Central limit theorems for derees of random directed geometric 度的随机有向几何中心极限定理.pptVIP

CLT for Degrees of Random Directed Geometric Networks Yilun Shang Department of Mathematics, Shanghai Jiao Tong University Context Background and Motivation Model Central limit theorems Degree distributions Miscellaneous (Static) sensor network Large-scale networks of simple sensors Static sensor network Large-scale networks of simple sensors Usually deployed randomly Use broadcast paradigms to communicate with other sensors Static sensor network Large-scale networks of simple sensors Usually deployed randomly Use broadcast paradigms to communicate with other sensors Each sensor is autonomous and adaptive to environment Static sensor network Sensor nodes are densely deployed Static sensor network Sensor nodes are densely deployed Cheap Static sensor network Sensor nodes are densely deployed Cheap Small size Communication Radio Frequency omnidirectional antenna directional antenna Communication Radio Frequency omnidirectional antenna directional antenna Optical laser beam need line of sight for communication An illustration Graph Models  Random (directed) geometric network Scatter n points on R2 (n large), X1,X2, …,Xn , i.i.d. with density function f and distribution F Given a communication radius rn, two points are connected if they are at distance ≤rn. Random geometric network Random geometric network Random geometric network Random directed geometric network Fix angle a ∈(0,2p]. Xn={X1,..,Xn} i.i.d. points in R2, with density f ,distribution F. Let Yn={Y1,..,Yn} be a sequence of i.u.d. angles, let {rn} be a sequence tends to 0. Ga (Xn ,Yn ,rn) is a kind of random directed geometric network, where (Xi, Xj ) is an arc iff Xj in Si=S(Xi ,Yi ,rn ). D.,Petit,Serna, IEEE Trans. Mobi. Comp. 2003 Random directed geometric network Random directed geometric network Ga ( Xn ,Yn ,rn ) is a digraph If x5 is not in S1 , to communicate from x1 to x5: Random directed geometric network No