Gugrajah_Yuvaan_ Ramesh_2003.pdf

Adaptation ofthe Fixed Point Approximation to Ad Hoc Networks Chapter 5
transmitted from nodes within a certain range of the target node, the nodes in the ad
hoc network also have an area that surrounds them that can be considered their "cell"
within which other nodes can transmit to them. The power control algorithm used in
the ad hoc network is assumed to be optimum, so that each node transmitting to its
target node is able 'to provide the signal power as required by the target node. To
simplify the analysis the medium access control is neglected and it is assumed that a
sufficient. number of receiver processors are provided to each node such that the
probability of a new arrival finding all receiver processors busy is negligible. This in
effect implies that blocking is only·interference-limited, since the greater the number
of calls in progress, the higher the interference is and the worse the resulting signal
quality will be.
A problem not yet overcome is the ability to inClude topology changes in the
analytical model. Since the fixed-point approximation is based on knowledge of the
routes that are available in an equilibrium state it is difficult to incorporate topology
changes into the analytical model for ad hoc networks. This problem is described
further in section 5.2. A fixed topology wireless multihop network is therefore
assumed. The analytical model is described in section 5.3 where the mappings that
are evaluated iteratively to find the fixed-point variables are described. Numerical
results obtained using the analytical model to evaluate a given fixed topology
wireless network are presented and discussed in section 5.4.
5.2. Problems with Analysing Topological Changes
The prediction of node position ID an ad hoc network is significantly more
complicated than that of the cellular network due to it involving more degrees of
freedom in mobility and there being no fixed point of reference. In order to take into
account all of the possible routes that could be available in an ad hoc network as the
topology varies over time, a fully connected network could be considered, consisting
of the number of nodes of the network of interest. Then each link has a certain
probability of being in existence. Consider for example Figure 5-1 where the random
topological structure of an ad hoc network consisting of 5 nodes is equivalent to a
5-2