IP networks have seen tremendous growth in not only their size and speed, but also in the volume of traffic they carry. Over-provisioning is commonly used to protect network performance against traffic variations, be they caused by failures or transient surges. This paper investigates the influence that increasing network size has on the efficacy of over-provisioning in absorbing a certain range of traffic variations and preserving performance guarantees. For that purpose, we develop a general model that accounts for network topology, base offered traffic, and traffic variations, and allows us to explore how their combination behaves as the network and the traffic it carries grow. The model's generality enables us to investigate several representative scenarios and to identify critical thresholds in the relation between network and traffic growth, which delineate regions where a given amount of over-provisioning provides increasingly better protection against traffic variations. The results offer insight into how to grow IP networks in order to enhance their robustness.