Reliable flow with failures in a network

In communication networks, there is a growing need for ensuring that networks maintain service despite failures. To meet this need, the concept of a δ-reliable channel is introduced; it is a set of communication channels along a set of paths. The δ-reliable channel meets the requirement that if a link or node fails, failure is limited to a maximum of δ·c (c≡total capacity of the channels, and 0<δ⩽1). A δ-reliable flow is such that the maximum number of flow failures is δ·f (f≡value of the flow) if an edge or vertex of a network fails. The max-flow min-cut theorem of δ-reliable flow is demonstrated for the single-commodity case