This article in German [1] and this source in Hungarian [2] demonstrate the concept with very clear charts you can likely understand without having to read the

This article in German [1] and this source in Hungarian [2] demonstrate the concept with very clear charts you can likely understand without having to read the labels. The distance-time graphs show that different trains move at different speeds: faster trains have a steeper slope, slower trains have a gentler slope and more spots where they dwell for a few minutes before advancing. You want your graph symmetric around various point-in-time axes, so that the scheduling is predictable. On the distance-time graph, if you've upgraded a line and can run faster trains, you can plot the train with an even steeper slope in the graph. But by doing so, you may miss more of the knots where many different lines in the graph come together. These knots in the graph are moments in space and time when several trains are at the same station around the same time: the time to change trains and make connections. The system works best when major hubs are roughly 1 hour apart, so you begin optimizing for that fact systemwide, instead of small, few-minute travel time reductions on individual lines. It may be the case that small improvements in travel time on one line don't outweigh the reduction in connection opportunities, so small improvements become harder to justify. You'd have to run certain trains much faster (and spend more money on faster tracks) to maintain the same level of connections in the network. [1] https://www.zukunft-mobilitaet.net/42868/analyse/integraler-taktfahrplan-itf-schweiz-deutschland-deutschlandtakt-umsetzbarkeit-konzept/ https://www.zukunft-mobilitaet.net/42868/analyse/integraler-... [2] http://www.itf.hu/index.php/alapfogalmak/integralt-uetemes-menetrend-itf http://www.itf.hu/index.php/alapfogalmak/integralt-uetemes-m...