The Network Model

Abstract

In many applications like the oil pipe-line or the telecommunication system, the mission of the system is to transmit something from a source to a sink. The consecutive-k condition can be interpreted as that a node is connected by links to the next k nodes, and the transmission will fail at the node if and only if the next k nodes all fail. Two assumptions are tacitly made in such an interpretation. The first is that links never fail. The second is that the first and the last node always work for either failure would fail the transmission mission. Therefore it is convenient not to count the first node, called the source, and the last node, called the sink, as part of the consecutive system.