Steven Harrod

Modeling Network Transition Constraints with Hypergraphs

Discrete time dynamic graphs are frequently used to model multicommodity flows or activity paths through constrained resources, but simple graphs fail to capture the interaction effects of resource transitions. The resulting schedules are not operationally feasible, and return inflated objective values. A directed hypergraph formulation is derived to address railway network sequencing constraints, and an experimental problem sample solved to estimate the magnitude of objective inflation when interaction effects are ignored. The model is used to demonstrate the value of advance scheduling of train paths on a busy North American railway.

Application of Data Clustering to Railway Delay Pattern Recognition

K-means clustering is employed to identify recurrent delay patterns on a high traffic railway line north of Copenhagen, Denmark. The clusters identify behavioral patterns in the very large (“big data”) datasets generated automatically and continuously by the railway signal system. The results reveal the conditions where corrective actions are necessary, showing the cases where recurrent delay patterns take place. Delay profiles and delay change profiles are generated from timestamps to compare different train runs and to partition the set of observations into groups of similar elements. K-means clustering can identify and discriminate different patterns affecting the same stations, which is otherwise difficult in previous approaches based on visual inspection. Classical methods of univariate analysis do not reveal these patterns. The demonstrated methodology is scalable and can be applied to any system of transport.

Delay estimation on a railway-line with smart use of micro-simulation

(27/10/2019) Delay estimation on a railway-line with smart use of micro-simulation This paper formulates a delay propagation model that estimates total railway line delay as a polynomial function of a single primary delay. The estimate is derived from a finite series of delays over a horizon that spans two dimensions: the length of the railway line and the number of trains in the service plan. The paper shows that the total delay estimate is a cubic relation for small primary delays. A probabilistic approach is presented to combine the total delay functions of primary delays given to different trains. The final estimate is the total delay on railway lines, after a random incident has occurred. The model can be integrated in railway timetable analysis to reduce the number of necessary simulations, and can be used when the computation speed is an issue, such as on-line rescheduling algorithms. The model is demonstrated with an analysis of a Danish suburban railway.