A Distributed Comparison Algorithm for Train Inauguration Protocols over Ethernet

In this paper, we carry out a detailed investigation on two Train Inauguration Protocols proposed by WG43 for IEC 61375-2-5: ETB Train Inauguration (ETBTI) and Train Topology Discovery Protocol(T$^2$DP). ETBTI uses Layer 2 LLDP to discovery neighbor peers and uses Layer 3 ETBIP to broadcast the information of single node to all the others. On the other hand, T$^2$DP focuses on Layer 2 and modifies LLDP protocol slightly to achieve topology discovery in a simple way. In our opinion, T$^2$DP is more simple and more efficient than ETBTI. At the same time, we propose a Distributed Comparison Algorithm(DCA) that can be adopted by both ETBTI and T$^2$DP, in order to establish a stable Connectivity Table. Through rigorous theoretical analysis, we proof that the DCA algorithm is convergent, and the broadcasting complexity and computation complexity of DCA algorithm are $\frac{2}{n}$ of the method used by both ETBTI and T$^2$DP. A significant performance improvement can be expected with a large number of $n$.