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At roundabouts where entering traffic is required to give way to traffic circulating in the roundabout, the traffic capacity of each entry is a function of the flow of traffic circulating past it. This relationship has previously been analysed in two main ways: using a linear relationship based on regression and using a non-linear relationship based on a model of entering drivers' acceptance of gaps in the circulating traffic. The linear analysis has previously been extended to estimation of the reserve capacity or degree of overload of the roundabout as a whole in relation to a given pattern of approaching traffic. The non-linear analysis is extended similarly in this paper.

The relationships between entry capacity and circulating flow imply in turn that the capacity of each entry is a function of the entering flows and the proportions of traffic making various movements through the junction from some or all of the entries. Equations are established for determining derivatives of capacity or delay on each entry with respect to the demand flow for each movement. In particular, it is shown that when the roundabout is overloaded the capacity of an entry can depend upon the demand flow on that same entry, giving rise to a corresponding term in the derivative of the delay-flow relationship for the approach concerned.