Abstract
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 , “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 , our results show that for an N × N network, a 4(2 <i>m</i>)-stage
WSNB network and a 4(2 <i>m</i>)-stage LRNB network have 16.114 N<sup>3/2</sup> and 12.669
N<sup>3/2</sup> crosspoints, respectively; 4(3 <i>m</i>)-stage WSNB and LRNB networks have
the same number of crosspoints, $11.657 N<sup>3/2</sup>; and 4(2 <i>m</i>)-stage RNB network
has 7.447 N<sup>3/2</sup> crosspoints.
© 2011 IEEE
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