Heavy competition between container terminals and the increasing volume of world-wide container shipment force container terminals to continuously increase productivity and reduce costs. An important condition for optimal operation of container terminals is that Quay Cranes (QCs) maximize their productive time, which requires a minimal lateness of Automated Guided Vehicles (AGVs) that bring and pick up containers at the QCs. In this research, the AGV driving strategy is investigated in order to reduce the time QCs are waiting for an AGV. A route plan scheduling module for AGVs is developed, in which the central system plans the driving positions of AGVs in advance, and determines in what order AGVs should cross intersections. For priority determination, a first-come first-served strategy is compared with an advanced priority strategy that gives priority to AGVs that are late or have an important job, like bringing a container to a QC. Furthermore, the impact of AGVs' greediness for crossing intersections is investigated by comparing a greedy strategy with a non-greedy strategy. By testing the priority and greediness strategies in a state-of-the-art simulation environment that was extended with our route plan scheduling module, it is found that advanced priorities reduce QC waiting time and improve QC productivity compared to the first-come first-served priority strategy. The non-greedy strategy gives a small decrease of the AGV driving delay compared to the greedy strategy. To investigate the full potential of using advanced priorities in a system with route plan scheduling, the route plans should better predict the AGV driving behavior, for which we suggest to use a more detailed AGV planning strategy. Finally, we discuss that AGV driving with reduced inter-vehicle distance is a promising approach to improve terminal performance.