Delay Management with Re-Routing of Passengers

The question of delay management is whether trains should wait for a delayed feeder trainor should depart on time. In classical delay management models passengers always taketheir originally planned route. In this paper, we propose a model where re-routing ofpassengers is incorporated.To describe the problem we represent it as an event-activity network similar to the oneused in classical delay management, with some additional events to incorporate originand destination of the passengers. We present an integer programming formulation ofthis problem. Furthermore, we discuss the variant in which we assume fixed costs formaintaining connections and we present a polynomial algorithm for the special case ofonly one origin-destination pair. Finally, computational experiments based on real-worlddata from Netherlands Railways show that significant improvements can be obtained bytaking the re-routing of passengers into account in the model.public transportation;OD-pairs;delay management;re-routing

Fast Heuristics for Delay Management with Passenger Rerouting

Delay management models determine which connections should be maintained in case of a delayed feeder train. Recently, delay management models are developed that take into account that passengers will adjust their routes when they miss a connection. However, for large-scale real-world instances, these extended models become too large to be solved with standard integer programming techniques. We therefore develop several heuristics to tackle these larger instances. The dispatching rules that are used in practice are our first heuristic. Our second heuristic applies the classical delay management model without passenger rerouting. Finally, the third heuristic updates the parameters of the classical model iteratively. We compare the quality of these heuristic solution methods on real-life instances from Netherlands Railways. In this experimental study, we show that our iterative heuristic can solve large real-world instances within a short computation time. Furthermore, the solutions obtained by this iterative heuristic are of good quality.public transportation;daily management;passenger rerouting;railway operations

Evaluation of the delay management potential on a macroscopic level

In general, macroscopic models in delay management allow for the optimization of large networks with reasonable computational effort. The main limitations here arise from the aggregated consideration of the infrastructure. In this paper, an evaluation of potential application of macroscopic models for delay management through a real case study is discussed. A macroscopic model is built by applying first a micro-macro transformation on a calibrated microscopic model, to provide an exact calculation of minimum running times and headways. On this macroscopic model, two disruption scenarios are analyzed and solved by using Event Activity Networks, to show the potential benefits and the limitations of delay management. The case study is based on a real railway infrastructure in Switzerland, and it is implemented in LinTim, an opensource software, which allows for an integrated development of both the macroscopic scenario and the delay management solutions

Delay Management including Capacities of Stations

The question of delay management is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. While the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the stations’ capacities. This model allows to reschedule the platform assignment dynamically. Furthermore, we propose an iterative algorithm in which we first solve the delay management model with a fixed platform assignment and then improve this platform assignment in each step. We show that the latter problem can be solved in polynomial time by presenting a totally unimodular IP formulation. Finally, we present an extension of the model that balances the delay of the passengers on the one hand and the number of changes in the platform assignment on the other. All models are evaluated on real-world instances from Netherlands Railways

Delay Management including Capacities of Stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations\u27 capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Delay management including capacities of stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations' capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Delay Management with Re-Routing of Passengers

The question of delay management is whether trains should wait for a delayed feeder train or should depart on time. In classical delay management models passengers always take their originally planned route. In this paper, we propose a model where re-routing of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in classical delay management, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections and we present a polynomial algorithm for the special case of only one origin-destination pair. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements can be obtained by taking the re-routing of passengers into account in the model

An Iterative Optimization Framework for Delay Management and Train Scheduling

Delay management determines which connections should be maintained in case of a delayed feeder train. Recent delay management models incorporate the limited capacity of the railway infrastructure. These models introduce headway constraints to make sure that safety regulations are satisfied. Unfortunately, these headway constraints cannot capture the full details of the railway infrastructure, especially within the stations. We therefore propose an iterative optimization approach that iteratively solves a macroscopic delay management model on the one hand, and a microscopic train scheduling model on the other hand. The macroscopic model determines which connections to maintain and proposes a disposition timetable. This disposition timetable is then validated microscopically for a bottleneck station of the network, proposing a feasible schedule of railway operations. This schedule reduces delay propagation and thereby minimizes passenger delays. We evaluate our iterative optimization framework using real-world instances around Utrecht in the Netherlands