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.

Interacting random processes; statistical mechanics type models; percolation theory (msc 60K35), Time-dependent percolation (msc 82C43), Population dynamics (general) (msc 92D25)
Logistics (theme 3), Energy (theme 4)
CWI
CWI. Probability, Networks and Algorithms [PNA]
Stochastics

van den Berg, J, & Tóth, B. (2000). A signal-recovery system : asymptotic properties, and construction of an infinite-volume limit. CWI. Probability, Networks and Algorithms [PNA]. CWI.