Gugrajah_Yuvaan_ Ramesh_2003.pdf

Adaptation ofthe Fixed Point Approximation to Ad Hoc Networks
Chapter 5
ADAPTATION OF THE FIXED-POINT
APPROXIMATION TO AD HOC NETWORKS
5.1. Introduction
Chapter 5
In this chapter an analytical model is proposed to evaluate the call blocking in a
wireless ad hoc network employing CDMA. In the literature [Kaufman8l],
[Kelly94], [Ross95], the reduced load method, in particular the' fixed-point
approximation, has been used to evaluate blocking probability in wired networks
modelled as loss networks. The call blocking probability in wireless CDMA systems
has been evaluated using the Erlang capacity of the CDMA system and is based on
the total interference being experienced by the base station. There is nothing in the
literature, as far as the author is aware, that attempts to analytically evaluate the
blocking probability in an ad hoc network due to the routing protocol that is
implemented. The analytical model proposed is a combination and modification of
the blocking probability methods used for wired networks proposed in [LiuOO] and
the blocking probability evaluation of wireless cellular CDMA systems as proposed
in [Gilhousen91], [Viterbi93], [Miller95], [Viterbi95] and [Narr99]. The blocking
probability evaluation of wired networks and wireless cellular networks are
discussed in Chapter 4.
Since the ad hoc network is a wireless environment, it is assumed that congestion is
due to the number of simultaneous calls being handled by a particular node, instead
of using the capacity of links as the limiting factor. Nodes in an ad hoc network
receiving transmissions from other peer nodes in the network are analogous to a base
station in a cellular network receiving transmissions from mobiles within its cell.
Since the only transmissions in an ad hoc network intended for a target node are
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