  This paper contributes to the modeling and analysis of unsignalized
intersections. In classical gap acceptance models vehicles on the minor road
accept any gap greater than the CRITICAL gap, and reject gaps below this
threshold, where the gap is the time between two subsequent vehicles on the
major road. The main contribution of this paper is to develop a series of
generalizations of existing models, thus increasing the model's practical
applicability significantly. First, we incorporate {driver impatience behavior}
while allowing for a realistic merging behavior; we do so by distinguishing
between the critical gap and the merging time, thus allowing MULTIPLE vehicles
to use a sufficiently large gap. Incorporating this feature is particularly
challenging in models with driver impatience. Secondly, we allow for multiple
classes of gap acceptance behavior, enabling us to distinguish between
different driver types and/or different vehicle types. Thirdly, we use the
novel M$^X$/SM2/1 queueing model, which has batch arrivals, dependent service
times, and a different service-time distribution for vehicles arriving in an
empty queue on the minor road (where `service time' refers to the time required
to find a sufficiently large gap). This setup facilitates the analysis of the
service-time distribution of an arbitrary vehicle on the minor road and of the
queue length on the minor road. In particular, we can compute the MEAN service
time, thus enabling the evaluation of the capacity for the minor road vehicles.
