Maximal selection in tandem networks with symmetric hearing range

We consider an infinite tandem network in which every node is capable of hearing its neighbors up to a given distancen. At any moment of time every node may contain in the top of its queue a message destined to one of its neighbors. This network can be used as a model for a microwave or optic link with many users. For small and largen we investigate the maximal selection of nodes in the network, for which their transmissions are collision-free. For a large hearing range we show that the upper bound on the maximal selection, which is found herein, is asymptotically achievable. For small hearing ranges we show that a greedy selection is better but not asymptotically optimal. We also specify a sequence of upper bounds which converge to the maximal throughput.This research was done while J. M. Jaffe was on leave at the IBM Israel Scientific Center.