  We analyse an ALOHA-type random multiple-access protocol where users have
local interactions. We show that the fluid model of the system workload
satisfies a certain differential equation. We obtain a sufficient condition for
the stability of this differential equation and deduce from that a sufficient
condition for the stability of the protocol. We discuss the necessary
condition. Further, for the underlying Markov chain, we estimate the rate of
convergence to the stationary distribution. Then we establish an interesting
and unexpected result showing that the main diagonal is locally unstable if the
input rate is sufficiently small. Finally, we consider two generalisations of
the model.
