Fig. 2. NSFNET topology with the lengths in km marked on links.
power in any link making congestion a parameter that is
straightforward to measure for an installed network.
VII. ESTIMATING THE NETWORK
BLOCKING PROBABILITY
A. Sequential Loading of the Network
In order to estimate the network blocking probability (NBP),
we follow the methodology of [13], sequentially loading
the network with bi-directional demands between randomly
selected pairs of nodes in the network. In this letter for
simplicity we restrict our discussion to uniformly generated
traffic with a demand granularity of 100 GbE, each of which is
independently optically routed through the network. The point
at which the path assigned by the routing algorithm cannot
physically be optically routed by the network is considered
blocking and the number of demands recorded. This procedure
is then repeated 10000 times to build up the statistical behavior
of the network blocking probability. From this we calculate the
probability that blocking is occurring within the network for
a given network load.
B. Statistical Analysis of Network Blocking Probabilities
Herein we focus on the number of demands that cause
blocking within the network in 1% of occasions. Given that
the network blocking occurs when blocking occurs in the
most congested link, in essence we are concerned with the
distribution of a minimum. We therefore propose to analyze
the networking blocking probability using a generalized
extreme value distribution whose cumulative distribution function
(CDF) may be expressed as [14]:
F (x|k,μ, σ) = exp
_
−
_
1 + k
(x − μ)
σ
−1k
_
(7)
where k,μ and σ are the shape, location and scale parameters
of the distribution, all of which may be determined from a
given data set using maximum likelihood estimation.
VIII. APPLICATION TO AN EXEMPLAR
OPTICAL NETWORK
So as to quantify the benefit afforded in an optical network
by using the algorithm proposed in this letter, we consider a
mesh topology the NSFNET shown in Fig. 2, having 14 nodes,
22 edges using the same path lengths as per [15].