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In this paper, we propose a new model to study traffic flow at a single-lane urban roundabout, using a multi-state cellular automata (CA) ring under the offside-priority rule (by which a vehicle entering gives way to one already on the roundabout). Each vehicle entering the roundabout is randomly characterized by a predetermined exit with specified probability. Driver behavior at the roundabout entrance is randomly grouped into four categories based on space required to enter the roundabout. Three aspects of roundabout performance in particular have been studied. The first looks at overall throughput (the number of vehicles that navigate the roundabout in a given time). This is considered for different geometries, turning and arrival rates (vehicles arrive at random with a Poisson distribution, with parameter λ⩽0.5 in general for free flow). The second investigates changes in queue length, delay time and vehicle …