The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks and (ii) modeling the impact of energy-saving algorithms. The approach is based on the fluid-flow approximation, which applies first-order differential equations to analyze the evolution of queues and flows. We demonstrate that the effective implementation of this method overcomes the constraints of storing large data in numerical solutions of transient problems in vast network topologies. The model is implemented and executed directly in a database system. It can analyze transient states in topologies of more than 100,000 nodes, i.e., the size which was not considered until now. We use it to investigate the impact of an energy-saving algorithm on the performance of a vast network. We find that it reduces network congestion and save energy costs but significantly lower network throughput.