Statistical Analysis and Modeling of Shortest Path Lengths in Optical Transport Networks

We analyze the shortest path lengths between node pairs of real optical transport networks. 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.