# Passenger Flow-Oriented Metro Operation without Timetables
## 2 Literature Review  
In recent years, rail operation problems have drawn tremendous attention from academia and industry [1; 2; 3; 4]. A trendy area of rail operation research is train schedule. This research aims to propose different timetables according to different objectives. In general, three main goals are involved: avoiding train delays [5; 6; 7; 8], reducing fuel consumption costs [9; 10], and improving the quality of services [11]. For a passenger railway system, especially for an urban rail system, it is essential to design a passenger flow-oriented scheduling strategy to improve the service quality, system reliability, and passenger satisfaction [12]. The research on meeting the requirements of passenger flow-oriented scheduling can be divided into two categories. The first kind of research proposes periodic timetables [13; 14; 15], which means that trains are scheduled at a specific frequency and that timetables keep repeating in a time horizon. This periodic scheduling method is easy to formulate and optimise based on regular passenger flow variations and periodic events [4]. Thus, most metro systems in real-life apply this periodic operation strategy. However, because more passenger flow data can be collected and analysed, in recent years, instead of considering periodic timetables, more research has focused on scheduling to propose dynamic timetables based on dynamic origin-destination (OD) passenger demands [3; 12; 16; 17]. For example, [PERSON] et al. used the passenger OD matrix data at stations through a single day to minimise total passenger waiting time [18]. [PERSON] et al. built an OD matrix to minimise the passenger waiting time and avoid high passenger loads [19]. The modelling method for scheduling is generally based on four main techniques: linear programming, integer programming (IP), nonlinear programming, and graph theory. For example, [PERSON] et al. used linear programming to develop a computer-assisted train dispatch system [20]. [PERSON] et al. built a multi-objective train scheduling model using IP [21]. [PERSON] et al. proposed a green train scheduling model and fuzzy multi-objective optimisation algorithm based on nonlinear programming [22]. [PERSON] et al. used graph theory to solve the real-time perturbations for a rail system [23]. The solution methodologies can be divided into three types: (1) commercial optimisation software, (2) heuristic algorithms (e.g., evolutionary algorithms [24]), and (3) simulation methods [25; 26]. Another form of rail operation research is train rescheduling, which mainly focuses on adjusting the train operation into a regular timetable when operational incidents occur [27]. There are two main research directions: (1) Disturbance management deals with short incidents. In this situation, the dispatch strategy needs to be modified to reduce the influence on the timetable in the future [23; 28]. (2) Disruption management deals with those events that cause a long delay. In this situation, it is not only the modification of the dispatch strategy that is needed--other measures, such as cancellation of trains, the addition of trains, and skipping stops, also need to be considered [29; 30]. In general, rescheduling strategies can be divided into five categories [31]: (1) Holding, which is used to modify the headway between trains by holding the early-departing trains [32]. (2) Zone scheduling, where the whole line is divided into different zones, and all underarted trains are divided into different groups, and a specific train only stops at all stations within a single zone. This scheduling method can deal with passengers piling up in a few specific stations [33]. (3) Short turning, a strategy that arranges several trains to only serve some zones with high demand defined by passenger flow speed and turn back [34; 35]. (4) Deadheading, a strategy in which several trains are dispatched without stopping and collecting any passengers at the beginning of their trips to reduce the headways with other trains in front [36].