  In our basic model, we study a stationary Poisson pattern of nodes on a line
embedded in an independent planar Poisson field of interfering nodes. Assuming
slotted Aloha and the signal-to-interference-and-noise ratio capture condition,
with the usual power-law path loss model and Rayleigh fading, we explicitly
evaluate several local and end-to-end performance characteristics related to
the nearest-neighbor packet relaying on this line, and study their dependence
on the model parameters (the density of relaying and interfering nodes, Aloha
tuning and the external noise power). Our model can be applied in two cases:
the first use is for vehicular ad-hoc networks, where vehicles are randomly
located on a straight road. The second use is to study a typical route traced
in a (general) planar ad-hoc network by some routing mechanism. The approach we
have chosen allows us to quantify the non-efficiency of long-distance routing
in pure ad-hoc networks and evaluate a possible remedy for it in the form of
additional fixed relaying nodes, called road-side units in a vehicular network.
It also allows us to consider a more general field of interfering nodes and
study the impact of the clustering of its nodes the routing performance. As a
special case of a field with more clustering than the Poison field, we consider
a Poisson-line field of interfering nodes, in which all the nodes are randomly
located on random straight lines. The comparison to our basic model reveals a
paradox: clustering of interfering nodes decreases the outage probability of a
single (typical) transmission on the route, but increases the mean end-to-end
delay.
