# Planning-Level Optimisation of Headway Regularity
## 6 Conclusions  
This research was carried out to create a tool that could be applied in practice to evaluate the benefits/drawbacks of splitting a diametrical line from the point of view of passenger travel time and headway regularity. The application of the optimisation procedure presented here is foreseen in the system design phase, as it can contribute to the robustness/resistance of the PPT to the propagation of headway disturbances. Line splitting interrupts the accumulation of headway disturbances and improves headway regularity. However, evaluating the positive and negative effects of line splitting is a complex problem, considering that these effects are a function of the primary headway disturbance values, transport demand, actual headways, number of stops and other parameters. As a part of this work, an optimisation procedure was developed to determine the change in the average passenger journey due to line splitting. Most of the currently available methods are based on mitigating the headway disturbances in real time, whereas the optimisation procedure developed as a part of the present study increases the PPT resistance to the propagation of headway disturbances in the design stage. This is also the first attempt to develop a model that can determine the change in average passenger travel time owing to line splitting. The validity of the optimisation procedure was confirmed on a real example, which indicated that line splitting is beneficial during peak periods because it results in significantly fewer primary headway disturbances. Moreover, the sensitivity analysis focusing on headway and transport demand demonstrated that the transport demand is positively correlated to the effects of the optimisation procedure, whereby increasing the primary headway disturbance increases the sensitivity of the optimisation procedure to the transport demand. On the other hand, there is a negative correlation between the headway duration and the optimisation procedure effects. Specifically, the sensitivity of the optimisation procedure to headway increases as the primary disturbance value increases. However, this effect is only observed for headway regularity, while the sensitivity does not increase when passenger travel time is observed. These analyses confirm the validity of the proposed model, but also indicate that the optimisation procedure (line splitting) is most beneficial for lines with short headway and high transport demand where the primary headway disturbances exceed 2 min. Figure 12: Sensitivity of passenger travel time to changes in headway. While these findings are certainly beneficial, the proposed optimisation procedure can be further enhanced by introducing additional criteria such as the load factor, allowing for multi-criteria evaluation. In addition, as the value and location of the headway disturbances are in practice rarely known with certainty, the existing model could be extended by incorporating a fuzzy logic approach. Finally, authors of future studies in this domain could develop a hybrid method that would combine the proposed optimisation procedure at the planning level with some of the models for increasing headway regularity in real time. Conceptualization, P.P. and M.S. ([PERSON]); methodology, P.P. and M.S. ([PERSON]); software, P.P. ; validation, T.K., M.M. and D.M. ; formal analysis, M.S. ([PERSON]), Z.C. and M.M. ; investigation, T.K. and M.S. ([PERSON]); writing--original draft preparation, P.P. and T.K. ; writing--review and editing, P.P., M.S. ([PERSON]) and T.K. ; visualization, P.P. and D.M. All authors have read and agreed to the published version of the manuscript. This research has been supported by the Ministry of Science, Technological Development and Innovation (Contract No. 451-03-65/2024-03/200156) and the Faculty of Technical Sciences, University of Novi Sad through project \"Scientific and Artistic Research Work of Researchers in Teaching and Associate Positions at the Faculty of Technical Sciences, University of Novi Sad\" (No. 01-3394/1). Not applicable.