Gugrajah_Yuvaan_ Ramesh_2003.pdf

Adaptation ofthe Fixed Point Approximation to Ad Hoc Networks
Chapter 5
fully connected network with some of the links not available. There are 5 active links
in the random topology network due to nodes being within range of each other. Each
link in the fully connected network is active if the equivalent link in the random
topology network is in existence.
Random Topology Network
Fully Connected Network
Figure 5-1. Random topology network and equivalent fully connected network with
some links inoperable
A probability of existence et, for a link t, needs to be found for the modelling of the
random topology network as a fully connected network. [McDonald99] develops a
mobility model that is used to predict the evolution of an ad-hoc network's topology.
Expressions are derived for the probability of the link being active as a function of
time based on different initial conditions for the nodes of interest. The distribution of
the mobility of one node with respect to the other is first be determined in order to
characterize the availability of a link over a period of time. It is therefore first
necessary to derive the mobility distribution of a single node in isolation and then
extend the distribution to derive the joint mobility distribution that accounts for one
node with respect to the other. Assuming that links fail independently, once the link
availability metric is known for each link along a path, [McDonald99] determines the
path availability as the product of the individual link availability metrics. This
approach is however not applicable to the analytical model for blocking probability
since path availability is determined as a function of time, whereas the fixed-point
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