Gugrajah_Yuvaan_ Ramesh_2003.pdf

Evaluation ofNetwork Blocking Probability Chapter 4
link, the stochastically most congested link on the route needs to be found. Let E[k]
be the expected number ofoccupied bandwidth units on a link which is given by
(4-28)
The proof of equation (4-28) can be found in [LiuOO] and is based on Kaufman's
recursion [Kaufman81]. Using equation (4-28) and equation (4-20) the stochastically
most congested link on route (r, m) becomes:
Defme for link} the probability ofno more than k trunks being free as:
k
t/k) = LPj(Cj -i)
i=O
(4-29)
(4-30)
A call will be admitted on route (r, m), which is one of the M r routes between node
pair r, if all the routes listed before (r, m) have fewer free trunks on their most
congested link and all routes listed after (r, m) have at most the same number of free
trunks on their most congested link. The probability that route (r, m) will be used can
be expressed as:
4.5.6. Blocking Probability
(4-31)
Once the four fixed-point variables have been solved, the blocking probability for a
call request (r, s) is given by
M r
Brs =1- Lqrms IT ajs
m=1 jE(r,m)
(4-32)
The equilibrium fixed-point is obtained using repeated substitution and the fixed
point is used to calculate the end-to-end blocking probabilities using equation (4-32).
4-14