# Passenger Flow-Oriented Metro Operation without Timetables
## 1 Introduction  
The metro system plays an essential role in urban public transportation. Because of its high speed, high capacity, and low energy consumption characteristics, the metro system has become the most popular type of urban transportation mode over the years, especially in large cities with many inhabitants, such as London, Tokyo, Beijing, Hong Kong, etc. Thus, plenty of effort is devoted to optimising the metro operation based on different demands.  
From the macroscopic perspective, a typical metro operation problem is to make schedules for trains regarding systems' constraints. Unlike a mainline railway system operated and restricted to a predetermined timetable, periodic operation strategies are the most common solution for a metro system. However, this traditional method cannot always satisfy the variation of passenger flow. In general, the variation of passenger flow is catalogued into two main kinds: regular variation and irregular variation. Regular variation occurs when predictable changes occur, such as the passenger flow caused by rush hours, summer holidays, significant events, etc. These regular variations could be predicted based on historical experiences in the early stage, and operators have enough time to design specialised dynamic timetables. For example, the London Underground established a specialised timetable for massive passenger flow caused by the football match at Arsenal Football Club to ensure sufficient system capacity. Contrarily, irregular variations occur occasionally, and they are unpredictable; for example, due to a sudden change of weather, many tourists choose to take the metro instead of walking to a tourist attraction; these irregular variations will invalidate well-designed timetables, which can cause passenger oversaturation and impact the service quality. Usually, though the approximate passengerflow distribution could be counted based on historical data, these real-time irregular variations will always exist, and predetermined dynamic timetables could not always satisfy these variations.  
With the development of the automatic fare collection system and the face recognition technology, the real-time variations of passenger flow are easier to be detected. As a result, a new operation method could be proposed to adjust operation strategies to satisfy the real-time detected passenger flow variation. Though scheduling in a fixed timetable has the advantage of predictability for the passengers, it also makes the operation of the train easier for the drivers. Unlike a mainline railway system which limits the number of passengers boarding and provides a prepared timetable for passengers to plan their journey before purchasing the tickets, with its high frequency characteristic, most metro systems only publish the timetables for the first and last service (such as the Wuhan Metro system, the Beijing Subway system, etc.), most passengers do not plan their journey and board the first train arriving at the platform. Furthermore, based on a field study in the London Underground Bakerloo line operation department, because of the uncertainty in actual operation, metro drivers have to modify the operation strategies according to the metro operators' real-time instructions instead of following a prepared timetable. Thus, a real-time passenger flow-oriented operation method is more advantageous than a preprepared timetable for a metro system. This real-time operation method is essential to guarantee the quality of services, avoid safety issues caused by passengers' oversaturation in metro stations, and ensure the robust operation of the metro system. The associated service quality function can be formulated by a single or by multiple features of the considered metro system, including the overall travelling time of passengers, the waiting time of passengers, the transport capacity of the metro system in a time window, and the particular definition of passenger satisfaction, etc.