Container terminal performance is largely determined by its design decisions, which include the number and type of quay cranes, stack cranes, transport vehicles, vehicle travel path and stack layout. We investigate the orientation of the stack layout (parallel or perpendicular to the quayside) on the throughput time performance of the terminals. Previous studies in this area typically use deterministic optimisation, and a few studies use probabilistic travel times and simulation to analyse the effect of stack layout on terminal throughput times. In this research, we capture the stochasticity with an integrated queuing network modelling approach to analyse the performance of container terminals with parallel stack layout using automated lifting vehicles. Using this analytical model, we investigate 1008 parallel stack layout configurations on throughput times and determine the optimal stack layout configuration. We find that, assuming an identical width of the internal transport area, container terminals with parallel stack layout perform better (from 4–12% in terms of container throughput times) than terminals with a perpendicular stack layout.