A Game-Theoretic Approach to Line Planning

We present a game-theoretic model for the line planning problem in public transportation, in which each line acts as player and aims to minimize a cost function which is related to the traffic along its edges. We analyze the model and in particular show that a potential function exists. Based on this result, we present a method for calculating equilibria and present first numerical results using the railway network of {it Deutsche Bahn}

Robust Line Planning in case of Multiple Pools and Disruptions

We consider the line planning problem in public transportation, under a robustness perspective. We present a mechanism for robust line planning in the case of multiple line pools, when the line operators have a different utility function per pool. We conduct an experimental study of our mechanism on both synthetic and real-world data that shows fast convergence to the optimum. We also explore a wide range of scenarios, varying from an arbitrary initial state (to be solved) to small disruptions in a previously optimal solution (to be recovered). Our experiments with the latter scenario show that our mechanism can be used as an online recovery scheme causing the system to re-converge to its optimum extremely fast.Comment: To appear in TAPAS 201

The line planning routing game

In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples

DC railway power supply system reliability evaluation and optimal operation plan

With the continuous and rapid development of the economy and the acceleration of urbanisation, public transport in cities has entered a period of rapid development. Urban rail transit is characterised by high speed, large traffic volume, safety, reliability and punctuality, which are incomparable with those of other forms of public transport. The traction power supply system (TPSS) is an important part of an electrified railway, and its safety issues are increasingly prominent. Different from the substation in a general power system, the load of a TPSS has a great impact on the traction transformer; moreover, in order to ensure normal operation of the train in case of failure, the traction substation must be able to access a cross-district power supply, as it has a high demand for reliable operation. The safe and reliable operation of DC TPSSs is the basis of the whole urban railway transit system. Previous studies have investigated the reliability of the TPSS main electrical wiring system. However, the impact of traction load and the actual operation of trains on system reliability has not been considered when designing a DC railway power supply system. The purpose of the research for this thesis is to find an optimal system operation plan for urban railways, considering load characteristics. This thesis begins with a review of the main arrangements of DC railway power supply systems and the literature on railway reliability studies. A model of single train simulation and a power supply system is established in MATLAB. The developed simulator is then integrated with a TPSS reliability model to evaluate the energy and reliability performance of DC railway power systems. Based on the train traction load model and train schedule, a comprehensive method for evaluating a DC TPSS considering traction load is proposed. Through simulation of the actual operation of the train group, the system energy consumption and substation life loss generated under different train operation diagrams and schedules are compared to provide a reference for the reasonable design of the timetable. Taking the life loss and energy consumption of the whole TPSS as the objective function, a genetic algorithm is used to optimise the train speed, coasting velocity, station dwell time and headway to find the optimal operation strategy. This is illustrated with a case study of the Singapore East–West metro line. The study has addressed the following issues: development of a multi-train power simulator, evaluation of reliability performance, and finally the search for an optimal operation plan. The train running diagram and timetable are optimised jointly. This can help railway operators make decisions for an optimal operation plan and reduce the operation risk of the power system