上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links Shizhen Zhao,Luoyi Fu,Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University,China Qian Zhang Department of Computer Scien Engineering Hong Kong,China
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links Shizhen Zhao, Luoyi Fu, Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University, China Qian Zhang Department of Computer Scien Engineering Hong Kong, China
Outline 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY ▣Background Large-scale Networks >Random Connection Model >First Passage Percolation Model Network Model Objective Q Main Results and Intuitions ▣Simulation Results ▣Concluding Remarks Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 2
Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 2 Outline ❑ Background ➢Large-scale Networks ➢Random Connection Model ➢First Passage Percolation Model ❑ Network Model & Objective ❑ Main Results and Intuitions ❑ Simulation Results ❑ Concluding Remarks
Large-scale Networks 上浒充通大￥ SHANGHAI JIAO TONG UNIVERSITY Network size is growing. Number of users is growing Need more base stations ▣Unreliable links. Communication between adjacent nodes is not always available Cause of the unreliability. Increased interference >Severe environment >Sleep-wake scheduling Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 3
3 Large-scale Networks ❑ Network size is growing. ➢ Number of users is growing ➢ Need more base stations ❑ Unreliable links. ➢ Communication between adjacent nodes is not always available ❑ Cause of the unreliability. ➢ Increased interference ➢ Severe environment ➢ Sleep-wake scheduling Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
Random Connection Model (RCM) 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY Ramdom Connection Model >Stationary point process(e.x.Poisson point process) Connection function 1.A non-increasing function h()defined on positive reals 2.An edge exists between nodes x1 and x2 with probability h(x1- X21) ▣Phase transition. Condition:<(dr > There exists a critical node density such that >lf入>乙e,an infinite large cluster exists. 1.if元<元.，all clusters are finite almost surely. Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 4
4 Random Connection Model (RCM) ❑ Ramdom Connection Model ➢ Stationary point process (e.x. Poisson point process) ➢ Connection function 1. A non-increasing function h(·) defined on positive reals 2. An edge exists between nodes x1 and x2 with probability h(|x1 - x2 |) ❑ Phase transition. ➢ Condition: ➢ There exists a critical node density , such that ➢ If , an infinite large cluster exists. 1. if , all clusters are finite almost surely. 2 0 ( ) R + h r dr c c c Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links
Random Connection Model (RCM) 上浒充通大￥ SHANGHAI JIAO TONG UNIVERSITY Poisson Boolean Model >Special case of RCM with hr）= 1,r≤0 0,r>6 >Two nodes are connected if and only if their distance is smaller or equal to 7o Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links 5
5 Random Connection Model (RCM) ❑ Poisson Boolean Model ➢ Special case of RCM with ➢ Two nodes are connected if and only if their distance is smaller or equal to 0 0 1, ( ) 0, r r h r r r = 0 r Fundamental Relationship between Node Density and Delay in Wireless Ad Hoc Networks with Unreliable Links