  This paper considers an unsignalized intersection used by two traffic
streams. A stream of cars is using a primary road, and has priority over the
other, low-priority, stream. Cars belonging to the latter stream cross the
primary road if the gaps between two subsequent cars on the primary road is
larger than their critical headways. Questions that naturally arise are: given
the arrival pattern of the cars on the primary road, what is the maximum
arrival rate of low-priority cars such that the number of such cars remains
stable? In the second place, what can be said about the delay experienced by a
typical car at the secondary road? This paper addresses such issues by
considering a compact model that sheds light on the dynamics of the considered
unsignalized intersection. The model, which is of a queueing-theoretic nature,
reveals interesting insights into the impact of the user behavior on the above
stability and delay issues. The contribution of this paper is twofold. First,
we obtain new results for the aforementioned model with driver impatience.
Secondly, we reveal some surprising aspects that have remained unobserved in
the existing literature so far, many of which are caused by the fact that the
capacity of the minor road cannot be expressed in terms of the \emph{mean} gap
size; instead more detailed characteristics of the critical headway
distribution play a role.
