One dimensional cellular network with "spatial-ALOHA" protocol

We address the transmission of data packets from base stations to mobile terminals in a one-dimensional cellular network. The probability that a data packet successfully arrives at the destined mobile terminal highly depends on the activity of nearby co-channel base stations. Motivated by favorable results from earlier studies we consider a network in which all base stations use the same radio channel. Packets lost because of mutual interference are retransmitted with a random backoff mechanism. Recursive arguments are applied for the calculation of the mean time necessary for a base station to deliver the packet, provided that in an initial state all stations have packets to transmit. The average delivery time, maximized over all base station locations, is also analyzed. The relations obtained give some further insight into the behavior of a (highway) cellular data network.