  We consider a stochastic queueing system modelling the behaviour of a
wireless network with nodes employing a discrete-time version of the standard
decentralised medium access algorithm. The system is {\em unsaturated} -- each
node receives an exogenous flow of packets at the rate $\lambda$ packets per
time slot. Each packet takes one slot to transmit, but neighboring nodes cannot
transmit simultaneously. The algorithm we study is {\em standard} in that: a
node with empty queue does {\em not} compete for medium access; the access
procedure by a node does {\em not} depend on its queue length, as long as it is
non-zero. Two system topologies are considered, with nodes arranged in a circle
and in a line. We prove that, for either topology, the system is stochastically
stable under condition $\lambda < 2/5$. This result is intuitive for the circle
topology as the throughput each node receives in a saturated system (with
infinite queues) is equal to the so called {\em parking constant}, which is
larger than $2/5$. (The latter fact, however, does not help to prove our
result.) The result is not intuitive at all for the line topology as in a
saturated system some nodes receive a throughput lower than $2/5$.

Networking and Internet Architecture;Probability