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Rapid transit systems timetables are commonly designed to accommodate passenger demand in sections with the highest passenger load. However, disruptions frequently arise due to an increase in the demand, infrastructure incidences or as a consequence of fleet size reductions. All these circumstances give rise to unsupplied demand at certain stations, which generates passenger overloads in the available vehicles. The design of strategies that guarantee reasonable user waiting time with small increases of operation costs is now an important research topic. This paper proposes a tactical approach to determine optimal policies for dealing with such situations. Concretely, a short-turning strategy is analysed, where some vehicles perform short cycles in order to increase the frequency among certain stations of the lines and to equilibrate the train occupancy level. Turn-back points should be located and service offset should be determined with the objective of diminishing the passenger waiting time while preserving certain level of quality of service. Computational results and analysis for a real case study are provided.

Railway scheduling and timetabling are common stages in the classical hierarchical railway planning process and they perhaps represent the step with major influence on user's perception about quality of service. This aspect, in conjunction with their contribution to service profitability, makes them a widely studied topic in the literature, where nowadays many efforts are focused on improving the solving methods of the corresponding optimization problems. However, literature about models considering detailed descriptions of passenger demand is sparse. This paper tackles the problem of timetable determination by means of building and solving a non-linear integer programming model which fits the arrival and departure train times to a dynamic behavior of demand. The optimization model results are then used for computing several measures to characterize the quality of the obtained timetables considering jointly both user and company points of view. Some aspects are discussed, including the influence of train capacity and the validity of Random Incidence Theorem. An application to the C5 line of Madrid rapid transit system is presented. Different measures are analyzed in order to improve the insight into the proposed model and analyze in advance the influence of different objectives on the resulting timetable.

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