## Project Example: Source detection of delays in public transportation networks

### Research Objective

Delays in public transportation networks, such as railway systems, are not only an inconvenience for passengers, but are also a significant economic burden for the system operator. For instance, between April 2012 and March 2013, 20.4% of the German long-distance high-speed trains were more than five minutes delayed. A key element in reducing delays in public transportation networks is the successful identification of the delay source (also called origin) from a specific delay pattern. In this project, two approaches were suggested. a effective distance median and a backtracking method. The former is based on the structurally generic effective distance-based approach for the identification of infectious disease origins, and the latter is specifically designed for delay propagation. The performance analysis of the simulation study and the real examples (provided by “Deutsche Bahn”) show that both methods are effective for source detection and their performance complement each other.

### Statistical Methodology

- Network-based source detection approaches: effective distance median, a backtracking method, and centrality-based source detection.
- Descriptive network analysis
- Generalized additive models for location, shape and scale (GAMLSS)

### Software

Open-source software as R package NetOrigin (Origin Estimation for Propagation Processes on Complex Networks) is available on CRAN.

### Related Publications

- J. Manitz, J. Harbering, M. Schmidt, T. Kneib, and A. Schöbel (2014): Source Estimation for Propagation Processes on Complex Networks with an Application to Delays in Public Transportation Systems. Accepted at JRSS-C (Applied Statistics).
- J. Manitz with contributions by J. Harbering (2016). NetOrigin: An R package for network-based Origin Detection. R package version 1.0-2.
- J. Manitz, J. Harbering, M. Schmidt, T. Kneib, and A. Schöbel (2014): Network-based Source Detection: From Infectious Disease Spreading to Train Delay Propagation. Proceedings of the 29th International Workshop on Statistical Modelling. Volume 1. pp. 201-205.

### Remark

- Invited talk at Workshop “Statistical Network Science and its Applications” Cambridge, UK, in August 2016.