The dynamic lines of collaboration model: Collaborative disruption response in cyber–physical systems

•Model is established for collaborative response to ongoing cascading disruptions.•Performance metrics of the model are designed: response time, preventability, etc.•Our model is validated by numerical experiments & case study on water supply system.•Small-worldness hampers the removing of cascading disruptions by responders.•Efficient collaboration & centrality-based depot allocation improve performance. Cyber–physical systems (CPSs) are emerging engineered systems with combined efforts in cybernetics and computerized physical components. The pervasive links between CPS elements improve their connectivity, but inevitably enable failures to propagate to large-scale disasters. External responders (repair-agents) often need to collaborate concurrently with peers to perform emergency services and repair operations. Systematic understanding of the collaborative response to ongoing cascading failures is required for responders to effectively prepare response teams and arrange disruption response. Previous modeling approaches are lacking the ability to capture the dynamic interactions between a CPS and its response teams. In this work, the Dynamic Lines of Collaboration model for Collaborative Disruption Response (DLOC/CDR) is established. It can capture general requirements of collaborative responders to respond to and to resolve ongoing disruptions with cascading effects. Two depot allocation policies are tested and compared to examine the new model over different CPS structures. Four performance measures (response time, maximum cascade, travel distance by responders, and preventability) are designed to compare different parametric settings. It is observed from the experiments that the small-world phenomenon increases the difficulty of resolving cascading failures in CPSs by response resources. Experiments on both conceptual networks and the Hetch Hetchy water system case study validate that the collaboration ability and the centrality-based depot allocation policy improve the disruption response performance with statistical significance. While these experimental observations support intuitive rational, the model for DLOC/CDR also provides specific guidelines for emergency responders, and serves as a base model for future research in the effective disruption management and response area.