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In our basic model, we study a stationary Poisson pattern of nodes on a lineembedded in an independent planar Poisson field of interfering nodes. Assumingslotted Aloha and the signal-to-interference-and-noise ratio capture condition,with the usual power-law path loss model and Rayleigh fading, we explicitlyevaluate several local and end-to-end performance characteristics related tothe nearest-neighbor packet relaying on this line, and study their dependenceon the model parameters (the density of relaying and interfering nodes, Alohatuning 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 randomlylocated on a straight road. The second use is to study a typical route tracedin a (general) planar ad-hoc network by some routing mechanism. The approach wehave chosen allows us to quantify the non-efficiency of long-distance routingin pure ad-hoc networks and evaluate a possible remedy for it in the form ofadditional fixed relaying nodes, called road-side units in a vehicular network.It also allows us to consider a more general field of interfering nodes andstudy the impact of the clustering of its nodes the routing performance. As aspecial case of a field with more clustering than the Poison field, we considera Poisson-line field of interfering nodes, in which all the nodes are randomlylocated on random straight lines. The comparison to our basic model reveals aparadox: clustering of interfering nodes decreases the outage probability of asingle (typical) transmission on the route, but increases the mean end-to-enddelay.

Random linear multihop relaying in a general field of interferers using spatial Aloha