Optimal resource allocation for network functionality

The traditional approach to network robustness, is based on comparing network parameters before and after an event of nodes removal, such as the change in network diameter, the change in giant component size and the existence of giant component. Compared to the traditional approach, there is a later and innovative approach to network robustness, where the network functionality during its entire life span (during the node removal event) is considered. This approach considers nodes removal due toaging-non functionality of nodes when their survival time duration-theirlifetime-is passed. Accordingly, a problem that has to be solved is: in the network design stage, how to allocate a budget of lifetime between the network's nodes, such that the network functionality during all the stages of nodes removal due to aging, is maximized. To date, the problem has been solved only partially and numerically. In this paper we solve the problem analytically. Based on a local information only on the network's degree distributionp(k)without knowing the network's structure and topology, we derive a criterion for choosing the right set of nodes on which the total lifetime budget should be allocated, and find analytically the optimal way of allocating the lifetime budget between the chosen set's nodes, such that the network robustness with consideration to its functionality in the entire life span, is maximized.