Gugrajah_Yuvaan_ Ramesh_2003.pdf
Gugrajah_Yuvaan_ Ramesh_2003.pdf
Gugrajah_Yuvaan_ Ramesh_2003.pdf
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Evaluation ofNetwork Blocking Probability· Chapter 4<br />
i) Link Independence: The blocking occurs independently from link to link, so<br />
the probability that a call is admitted on a given route is the product of the<br />
probabilities that the call is admitted on each individual link of that route.<br />
ii) Poisson Arrival: The offered load to a link is a Poisson process with rate<br />
reduced by blocking on other links. In cases of multi-rate traffic, the offered<br />
load of each class of traffic onto a link is a Poisson process with its rate<br />
reduced by blocking on other links.<br />
The Erlang Fixed Point Approximation (EFPA) is a member of the reduced load<br />
class, one that analyses each link as a separate subnetwork. The EFPA performs well<br />
asymptotically and [Kelly91] proved that the estimates for a network with fixed<br />
routing tends towards the exact probabilities when,<br />
i) the link capacities and arrival rates are increased simultaneously keeping the<br />
network topology fixed, and<br />
ii) when the number of links and routes are increased while the link loads are<br />
held constant.<br />
The EFPA is a solution to the set of fixed point equations<br />
B. =E(p. C.)<br />
] J' ]<br />
Pj = L U jm ArIT(1-B i )<br />
mEM iEm<br />
itJ.j<br />
(4-16)<br />
(4-17)<br />
Bj is the probability that link j is full given its offered traffic load is Pj, and uses the<br />
Erlang Loss Formula from equation (4-9). The offered traffic load is an<br />
approXimation obtained by considering the sum of the contributions made by each<br />
route m toj's carried load. Applying the independent blocking assumption results in<br />
L r = 1- Pr(call is accepted on each link i Er)<br />
= 1- IT Pr(call is accepted on each link i)<br />
iEm<br />
=1-IT (1- B i )<br />
iEm<br />
4-9<br />
(4-18)