Table 1 Overview of the model variables and parameters
From: Modelling railway delay propagation as diffusion-like spreading
Variable | Description |
|---|---|
\(D_{i}(t)\) | Delay at station i and time t |
\(A_{ji}\) | Adjacency matrix of the railway network |
\(B_{i}\) | Train turnover rate of station i |
\(d_{T}(t)\) | Delay carried by train T at time t |
\(f_{ij}\) | Train frequency from stations i to j |
\(\bar{t}_{ij}\) | Average travel time from station i to j |
\(p_{ji}\) | Fraction of trains to j that continues to i |
\(r_{ji}\) | Fraction of trains to j that continue to i if they do not end at j |
\(s_{j}\) | Fraction of trains that end at station j |
\(\mathcal{T}(i,t)\) | Set of trains moving to station i at time t |
\(\mathcal{N}_{\text{out}}(j)\) | Set of stations to which there is an edge from j |
\(\mathcal{N}_{\text{in}}(j)\) | Set of stations from which there is an edge towards j |
N | Amount of stations |
\(\delta _{ij}\) | Kronecker delta (\(\delta _{ij}=1\) if i = j, and 0 otherwise) |