# Planning-Level Optimisation of Headway Regularity
## 1 Introduction  
Public passenger transport (PPT) service operation reliability has a great influence on the passengers' perception of service quality. Ample body of evidence indicates that headway variability has a negative impact on the PPT operational functioning, as it results in increased cycle time and delays in the next vehicle departure, as well as in vehicle loading above capacity and vehicle bunching [1; 2; 3]. This operational variability also exerts a negative effect on the passengers' journey experience, as it increases the expected waiting times [4; 5; 6] and travel time uncertainty [7; 8] while reducing passenger comfort in the vehicle [9; 10; 11; 12]. Accordingly, maintaining regular headways and consistent travel times are the key attributes of reliable PPT services [6; 13; 14; 15]. However, in practice, effectively managing headway variability and vehicle bunching requires expert knowledge, data, technology and driver engagement [16]. Consequently, many control methods have been developed to assist with this process and mitigate the negative effects of vehicle bunching to improve PPT service quality. The planning process includes all the decisions that must be made before the system starts operation. The PPT system is complex in both structure and operation [17]. System management takes place sequentially through different planning phases--strategic, tactical and operational--and even during the actual functioning of the system, through real-timeoperations management [18; 19; 20]. The design of PPT lines and networks is implemented at a strategic level. Solving line design problems aims to maximize service quality within budget constraints [21]. Headway regularity and vehicle bunching problems occur in real-time operations, and they are stochastic in nature. It is difficult to prevent headway disturbances in advance. As a result, most of the methods developed at the operations management level regulate the real-time movement of vehicles (vehicle holding, skipping stops, limited passenger access, earlier vehicle turning) to resolve headway disturbances immediately. These methods aim to maintain headway regularity in Operations Management, intervening in the phase when the disturbance occurs. However, some methods are aimed at solving the problem of headway regularity in the earlier phase of the system management. At the planning level, the most commonly used methods are vehicle and crew scheduling problems [22; 23; 24; 25], signalised intersections [26; 27; 28], line length optimisation [13; 29; 30], line splitting [13], optimizing buffer time and cycle time [31; 32; 33; 34], introducing a PPT lane [35; 36] and increasing passenger boarding intensity [37; 38]. Unlike real-time methods, planning-level methods do not affect pre-existing headway disturbances. These methods pre-emptively increase the robustness and resistance of the PPT system to the occurrence and propagation of headway disturbances. Robustness is the ability of the system to withstand negative influences without the need for adaptation. [PERSON] and others point out that increasing robustness is the future direction of PPT system development to improve service reliability [19]. Headway disturbance tends to accumulate and propagate along the line [39]. Lines with a greater number of stops create more opportunities for headway disturbances to accumulate [13; 39]. On the other hand, owing to the technical-spatial conditions in the city centre (terminus), splitting diametrical lines into two radial lines can significantly improve the robustness of the PPT system to the propagation of headway disturbances, while also enhancing the headway regularity. However, line splitting also has some drawbacks, as it may result in journey disruption for a certain number of passengers who are required to make an additional transfer. In such cases, the splitting process can significantly increase the passenger travel time and reduce service quality.