Delay Valuation in Rail Transport and Train Scheduling: a Simple Stylised Model 

Delay Valuation in Rail Transport and Train Scheduling: a Simple Stylised Model 


David MEUNIER, LVMT (UMR-T 9403, École Des Ponts, IFSTTAR, UPEM, UPE), Maria PEREZ-HERRERO, SNCF Réseau


We present a stylised model capturing basic mechanisms of train delays and use data from the French rail network for calibration and comparison with purely econometric estimates.


Road congestion speed-flow curve is well identified in the economics and transportation engineering literature. Static speed–traffic flow curves plotted by traffic engineers, which can be observed through road statistics, confirms for roads that a clear relationship exists between infrastructure usage (flow F) and service quality (speed S). As Hau (1992) shows, this engineer curve derived from observations of vehicle flows’ behaviour, can be converted to a travel time-flow curve. Using a constant value of time as a shadow price for the representative driver, travel time is then converted to a money basis which yields time cost, as for instance, congestion costs.

Despite the parallels between road and rail congestion described, rail sector presents special features that must be taken into account. In fact, no such curve exists in the much less atomistic rail mode, and very few studies have tried to estimate econometric relationships between train delays and train traffic (Gibson et al., 2002; Arup, 2013; Haith et al. 2013; Pérez-Herrero et al, 2014).

Rather than a statistical « macro » approach, we try here to start from a micro point of view, proposing a simple and stylised model which, although letting aside important rail features such as heterogeneity of train types and speeds or variability of train schedules, tries to capture basic mechanisms of the transmission of delays between trains.

We explore the relationship between initial train delay and total train delays, and between average delay and train frequency.

This approach will be based on an empirical research, using delay and traffic data from a mesh of data collection points over the French rail network. The data employed will allow us to know precisely the performance (reliability rate and delay) of the lines for diverse levels of traffic.

Deriving stylised indicator values from data on spot delays on the French rail network, we will estimate orders of magnitude of indicators such as delay transmission ratios and marginal congestion costs and, when possible, compare them with purely econometric estimates.


Association for European Transport