This paper describes the road traffic assignment model Static Traffic Assignment with Queuing (STAQ) that was developed for situations where both static (STA) and dynamic (DTA) traffic assignment models are insufficient: strategic applications on large-scale congested networks. The paper demonstrates how the model overcomes shortcomings in STA and DTA modelling approaches in the strategic context by describing its concept, methodology and solution algorithm as well as by presenting model applications on (small) theoretical and (large) real-life networks. The STAQ model captures flow metering and spillback effects of bottlenecks like in DTA models, while its input and computational requirements are only slightly higher than those of STA models. It does so in a very tractable fashion, and acquires high-precision user equilibria (relative gap < 1E-04) on large-scale networks. In light of its accuracy, robustness and accountability, the STAQ model is discussed as a viable alternative to STA and DTA modelling approaches.