On path dependent loss and switch crosstalk reduction in optical networks

Although optical multistage interconnection networks (OMINs) promise to meet the ever growing demands of communication networks and multiprocessor systems in fast communication, they suffer from challenges such as path dependent loss and switch crosstalk. In this paper, we propose an innovative approach for reducing not only the path dependent loss but also the number of switch crosstalks in OMINs. Our approach is centered upon modelling OMINs with Petri nets and using the P-invariants method to determine the minimum number of stages image that is sufficient to establish requested communication patterns in variable-stage OMINs. Being composed of the smallest number of stages and consequently directional couplers (or photonic switches), image-stage OMIN employs minimal structure and, therefore, path dependent loss and also number of switch crosstalks reach the least possible values in the realization of requested communication patterns. We prove that the size of Petri nets created in this work is in polynomial dependence on the problem size which alleviates memory consumption significantly and ascertains the fact that memory capacity and performance of modern computers are indeed sufficient to run our task. We also show that the complexity results obtained in this research improve similar results reported in our previous paper. We carry out a series of computer experiments to confirm the effectiveness of the proposed approach.