A network appliance includes a network processor and several processing units. Packets a flow pair are received onto the network appliance. Without performing deep packet inspection on any packet of the flow pair, the network processor analyzes the flows, estimates therefrom the application protocol used, and determines a predicted future time when the next packet will likely be received. The network processor determines to send the next packet to a selected one of the processing units based in part on the predicted future time. In some cases, the network processor causes a cache of the selected processing unit to be preloaded shortly before the predicted future time. When the next packet is actually received, the packet is directed to the selected processing unit. In this way, packets are directed to processing units within the network appliance based on predicted future packet arrival times without the use of deep packet inspection.