Clustering techniques to optimize railway daily path utilization for non-daily trains

A typical rail-network has a combination of daily trains and non-daily trains that have a weekly-pattern. Being non-daily, such trains run sporadically across the week and thus creates the problem of inefficient timetabling. Further, for large rail-networks, the timetabling is often done decentrally zone-wise without explicitly ensuring that groups of non-daily trains have similar running times on the bottleneck sections. In this paper, we use a notion of ‘dailyzing’ (making a daily path of non-daily trains) by performing a modulo 24 hours operation and then using Hierarchical Agglomerative Clustering (amongst other techniques) to group the trains. These clusters of trains share the same railway resources almost simultaneously but on different days of the week. Thus the scheduling of one representative train of the cluster as a ‘daily train’ would automatically schedule non-daily ones in that group. Hence, the daily path for non-daily trains provides a systematic and more efficient way of timetabling. The clustering/grouping of trains can also help find an empty slot for a new train scheduling/addition or help in point towards resource under-utilization.