We consider a linear sequence of `nodes', each of which can be in state 0
(`off') or 1 (`on'). Signals from outside are sent to the rightmost node and
travel instantaneously as far as possible to the left along nodes which are
`on'. These nodes are immediately switched off, and become on again after a
recovery time. The recovery times are independent exponentially distributed
random variables.
We present properties for finite systems and use some of these properties to
construct an infinite-volume extension, with signals `coming from infinity'.
This construction is related to a question by D. Aldous and we expect that it
sheds some light on, and stimulates further investigation of, that question.Comment: 16 page