We analyze the shortest path lengths between
node pairs of real optical transport networks
(OTNs). From the analysis, we find that Johnson SB
distribution is suitable for the shortest path length
modeling. The validity of the distributions is evaluated
in terms of the Kolmogorov-Smirnov (KS) statistic.
Johnson SB distribution provides an average KS
statistic of 0.0423, which indicates its good accuracy.
We also show that the key parameters of the shortest
path lengths, such as the mean, the median, and the
standard deviation, can be estimated from the convex
area of the network. We develop the proposed Johnson
SB distribution model for the shortest path lengths using
the basic information of the networks. The developed
model is able to estimate path-length dependent system
parameters, such as the appropriate modulation formats
in transparent optical networks with an average error
of only 6.4%. It is noteworthy that these estimations can
be made without full knowledge of the network. Only
the node locations are required.