Abstract
In this paper, we investigate the four-stage multicast network with
only two multicast stages (the second and output stages) being multicast-capable,
which is called 4(2 m)-stage multicast network. We first derive the sufficient
wide-sense nonblocking (WSNB) and rearrangeable nonblocking (RNB) conditions
for the 4(2 m)-stage multicast network. The WSNB and RNB conditions are also
presented for multicast request with limited multicast degree. The 4(2 m)-stage
multicast network needs at least O$(N^{3
/ 2})$ crosspoints to be WSNB and RNB, which is a lower bound
than the three-stage Clos network with two multicast stages and the same bound
with the four-stage network with three multicast stages. Then we design full
and partial multicast-capable optical cross connects (MC-OXCs) applying the
4(2m)-stage multicast network. The proposed WSNB full MC-OXC with two multicast
stages is power efficient in reducing splitting loss and has lower multicast
cost, compared with the one having three multicast stages. Partial MC-OXC
with only one multicast stage is proposed to further reduce the multicast
cost and splitting loss. The RNB MC-OXCs with one or two multicast stages
provide better performance at the respects of crosspoints, multicast cost,
and splitting loss than their WSNB counterparts.
© 2009 IEEE
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