A new variant of cellular automata (CA) models is proposed, based on Minimum Acceptable Space (MAP) rules, to study unsignalised traffic flow at two-way stop-controlled (TWSC) intersections and roundabouts in urban and interurban networks. Categorisation of different driver behaviour is possible, based on different space requirements (MAPs), which allow a variety of conditions to be considered. Driver behaviour may be randomly categorised as rational, (when optimum conditions of entry are realised), conservative, urgent and radical, with specified probabilities at each time step. The model can successfully simulate both heterogeneous and inconsistent driver behaviour and interactions at the different road features. The impact of driver behaviour on the overall performance of intersections and roundabouts can be quantified and conditions for gridlock determined. Theorems on roundabout size and throughput are given. The relationship between these measures is clearly non-monotonic. Whereas previous models consider these road features in terms of T-intersections, our approach is new in that each is a unified system. Hence, the relationship between arrival rates on entrance roads can be studied and critical arrival rates can be identified under varied traffic and geometric conditions. The potential for extending the model to entire urban and interurban networks is discussed.