Computing approximate blocking probability in hierarchical wavelength routing optical networks

Rapid development of optical communication techniques has made possible large scale wavelength routing optical networks. Nowadays, these networks are deployed worldwide. Large scale networks have natural hierarchies due to either geographical reasons or administrative consideration and are therefore managed in a hierarchical way correspondingly. That is, networks are composed of several subnetworks, which are themselves composed of other even smaller subnetworks. Erlang fixed point approximation (reduced load approximation) has been extensively used in performance evaluation of end to end call blocking probability in traditional circuit switching networks, which are also called loss networks. This method has also been extended for hierarchical loss networks. However, performance evaluation of call blocking probability in hierarchical wavelength routing optical networks has not yet been presented. In this paper, a kind of approximation method is developed for analyzing end to end call blocking probability in hierarchical wavelength routing optical networks. By iteratively running processes combining a top-down load distribution and a bottom-up calculation of node-pair blocking in the network hierarchy, a steady state will be reached and approximate end to end call blocking probability in hierarchical wavelength routing optical network is obtained. Both the link independent model and the link correlation model are used in our analysis. By comparing theoretical results derived from our approximation method and results obtained from discrete event simulation, we illustrate that our method gives reasonable estimate of end to end call blocking probability in hierarchical wavelength routing optical networks, with the correlation model giving much more accurate estimate than the independent model.