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• A non-linear programming model to design full-day demand-adapted timetables is proposed. • The time-dependent maximum sectional passenger flow is used as input data. • A new algorithm is proposed to match demand and services' supply. • The algorithm uses a rolling-horizon mechanism to iteratively compute departure times. • The effectiveness of the proposed algorithm is illustrated using real data of Chengdu Metro line 1. This paper focuses on the problem of designing the schedule of urban rail transit systems under dynamic passenger demand considering limited train capacity and congestion. From the point of view of operators, the goal of timetable optimization consists of using as few as possible service trains to transport the arriving passengers to their destinations securely and quickly. On the other hand, passengers want to spend the minimum time travelling to their destinations, including the time they wait on platforms until they board the first and successive trains in case of transferring between lines. Due to the variability of passenger flows and the difficulty in exactly solving full-day timetabling problems in short computation times, it is difficult in practice to use the approaches proposed in the literature. Moreover, when the capacity of trains is considered and oversaturation conditions emerge, the problem becomes even more complex, converting into a challenge the design of schedules from an operational point of view. By considering fixed train dwell times at stations and train running times between stations, we first propose a non-linear programming formulation to model the problem of determining the most convenient interdeparture times of services at the first station of a line, aiming at minimizing the waiting time of passengers. Since the dynamic behaviour of passenger demand and the maximum sectional passenger flow are approximately synchronous, an innovative method, the spatiotemporal synchronization coupling algorithm, based on working with the time-varying maximum sectional passenger flow instead of the demand patterns is proposed to quickly solve in an approximate way the demand-driven timetabling problem. The proposed approach is applied to a real case of Chengdu Metro Line 1 in China. The results show the effectiveness of the algorithm, both in terms of computational effort and in terms of reducing the waiting time currently experienced by passengers. [ABSTRACT FROM AUTHOR]

A methodology to design energy-efficient timetables in Rapid Railway Transit Networks is presented. Using an empirical description of the train energy consumption as a function of running times, the timetable design problem is modelled as a Mixed Integer Non-Linear optimization problem (MINLP) for a complete two-way line. In doing so, all the services in both directions along a certain planning horizon are considered while attending a known passengers’ demand. The MINLP formulation, which depends on train loads, is fully linearised supposing train loads are fixed. A sequential Mixed Integer Linear solving procedure is then used to solve the timetabling optimization problem with unknown train loads. The proposed methodology emphasizes the need of considering all the services running during the planning horizon when designing energy-efficient timetables, as consequence of the relationship among train speeds, frequency and fleet size of each line. Moreover, the convenience of considering the energy consumption as part of a broad objective function that includes other relevant costs is pointed out. Otherwise, passengers and operators could face up to an increase in the whole cost and a decrease in the quality of service. A real data scenario, based on the C-2 Line of the Madrid Metropolitan Railways, is used to illustrate the proposed methodology and to discuss the differences between the energy-efficient solutions and those obtained when considering operation and acquisition costs. [ABSTRACT FROM AUTHOR]

We propose a Mixed Integer Non-Linear Programming (MINLP) model in order to determine optimal line frequencies and capacities in dense railway rapid transit (RRT) networks in which typically several lines can run over the same open tracks. Given a certain demand matrix, the model determines the most appropriate frequency and train capacity for each line taking into account infrastructure capacity constraints, allocating lines to tracks while assigning passengers to lines. The service provider and the user points of view are simultaneously taken into account. The first one is considered by selecting the most convenient set of frequencies and capacities and routing passengers from their origins to their destinations while minimizing the average trip time. The second one by minimizing operation, maintenance and fleet acquisition costs. Due to the huge number of variables and constraints appearing in real size instances, a preprocessing phase determining the best k-paths linking origin and destination stations is followed. Then, the best paths are used to define sparse index sets in order to drastically reduce the size of the problem. As illustration, the model is applied to a simplified version of the Madrid Metropolitan Railway network. [ABSTRACT FROM AUTHOR]