2. Literature Review
Maintaining a headway on a bus route is one of the key tasks for operators to keep bus systems running on schedule. The phenomenon of bus bunching, first studied by Newell and Potts [
6,
7,
8], refers to two or more buses on the same route arriving at the same time at a bus stop. Among the many studies on bus bunching, most have focused on mitigating the phenomenon after its occurrence in the past several decades.
Generally, the approaches used to mitigate bus bunching and improve the reliability of bus services can be divided into two categories based on the types of strategies designed by bus operators: schedule-based methods and operational-based methods. Schedule-based methods are conventional approaches that incorporate slack time (the difference between scheduled and actual arrival time) into schedules to alleviate bus bunching and maintain regular schedules [
9,
10,
11,
12]. However, schedule-based methods are suitable for a bus system with a low density of services. For high-density services, it is difficult for buses to follow fixed timetables, especially in areas with irregular ridership and frequent traffic congestion [
11]. Therefore, schedule-based methods are not effective for solving bus bunching problems practically. Operational-based methods refer to a series of control strategies, such as dynamic holding [
12,
13,
14], stop-skipping [
15,
16] and limiting the number of people on board [
17]. These strategies can overcome small perturbations and alleviate bus bunching problems, but some negative influences are generated, such as holding strategies reducing the bus speed significantly [
7].
To overcome the weakness of schedule-based and operational-based methods, road network operators can control signal timings to alleviate bus bunching with bus operators [
7]. Signal-timing schemes with BSP/TSP can not only improve traffic efficiency [
18,
19] but also improve the reliability of bus services [
20,
21]. For better reliability and punctuality of bus services, a series of Conditional Signal Priority (CSP) models were built to serve the bus priority requests distinctively [
7,
22,
23,
24,
25,
26]. The impacts of CSP on service reliability were investigated using a simulation platform, and the findings showed that the improvement of the CSP in bus service reliability was 3.2% when compared with a non-priority scenario [
24]. However, one limitation is that bus arrival times at the following downstream intersections had not been considered in the CSP strategies. To address this limitation, multi-objective optimal CSP frameworks for maximising bus service reliability were developed where both deviations with respect to the headway as well as corresponding additional delays induced by general traffic were considered [
21,
22,
23]. Recently, a selective CSP scheme was introduced, which set bus priority only when the requests could improve service reliability [
7].
Although the above studies have demonstrated the effectiveness of the existing CSP when compared to no-CSP cases, there remain several challenges in the application of the CSP in practice. Firstly, most existing strategies are often off-line calibrated using historical statistical data to evaluate the effect of signal controls [
7,
21,
22,
23]. Among the many examples of the CSP strategies that can respond to real-time traffic situations simulated by professional traffic simulation platforms (such as VISSIM and SUMO) have not been extensively studied. Secondly, many existing studies on the CSP focus on the improvement of buses which are behind schedule. For a bus system with high-frequency services, however, it is more practical to balance the headway when compared with keeping buses following a regular headway. Any buses that disturb the headway balance should be controlled. Finally, given that the cycle duration is a variable in these CSP studies, signal operators need to know when and how to induce the signal timing back to the baseline. Few of the above studies have discussed this practical question.
Therefore, the main objective of this paper is to propose an online optimisation model to minimise the variability of the headway of the bus sequence by adjusting signal restoration, cycle extension and splits. The specific modelling process is introduced in the following sections.
Author Contributions
Conceptualization, X.Z.; methodology, X.Z.; simulation, X.Z.; formal analysis, X.Z.; writing—original draft preparation, X.Z.; writing—review and editing, X.Z., F.G. and R.K.; supervision, F.G. and R.K. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
No new data were created or analysed in this study.
Conflicts of Interest
The authors declare no conflict of interest.
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