TY - JOUR
T1 - Towards a better understanding of large-scale network models
AU - Mao, Guoqiang
AU - Anderson, Brian D.O.
PY - 2012/4
Y1 - 2012/4
N2 - Connectivity and capacity are two fundamental properties of wireless multihop networks. The scalability of these properties has been a primary concern for which asymptotic analysis is a useful tool. Three related but logically distinct network models are often considered in asymptotic analyses, viz. the dense network model, the extended network model, and the infinite network model, which consider respectively a network deployed in a fixed finite area with a sufficiently large node density, a network deployed in a sufficiently large area with a fixed node density, and a network deployed in Re 2 with a sufficiently large node density. The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks. In this paper, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order 1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models. Therefore, extra scrutiny has to be used in order for the results obtained from the infinite network model to be applicable to the dense and extended network models. Asymptotic results are also obtained on the expected number of isolated nodes, the vanishingly small impact of the boundary effect on the number of isolated nodes, and the vanishing of components of finite order k in the dense and extended network models using a generic random connection model.
AB - Connectivity and capacity are two fundamental properties of wireless multihop networks. The scalability of these properties has been a primary concern for which asymptotic analysis is a useful tool. Three related but logically distinct network models are often considered in asymptotic analyses, viz. the dense network model, the extended network model, and the infinite network model, which consider respectively a network deployed in a fixed finite area with a sufficiently large node density, a network deployed in a sufficiently large area with a fixed node density, and a network deployed in Re 2 with a sufficiently large node density. The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks. In this paper, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order 1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models. Therefore, extra scrutiny has to be used in order for the results obtained from the infinite network model to be applicable to the dense and extended network models. Asymptotic results are also obtained on the expected number of isolated nodes, the vanishingly small impact of the boundary effect on the number of isolated nodes, and the vanishing of components of finite order k in the dense and extended network models using a generic random connection model.
KW - Connectivity
KW - continuum percolation
KW - dense network model
KW - extended network model
KW - infinite network model
KW - random connection model
UR - http://www.scopus.com/inward/record.url?scp=84859944056&partnerID=8YFLogxK
U2 - 10.1109/TNET.2011.2160650
DO - 10.1109/TNET.2011.2160650
M3 - Article
SN - 1063-6692
VL - 20
SP - 408
EP - 421
JO - IEEE/ACM Transactions on Networking
JF - IEEE/ACM Transactions on Networking
IS - 2
M1 - 5948400
ER -