Telecom mesh networks require periodic upgrades to support increasing traffic. Such upgrades, which are referred to as network engineering (NE), determine the additional network resources that must be provided to meet the network performance while minimizing the incremental network cost. To facilitate such network growth, considering dynamic routing, attention should be directed toward critical cut sets rather than individual links. Our analysis in this paper shows how capacity exhaustion of critical cut sets indicates urgency of the need for upgrading a mesh network. To handle traffic growth, we also introduce a new parameter called the network-cut exhaustion probability. This parameter is efficient and appropriate to assist incremental growth of the existing network as well as new network design. Finally, we provide an algorithm to calculate the urgency and the pointers to specific locations that require upgrade under desired performance constraints.