Validation of a mathematical model to estimate turning movements as roundabouts using field data

In this paper, a mathematical model was presented and used to determine turning movements at roundabouts based on field data. Assumptions were made in order to simplify the model; such as no U_turns from and to the same arm of a roundabout, total traffic into the roundabout is equal to total traffic out of the roundabout and traffic is homogenous (i.e. mainly consisting of cars). Using Gaussian elimination, turning movements could be estimated for 3_, 4_ and 5_arm roundabouts for the indeterminate traffic stream movements when inflows and outflows for each arm of the roundabout is known together with a flow stream on one internal circulating (weaving) section between any two arms of the roundabout. The model has practical use in reducing the number of detectors or counters (whether automatic, videoing techniques or manual methods are in use) which are needed in collecting data to determine the estimated flows from and to the different parts of a roundabout. The reduction in the number of detectors (or traffic counts) could be due to site limitations caused by faulty or limited number of counters used, inaccessible sections for obtaining video images for later analysis (e.g. presence of sharp bends, buildings or large trees obscuring vision). The benefits in cut saving costs could be significant in terms of time and man-power needed on site, and this could depend on the amount of traffic flow through the roundabout. The model was validated against data obtained from different sites and the results were found to be satisfactory.