A generalized mathematical model to determine the turning movement counts at roundabouts

Traffic turning movement counts at roundabouts is one of the key inputs required for roundabout assessment, control and management. Traditionally, a direct counting is conducted to track a vehicle from entering through circulation until exiting. This counting may be difficult and costly due to the size of roundabout, the vision obstacles, and the continuous traffic flow. Many researchers tried to avoid the tracking problem by counting only at entries and exits, then estimating the movements based on historical data which unfortunately affect the results. Other researchers reduced the tracking problem by counting some turning movements in addition to at entries and exits, then calculating mathematically the remaining movements. This approach is practical and accurate; however, it was applied on limited cases. In this paper, a generalized mathematical model was developed to calculate the most difficult movements based on the easiest movements determined based on the size of monitoring area. The developed model can be used to calculate the turning movements, including the u-turns, for roundabouts with any number of legs. The developed model was presented in O–D matrix forms to be practical and user-friendly. The model was validated against reference count data and the results were found to be satisfactory.