Gugrajah_Yuvaan_ Ramesh_2003.pdf

Evaluation ofNetwork Blocking Probability· Chapter 4
i) Link Independence: The blocking occurs independently from link to link, so
the probability that a call is admitted on a given route is the product of the
probabilities that the call is admitted on each individual link of that route.
ii) Poisson Arrival: The offered load to a link is a Poisson process with rate
reduced by blocking on other links. In cases of multi-rate traffic, the offered
load of each class of traffic onto a link is a Poisson process with its rate
reduced by blocking on other links.
The Erlang Fixed Point Approximation (EFPA) is a member of the reduced load
class, one that analyses each link as a separate subnetwork. The EFPA performs well
asymptotically and [Kelly91] proved that the estimates for a network with fixed
routing tends towards the exact probabilities when,
i) the link capacities and arrival rates are increased simultaneously keeping the
network topology fixed, and
ii) when the number of links and routes are increased while the link loads are
held constant.
The EFPA is a solution to the set of fixed point equations
B. =E(p. C.)
] J' ]
Pj = L U jm ArIT(1-B i )
mEM iEm
itJ.j
(4-16)
(4-17)
Bj is the probability that link j is full given its offered traffic load is Pj, and uses the
Erlang Loss Formula from equation (4-9). The offered traffic load is an
approXimation obtained by considering the sum of the contributions made by each
route m toj's carried load. Applying the independent blocking assumption results in
L r = 1- Pr(call is accepted on each link i Er)
= 1- IT Pr(call is accepted on each link i)
iEm
=1-IT (1- B i )
iEm
4-9
(4-18)