Impact of Exit Flow on the Upstream Entry Capacity at Single-Lane Roundabouts Depending on Geometric Design

Traditionally, the quality-of-service assessment of a roundabout is only focused on the capacity of the individual entries. However, the exits also have an important impact on the performance of a roundabout since they can be temporarily blocked by prioritized crossing pedestrians. As a consequence, exiting vehicles may spill back from the blocked pedestrian crossing onto the circular roadway. At single-lane roundabouts this will cause a queue on the circle, which again can block the upstream entries and reduce their capacity. The extent of this effect is influenced by vehicle traffic volumes, pedestrian volumes, and also the geometric design of the specific roundabout. In practice, an analytical method would be desirable to estimate the effects of this phenomenon. This paper presents such a solution. As a starting point a mathematical model based on queuing theory is developed which calculates the probability of an entry to the roundabout being obstructed by a queue originating from the next exit downstream. This probability is applied to reduce the usual estimated capacity of the entry. The theoretical model is compared with microscopic simulations of a single-lane roundabout. As a result, a high correspondence between the theoretical approach and the simulation, along with a measurement at a real-world roundabout, becomes evident. Therefore, the model is recommended for practical application in, for example, the Highway Capacity Manual (HCM) or the German Highway Capacity Manual (HBS). A set of graphs is presented which can be introduced into such a standardized calculation procedure.