On the multicast capacity of unidirectional and bidirectional packet-switched WDM ring networks

In this paper we examine the relationship between the effective capacity (stability limit) of unidirectional and bidirectional packet-switched wavelength division multiplexing (WDM) ring networks for multicast traffic. We consider both bidirectional rings with one packet copy transmission per wavelength channel and two packet copy transmissions. We first prove bounds for the ratio of the multicast capacity of the bidirectional ring to the multicast capacity of the unidirectional ring. Specifically, we show that this ratio is at least two for two copy transmission in the bidirectional ring, and at most two for one copy transmission. We derive closed form expressions of the multicast capacity ratios for networks with a large number of nodes and from these expressions show that the ratios tend to two for a large number of multicast destinations. We demonstrate that for the bidirectional ring with two copy transmission the ratio becomes as large as 2.276. We also find that in the bidirectional ring, the capacity gain with two copy transmission over one copy transmission reaches 30.4%