Gugrajah_Yuvaan_ Ramesh_2003.pdf

Evaluation ofNetwork Blocking Probability
Chapter 4
[Kelly86] proved that there is a unique vector (B" ..., Bj) E [O,1]J satisfying (4-16)
and (4-17).
Other approximation techniques include the Knapsack Approximation [Kaufman81],
Pascal Approximation [Ross93] and the Markov Random Field Method [Zachary99].
None of the abovementioned approximations take into account multihop networks
together with state dependent routing. The networks tend to be modelled as fully
connected, so even when adaptive routing is used, it is assumed that the one-hop
route is always first attempted and overflows to a selected two-hop route, based on
expected free capacity. The call is lost if it cannot be completed on the two-hop
route.
[LiuOO] proposes a scheme in order to tackle the following characteristics of
currently evolving integrated service networks:
i) Sparse topologies, where the assumption of a direct route between source
and destination nodes does not always hold.
ii) Routes comprise a large number of hops with many possible routes between
. the source and destination nodes.
iii) Different traffic classes characterized by widely varying bandwidth
requirements and different mean holding times.
The following Section describes the Fixed Point Approximation (FPA) proposed by
[LiuOO]. In Chapter 5 the adaptation of this FPA to evaluate the call blocking
probability of an ad hoc network employing CDMA is described.
4.5. Blocking Probability in Multirate Multihop Loss Networks
In [LiuOO] a Fixed Point Approximation to evaluate the end-to-end blocking
probability in multirate multihop loss networks is proposed. The approximation
method involves solving simultaneously for four fixed point variables using three
mappings. Once solved iteratively, the fixed point variables are used to calculate the
blocking probability of each class of call between each node pair. The terms "units of
4-10