Communication networks

We consider the problem of sending a message in a communication network. Our networks are modeled by graphs. In our graphs we want to send a message from a vertex s, the sender, to a vertex r, the receiver, via paths from s tor. One difficulty we may encounter if we try sending the message along every possible s, r-path is that the receiver r will be flooded, so we focus our attention on certain finite protocols for sending the message from s to r. We study the probability that such a protocol successfully sends a message from s to r if the edges of the network live with probability p. We present some results and some open problems on this topic. Keywords: network, communication, protocol, two-terminal graph, two-terminal reliability polynomial