The aim of this paper is to analyze the Aloha medium access (MAC) scheme in one-dimensional, linear networks, which might be an appropriate assumption for Vehicular Ad-hoc NETworks (VANETs). The locations of the vehicles are assumed to follow a homegeneous Poisson point process. Assuming powerlaw mean path-loss and independent point-to-point fading we study performance metrics based on the signal-over-interference and noise ratio (SINR). In contrast to previous studies where the receivers are at a fixed distance from the transmitter, we assume here that the receivers are the nearest neighbors of the transmitters in the Poisson process and in a given direction. We derive closed formulas for the capture probability and for the density of progress of a packet sent by a given node. We compute the mean delay to send a packet transmitted at each slot until successful reception. We also evaluate an upper bound to discover the neighborhood within a given space interval. We show that we can include noise in the previous models.