All-to-all broadcast communication, distributing messages from each node to every other node, is a dense communication pattern and finds numerous applications in advanced computing and communication networks from the control plane to datacenters. A ring network topology is one of the important regular network topologies due to its simple structure, high speed, easy to extend and tolerant to link and node failures. Few researchers recommended connecting the alternate nodes of the ring with additional fibers in the ring network, to support increased call connection probability, higher tolerable to multiple link and node failures, enormous traffic handling capability and improved survivability. To reduce the complicatedness and cost of the network, it is essential to reduce the wavelength-number required to establish all-to-all broadcast in wavelength-division multiplexed ring network. In this paper, a ring network is extended by directly linking all nodes which are separated by two intermediate nodes with additional fibers and this network is referred as ring with 3-length extension. The wavelength allotment methods are proposed for realizing all-to-all broadcast over a WDM optical bi-directional ring with 3-length extension under multiple unicast routing model using a two-stage heuristic algorithm. The heuristic algorithm is developed to identify non-overlapping connections and an explicit wavelength allotment method based on the output of the heuristic technique is given. The result obtained shows that wavelength-number required atmost to establish all-to-all broadcast in a bi-directional ring with 3-length extension is reduced by a minimum of 57% and a maximum of 66% when compared to bi-directional primary ring. Similarly, the wavelength-number required atmost to establish all-to-all broadcast in a bi-directional ring with 3-length extension is reduced by a minimum of 20% and a maximum of 33% when compared to a bi-directional ring with 2-length extension.
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