First Passage Percolation Model 上浒充通大￥ SHANGHAI JIAO TONG UNIVERSITY First Passage Percolation Model. >Assign a random variable T(e)to each link e. > Define the passage time for a pathπ： T,(π)=∑T.(e) e∈π > Define the first passage time between nodesx and y: T(x,y)=infT,(π)：πis a path from x to y ▣Remark. Use first passage time to model delay Use the random variable T(e)to model the unreliability of links Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 66 First Passage Percolation Model ❑ First Passage Percolation Model. ➢ Assign a random variable to each link . ➢ Define the passage time for a path : ➢ Define the first passage time between nodes and : ❑ Remark. ➢ Use first passage time to model delay ➢ Use the random variable to model the unreliability of links ( ) T e c e  ( ) ( ) p c e T T e    = ( , ) inf{ ( ): } T x y T is a path from x to y = p   x y ( ) T e c Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links