Figure 2

Delays and train interactions. (A) Distributions of the delay at the final and at the intermediate stations trains in both Italian and German datasets. Departure delays at the initial station has been subtracted, hence these delays originated during the travel. As a guide for the eye, a power-law has been added in the positive delay area and an exponential in the advance area (negative delay). (B) Average delay of a link as a function of the link k-order co-activities, with Spearman’s correlation coefficients showing the existence of a relation between the co-activity and the average delay. The curves have been obtained by binning the data on the x-axis at steps of 0.2 and reporting the average and the standard error. (C) Cross-Correlations \(C(dt)\) from equation (1) as a function of dt for the average delay time series of pairs of nearby links in the railway networks in the “Forward” and “Backward” configurations (shown in Fig. 3), and in the “Connection” configuration