Crosstalk-Free Widesense Nonblocking Multicast Photonic Switching Networks

We analyze crosstalk-free widesense nonblocking multicast multi-log networks. Widesense nonblocking strikes a balance between strictly nonblocking and rearrangeably non- blocking both in terms of cost-effectiveness and route establishment efficiency. The problem is important as cost-effective and efficient crosstalk-free multicast photonic switching networks are likely to play an important role at the optical Internet core in the future. Particularly, for the first time in the literature we derive conditions for the d-ary multi-log network to be crosstalk-free multicast widesense nonblocking under the window algorithm for any given window size. Several interesting by-products follow from our approach and result. Firstly, our result allows for computing the best window size minimizing the fabric cost, showing that the multi-log network is a very good candidate for crosstalk-free multicast switching architectures. Secondly, our analytical approach - partly based on applying the celebrated Konig-Egevary theorem - also gives a much simpler proof of the known case when the network is not required to be crosstalk-free. Thirdly, for window sizes of 1 and dⁿ, we re-discovered known results for the multi-log multicast networks under the so-called fanout constraints.