# Planning-Level Optimisation of Headway Regularity
## 2 Literature Review  
[PERSON] [40] was one of the first researchers to analyse headway variability. As a part of his work, [PERSON] studied the operation of buses and trains in London, aiming to identify the causes and effects of headway variability as well as factors that lead to bus bunching on the line. This research motivated [PERSON] and [PERSON] [1] to examine the movement of buses when a bus travelling on the same line arrives late at a stop. Their findings revealed that headway disturbances exert two basic effects on bus movement--delays resulting in late arrival at the stop, along with the tendency of vehicles following the late vehicle to move ahead--resulting in vehicle bunching. In contrast to previous research [1; 2], [PERSON] and [PERSON] [3] emphasised the significant influence of vehicle movement variation between stops on vehicle bunching. According to these authors, the generated headway disturbance is propagated by stops along the line as well as by scheduled vehicles. Subsequent research confirms these findings, indicating that, if headway regularity is not actively controlled, vehicle bunching may occur [13; 41; 42; 43]. It has been empirically demonstrated in several studies that vehicle bunching is primarily caused by variability in vehicle movements at the beginning of the route, vehicle frequency, number of passengers boarding or alighting from the vehicle, boarding intensity, and number of stops/line length [2; 14; 39; 44; 45]. In the latest research, the authors evaluate already developed methods under different conditions. [PERSON] et al. [46] examined the impact of bus driver behaviour variability on the performance of the vehicle holding method developed by [PERSON] et al. [47]. In their paper, [PERSON] et al. [48] used deep reinforcement learning and existing methods (dwell time at stops, speed between stations, and signal priority) to minimize travel duration and ensure bus stability to avoid bus bunching. On the other hand, [PERSON] and [PERSON] [49] conducted a service quality risk assessment for a PPT system by constructing a quality risk assessment model that integrated [PERSON]'s model, IPA and FMEA. Given the adverse impacts of vehicle bunching on the PPT service quality, many control methods have been developed to mitigate this issue, which can be broadly divided into two groups [50]:  
* Real-time strategies: operational-level methods aimed at increasing service quality by introducing additional vehicles to the line, stop skipping and/or vehicle holding;
* Strategies implemented at the planning level: long-term strategies that require route and timetable information, including any changes. Well-designed management methods can simultaneously reduce users' travel time and operational costs [51], which is typically achieved through vehicle holding based on either schedule or headway [5]. The schedule-holding method involves holding vehicles at stops and/or additional control points that are ahead of schedule. While this method is effective in mitigating vehicle bunching, it also reduces the PPT operating speed. On the other hand, the headway-based holding method aims to maintain the designed headway. [PERSON] and [PERSON] [4] were the first to apply this method to a circular route in an idealised environment. These authors analysed the movement of two buses using a single control point and concluded that bunching could be adequately mitigated using this approach. In the subsequent period, several attempts have been made to improve the vehicle holding method by applying it at only one control point [52; 53], or at several control points along the corridor [54; 55; 56]. In a number of the proposed models, the vehicle capacity is limited, i.e., passengers cannot board the vehicle once it has reached the maximum capacity [5; 47; 50; 57]. More recently, motivated by advances in machine learning technologies, [PERSON] and [PERSON] [58] adopted a reinforcement learning framework to determine the most optimal vehicle holding time.