Efficient handling of containers at a terminal can reduce the overall vessel sojourn times and minimise operational costs. The internal transport of containers in these terminals is performed by vehicles that share a common guide path. The throughput capacity of a terminal may increase by increasing the number of vehicles; however, simultaneously congestion may reduce the effective vehicle speed. We model this situation accurately using a traffic flow-based closed queuing network model. The vehicle internal transport is modelled using a load-dependent server that captures the interaction between the number of vehicles in a transport segment and the effective vehicle speed. Using a non-linear traffic flow model, we show that the throughput reductions due to vehicle congestion can be as large as 85%. Hence, the effect of vehicle congestion during internal transport cannot be ignored. The model can also be used to determine the appropriate number of vehicles required to achieve the required terminal throughput by explicitly considering the effect of vehicle congestion.