Modeling train delays in urban networks

The reliability of urban passenger trains is a critical performance measure for passenger satisfaction and ultimately market share. A delay to one train in a peak period can have a severe effect on the schedule adherence of other trains. This paper presents an analytically based model to quantify the expected positive delay for individual passenger trains and track links in an urban rail network. The model specifically addresses direct delay to trains, knock-on delays to other trains, and delays at scheduled connections. A solution to the resultant system of equations is found using an iterative refinement algorithm. Model validation, which is carried out using a real-life suburban train network consisting of 157 trains, shows the model estimates to be on average within 8% of those obtained from a large scale simulation. Also discussed, is the application of the model to assess the consequences of increased scheduled slack time as well as investment strategies designed to reduce delay.