission radius for greedy forward routing, and βo = 1/ (2/3 -- √3/2π) ≈ 1.62. It was recently proved that for any constant ε 0, it is asymptotically almost sure that (1 -- ε) √βo in n/πn ≤ σn ≤ (1 + ε) √βo in n/πn. In this paper, we obtain tighter asymptotic bounds on σn. Specifically, we prove that for any constant c, the asymptotic probability of σn ≤ √βo in n + c/πn is at least 1 -- ( 1/1/βo--1/3 -- βo/2) e -c and at most e -βo/2 e -- c. Consequently, for any positive sequence (εn : n ≥ 1) with εn = o(In n) and εn → ∞, it is asymptotically almost sure that √βo in n --εn/πn ≤ σn ≤ √βo in n + εn/πn. We also conjecture that for any constant c, the asymptotic probability of σn ≤ √βo 1n n + c/σn is exactly exp (--(1/1/βo--1/3 -- β;o/2) e --c).