A two component railway model exhibiting service collapse

We model a railway network in terms of the flow of trains, and of memory of how long crews have been on duty. We impose limits at stations on the throughput of trains, the duty time of crew, and the availability of fresh crew. In the regime where the traffic is limited by crew renewal, we find the system is linearly unstable with respect to spatial fluctuations leading to lengthening queues of trains. Numerical simulations show that this instability can lead to a collapse in service in which a majority of all trains are trapped queuing at a minority of stations.