We propose a membership protocol for group communications in mobile Internet. The protocol is called RGB, which is the acronym of "a Ring-based hierarchy of access proxies, access Gateways, and Border routers". RGB runs in a parallel and distributed way in the sense that each network entity in the ring-based hierarchy maintains local information about its possible leader, previous, next, parent and child neighbors, and that each network entity independently collects/generates membership change information, which is propagated by the one-round membership algorithm concurrently running in all the logical rings. We prove that the proposed protocol is scalable in the sense that the scalability of a ring-based hierarchy is as good as that of a tree-based hierarchy. We also prove that the proposed protocol is reliable, in the sense that, with high probability of 99.500%, a ring-based hierarchy with up to 1000 access proxies attached by a large number of mobile hosts will not partition when node faulty probability is bounded by 0.1%; if at most 3 partitions are allowed, then the Function-Well probability of the hierarchy is 99.999% accordingly. |