Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links

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 6

6 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

Outline 上游充通大学 SHANGHAI JIAO TONG UNIVERSITY ▣Background QNetwork Model Objective Network Model >Objective QMain Results and Intuitions ▣Simulation Results ▣Concluding Remarks Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 7

7 Outline ❑Background ❑Network Model & Objective ➢Network Model ➢ Objective ❑Main Results and Intuitions ❑Simulation Results ❑Concluding Remarks Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links

Network Model-Connectivity 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY Delay is a basic concern in designing and implementing large scale wireless networks.However,the premise of communication is connectivity. In large scale wireless network with unreliable links,it is too costly to maintain full connectivity.Therefore,we consider a slightly weaker connectivity-connectivity in percolation sense. Random Connection Model(RCM) Instantaneous and Long-term Connectivity Instantaneous Critical Density()and Long-term Critical Density (九z) Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 8

8 Network Model-Connectivity ❑ Delay is a basic concern in designing and implementing large scale wireless networks. However, the premise of communication is connectivity. ❑ In large scale wireless network with unreliable links, it is too costly to maintain full connectivity. Therefore, we consider a slightly weaker connectivity-connectivity in percolation sense. ➢ Random Connection Model (RCM) ➢ Instantaneous and Long-term Connectivity ➢ Instantaneous Critical Density ( ) and Long-term Critical Density ( ) I  L Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links

Network Model-Connectivity 上洋充通大学 SHANGHAI JIAO TONG UNIVERSITY g(r) 8(r) O 几，灵4， Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 9

9    I    I L      L Network Model-Connectivity g r( ) g r( ) O r0 r Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links