TY - GEN

T1 - Asymptotic critical transmission radius for greedy forward routing in wireless ad hoc networks

AU - Wan, P. J.

AU - Ik, Tsi-Ui

AU - Yao, F.

AU - Jia, X.

PY - 2006/9/4

Y1 - 2006/9/4

N2 - Greedy forward routing (abbreviated by GFR) in wireless ad hoc networks is a localized geographic routing in which each 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 of the packet. If all nodes have the same transmission radii, the critical transmission radius for GFR is the smallest transmission radius which ensures that packets can be delivered between any source-destination pairs. In this paper, we study the asymptotic critical transmission radius for GFR in randomly deployed wireless ad hoc networks. We assume that the network nodes are represented by a Poisson point process of density n over a convex compact region of unit area with bounded curvature. Let β 0 = 1/ (2/3 - √3/2π) ≈ 1.6 2. We show that √β 0 ln n/πn is asymptotically almost surely (abbreviated by a.a.s.) the threshold of the critical transmission radius for GFR. In other words, for any β > β 0, if the transmission radius is √β ln n/πn, it is a.a.s. packets can be delivered between any source-destination pairs; for any β < β 0, if the transmission radius is √β ln n/πn, it is a.s.s. packets can't be delivered between some source-destination pair.

AB - Greedy forward routing (abbreviated by GFR) in wireless ad hoc networks is a localized geographic routing in which each 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 of the packet. If all nodes have the same transmission radii, the critical transmission radius for GFR is the smallest transmission radius which ensures that packets can be delivered between any source-destination pairs. In this paper, we study the asymptotic critical transmission radius for GFR in randomly deployed wireless ad hoc networks. We assume that the network nodes are represented by a Poisson point process of density n over a convex compact region of unit area with bounded curvature. Let β 0 = 1/ (2/3 - √3/2π) ≈ 1.6 2. We show that √β 0 ln n/πn is asymptotically almost surely (abbreviated by a.a.s.) the threshold of the critical transmission radius for GFR. In other words, for any β > β 0, if the transmission radius is √β ln n/πn, it is a.a.s. packets can be delivered between any source-destination pairs; for any β < β 0, if the transmission radius is √β ln n/πn, it is a.s.s. packets can't be delivered between some source-destination pair.

KW - Greedy forward routing

KW - Random deployment

KW - Wireless ad hoc networks

UR - http://www.scopus.com/inward/record.url?scp=33748053014&partnerID=8YFLogxK

U2 - 10.1145/1132905.1132909

DO - 10.1145/1132905.1132909

M3 - Conference contribution

AN - SCOPUS:33748053014

SN - 1595933689

SN - 9781595933683

T3 - Proceedings of the International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc)

SP - 25

EP - 36

BT - Proceedings of the Seventh ACM International Symposium on Mobile Ad Hoc Networking and Computing, MOBIHOC 2006

Y2 - 22 May 2006 through 25 May 2006

ER -