Capacity at Unsignalized Intersections

This report presents a unified theoretical analysis of capacity at unsignalized intersections. Potential capacity equations for different headway and gap acceptance functions are persented following the results of earlied researchers. The capacity analysis for multiple independent major streams is based on the theory of superimposed point processes. A very general capacity equation is presented, which can also be applied in the Rank 3 capacity analysis. Gap acceptance and queue discharge of a Rank 3 stream is described as a queuing model. It demonstrates that in the current methodology the probability of a queue-free state in Rank 2 streams should be modified. In addition, the headway distribution during a queue-free state should have a minimum headway equal to the follow-up time, and the flow rate should be adjusted accordingly. If the arrivals to an intersection are Poisson processes, the headways of Rank 2 streams during the queue-free periods follow shifted exponential distribution. The modified movement capacity equations are presented. The resulting capacities are higher than the HCM2000 capacities, especially at low traffic volumes. In the analysis of Rank 4 capacity the dependency of Rank 3 queues on Rank 2 queues has been considered problematic. However, it is demonstrated that the v/c ratio of a Rank 3 stream j gives the probability that a stream j vehicle is being served (waiting for a gap or a follow-up time) given that there are no Rank 2 vehicles in the service system. Therefore, the v/c ratio contains the necessary information of this dependency. Thus, when the capacities of major streams are known, their relative priorities can be ignored in the capacity estimation of a minor flow. This makes the analysis much simpler, and the capacity equation for Rank 4 streams does not become too complicated. In fact, the same equation can be used to estimate the movement capacity of both Rank 3 and Rank 4 streams. The resulting capacities are higher than suggested by the HCM2000 method.

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