The divisibility index as a theoretical tool to support public transport design

Abstract Along a corridor, a service may operate as a single line or be divided into segments. We investigate theoretically under which conditions a divided line is better than a single line. We identify three conditions that favor the line split at a particular stop, namely (i) few induced transfers, (ii) a large difference in the maximum flows between the two segments, and (iii) the segment with the lower maximum flow being long. These elements are combined into a single metric, the Divisibility Index (DI). Using the DI, we propose two algorithms that quickly determine whether and where to divide a line, and that can be integrated into existing network design tools. The approach is numerically tested in a simulated linear city and with Canberra light-rail data, producing results that reproduce the optimal division cost with an average error of 0.1% and demonstrate the correlation between DI and optimal division, respectively.