A new measure of resilience: An application to the London Underground

The many varied views on resilience indicate that it is an important concept which has significance in many disciplines, from ecology to psychology to risk/disaster management. Therefore, it is important to be able to quantifiably measure the resilience of systems, and thus be able to make decisions on how the resilience of the system can be improved. In this paper we will work with the definition, due to Pimm (1991), that resilience is “how fast a variable that has been displaced from equilibrium returns to it.” We will think of a system as being more or less resilient depending on the speed with which a system recovers from disruptive events or shocks. Here we consider systems which revert to an equilibrium state from shocks, and introduce a measure of resilience by providing a quantification of the rapidity of these systems’ recovery from shocks.We use a mean-reverting stochastic model to study the diffusive effects of shocks and we apply this model to the case of the London Underground. As a shock diffuses through the network, the human-flow in the network recovers from the shock. The speed with which the passenger counts return to normal is an indicator of how quickly the line is able to recover from the shock and thereafter resume normal operations.