Circular and radial design comparison of survivability in asymmetrical hierarchical networks

Communication networks are immensely important today, since both companies and individuals use numerous services that rely on them. This paper considers the design of hierarchical (communication) networks. We consider the survivability of asymmetrical hierarchical network flows (AHNF), when arcs failure and, hence, flow destruction is probable. In such networks, it is supposed that the remaining arc capacities are known and the guaranteed evaluation of the functional capability assumes finding the worst distribution of flow in the destructed network. Since, in the network flows, a unique efficiency criterion is not generally known or defined, we assess the quality of the network functioning by a measure of demands satisfaction, i.e. the fraction of satisfied demands at the sink nodes. With regard to this criterion, we construct the mathematical model of the network regardless of the design structure. Then, by defining a measure of satisfying the demands, we compute and compare the survivability of two well-known reserve designs, namely radial and circular reserves.