# Optimal resource allocation for network functionality

## TL;DR

This paper analytically addresses optimal lifetime resource allocation among network nodes to maximize overall network functionality during aging-induced node removal, advancing beyond previous partial and numerical solutions.

## Contribution

It provides an analytical solution and criterion for dividing node lifetimes to enhance network robustness over its entire lifespan.

## Key findings

- Derived an analytical criterion for node selection.
- Established the optimal division of lifetime budget.
- Maximized network functionality throughout node aging process.

## Abstract

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. Recently, a new approach to network robustness was presented, where the network functionality during its entire life span (during the node removal event) is considered. This approach considers nodes removal due to aging - a state where nodes can be degenerated and become nonfunctional, when their survival time duration - their lifetime - is passed. Accordingly, a problem that has to be solved is: in the network design stage, how to divide 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, and derive a criterion for choosing the right set of nodes on which the total lifetime budget should be divided. We also find analytically the best way of dividing the lifetime budget between the chosen set nodes, such that the network robustness with consideration to its functionality in the entire life span, is maximized.