Four-Stage Multicast Switching Networks: Nonblocking Conditions and Cost Analysis

In this paper, we consider four-stage multicast switching networks with different types of nonblocking capability. The goal of the paper is multifold. First, we evaluate and summarize various nonblocking conditions of four-stage multicast switching networks in recent work [Y. Yang and J. Wang, “A New Design for Wide-Sense Nonblocking Multicast Switching Networks,” IEEE Trans. Commun., vol. 53, no. 3, pp. 497-504, Mar. 2005, and F. Yan et al., “Nonblocking Four-Stage Multicast Network for Mulicast-Capable Optical Cross Connects,” J. Lightw. Technol., vol. 27, no. 17, pp. 3923-2932, Sep. 2009], and then propose a locally-rearrangeable nonblocking (LRNB) multicast switching network as a trade-off for nonblocking capability and network hardware cost between wide-sense nonblocking (WSNB) networks and rearrangeable nonblocking (RNB) networks. We further derive optimized network parameters and present a comprehensive cost analysis for different types of four-stage nonblocking multicast switching networks. Using the terms defined in F. Yan et al., our results show that for an N × N network, a 4(2m)-stage WSNB network and a 4(2 m)-stage LRNB network have 16.114 N³/₂ and 12.669 N³/₂ crosspoints, respectively; 4(3 m)-stage WSNB and LRNB networks have the same number of crosspoints, 11.657 N³/₂; and 4(2 m)-stage RNB network has 7.447 N³/₂ crosspoints.