Quantum routing protocols seek to distribute entanglement across different nodes of a quantum network. A recently popular approach for quantum routing is to cut down the latency times for sharing entanglement by using virtual edges in addition to physical ones. While a physical edge is associated with the presence of a quantum channel, virtual edges correspond to pre-existing entanglement between some nodes which can be leveraged for entanglement swapping. Distributed routing protocols for quantum networks have been proposed and analyzed using this idea. These analyses have also been backed up by simulations. However, to the best of our knowledge, existing simulation approaches consider a static picture, where the demands for entangled pairs are presented upfront. In this paper, we study routing algorithms through time-driven simulations. Such an approach allows for the demands to emerge in real-time as the simulation proceeds, and therefore mimic realistic scenarios better. This also facilitates studying routing protocols in the presence of dynamic replenishment of entangled pairs, and exposes issues like occurrence of deadlocks in the context of limited quantum resources. As a demonstration of the approach, we show simulation results that analyze the performance of various physical and virtual graph topologies in terms of average latency time. Finally, we show the change in performance and network saturation in the presence of replenishment of entanglement resources. © 2021 IEEE.