A universal procedure for capacity determination at unsignalized (priority-controlled) intersections

This paper introduces a universal procedure for calculating the capacity at unsignalized (priority-controlled) intersections. This procedure can handle all possible stream and lane configurations (e.g., number of lanes and ranks of streams, etc.) at unsignalized intersections. For the simplest configuration with one major stream and one minor stream, a new universal capacity formula is introduced. The formula is based on the idea that the time scale of the major stream can be divided into four regimes according to the relative positions between the vehicles in the major stream: (1) that of free space (no vehicle), (2) that of single vehicle, (3) that of bunching, and (4) that of queuing. The probability of these regimes can be calculated according to queuing theory. Therefore, the capacity of the minor stream that depends predominantly on the probability of the state that no vehicle blocks the major streams (state of free space) can also be calculated. Combining the basic idea of Heidemann and Wegmann, some new explicit capacity formulae are derived considering the distributions of critical gaps, move-up times, and minimum time headways between two vehicles going in succession. Starting from this capacity formula for the simplest configuration with one major stream and one minor stream, a universal calculation procedure for configurations with arbitrarily many streams of arbitrary ranks is derived. This procedure is constructed according to the parallel or serial configurations of the streams. The present procedure is derived mathematically using queuing theory. It is a generation of all of the known procedures for calculation capacities at unsignalized intersection. The model is calibrated and verified by measurements at roundabouts and by intensive simulations. Based on the theoretical background, the model can easily be extended to other priority systems with arbitrary priority ranks.