# Passenger Flow-Oriented Metro Operation without Timetables
## 2 Literature Review
(5) Skipping strategy, used by most metro systems with high passenger demands, allows some late trains online to skip low-demand stations to recover the timetable. Real-time rail operation research is also popular in the current decade. Some existing research has focused on fast optimisation for a specific operation in a particular circumstance to increase the stability of the system and avoid delay, such as the authors of [24; 27; 37] considering the optimisation of the trains' order in the junction area to minimise delay. The other real-time research is about rescheduling after an incident; this research focused on correcting the timetable to normal to minimise the impacts from disturbance or disruption that already occurs, such as [29; 38; 39]. As is apparent from the above review, most rail operation research is based on a predefined timetable, and most scheduling-related research is engaged to propose a robust timetable (dynamic or periodic) according to different requirements. Most rescheduling-related research focuses on reducing the impact on the timetable from incidents to recover trains' operation or to optimise a specific operation to increase system stability. The comparisons of representative metro operation research and this research are listed in Table 1 below. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Studies** & **Modelling Method** & **Methodologies** & **Proposal** \\ \hline [PERSON] et al. (2011) & Mixed-integer nonlinear programming & Heuristic algorithm & Periodic timetables \\ \hline [PERSON] et al. (2017) & Mixed-integer linear programming & Heuristic algorithm & Dynamic timetables \\ \hline [PERSON] et al. (2004) & Integer programming & Epsilon constrained method & Dynamic scheduling method \\ \hline [PERSON] et al. (2013) & Nonlinear programming & Fuzzy multi-objective optimisation algorithm & Dynamic scheduling method \\ \hline [PERSON] et al. (2007) & Graph model & Graph theory & Rescheduling after disturbance \\ \hline [PERSON] et al. (2012) & Mixed-integer linear programming & Heuristic algorithm & Real-time traffic management in junction areas \\ \hline This research & Integer programming & Heuristic algorithm and simulation method & Real-time passenger flow monitoring based metro operation method \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons of representative metro operation research. In this paper, the authors focus on proposing a new metro operation method to satisfy real-time detected passenger flow without timetables. As a result, the overall objective is to establish a systematic methodology to keep adjusting operation strategies for an urban metro line to replace predetermined timetables, which is applied to reduce the total waiting time for all passengers under the vehicle number constraint. The main innovations of this research are:  
1. Proposal for a real-time passenger flow-monitoring-based urban metro operation method without timetables;
2. Formal formulation of the proposed metro operation method;
3. Development of a modified genetic algorithm to solve the problem. This paper is organised as follows. The overall research motivations and background are introduced in Section 1; Section 2 gives a general introduction and review of related research. Section 3 formulates the real-time passenger flow-oriented operation problems for urban metro systems. A \"real-time passenger-oriented operation method (RPOM)\" based on nonlinear integer programming is proposed. To solve RPOM, Section 4 introduces an innovative algorithm, GA_RPOM, based on a modified generic genetic algorithm and a macroscopic metro system simulator. In Section 5, the proposed method is tested and evaluated based on the data from the Beijing Metro Line 19, and the results are compared with the other operation strategies with timetables in real life. Conclusions are presented in Section 6.