Queuing delay models for single-lane roundabouts†

This article presents an analytical model for a few important operational characteristics of single-lane roundabouts in the United States. In particular, we obtain renewal-based analytical expressions for the mean and variance of the time required for entry into the circulating stream for an arbitrary vehicle occupying the first position of the approach, regardless of the distribution of time headways for the circulating stream. These analytical models are subsequently applied in a M/G/1 queuing model to compute the steady-state average delay and length of the queue at the approach under stable conditions. The analytical models are validated by comparing numerical results for average delay with field observations obtained at six single-lane roundabout sites in the United States. The models are shown to perform well under a range of circulating stream flow rates.