A signal-recovery system: asymptotic properties, and construction of an infinite-volume process

We consider a linear sequence of 'nodes', each of which can be in state 0 ( 'off') or I ('on'). Signals from outside are sent to the rightmost node and travel instantaneously as far as possible to the left along nodes which ar e 'on'. These nodes are immediately switched off, and become on again after a recovery time. The recovery times are independent exponentially distribu ted random variables. We present results for finite systems and use some of these results to construct an infinite-volume process (with signals 'comin g from infinity'), which has some peculiar properties. This construction is related to a question by Aldous and we hope that it sheds some light on, a nd stimulates further investigation of, that question. (C) 2001 Elsevier Sc ience B.V. All rights reserved.