Timetable rearrangement to cope with railway maintenance activities
Introduction
The railway capacity can be defined as the maximum number of trains that would be able to operate on a given railway infrastructure, during a specific time interval, given the operational conditions (Hachemane, 1997). Currently, most railway systems around the world experience an increasing demand for railway capacity which can only be achieved either by the construction of new infrastructure or by the improvement of the exploitation of the existing one.
Maintenance Activities (MAs) are necessary to maintain the good state of the railway infrastructure, allowing trains to circulate safely and fluidly, thus ensuring the availability of the railway capacity. However, while performing MAs (note that a table of acronyms is provided), the train circulations in the concerned locations are impacted. This impact depends on the type of MA performed, which in general implies circulation interdiction on some track segments and temporary speed limitations on neighbouring ones. This means that during the performance of MAs the available railway capacity is reduced. Moreover, most MAs require one or more Maintenance Trains (MTs). These are particular trains whose rolling stock is specifically equipped to perform maintenance tasks or to transport maintenance materials. The circulations of these MTs may also impact other trains.
Timetables are typically elaborated by considering the track unavailability periods due to MAs. A timetable is feasible if all planned train circulations are conflict-free. A conflict exists when two trains travelling at the planned speed would concurrently require the same track segment. To guarantee the feasibility of a timetable, the minimum separation between trains is often overestimated during the planning process. This often brings to an inefficient capacity utilization, since more capacity than what strictly necessary is allocated to each train.
Unplanned MAs may be necessary, e.g., due to an accident or tracks malfunction, and may require some rearrangements of the existing timetable. These activities are typically scheduled a few days or few hours in advance. If complex operations are necessary, these are divided into smaller operations that are scheduled separately from one another. In this paper, we assume that this division has already been performed and thus, we deal with the smaller, indivisible activities defined by the infrastructure manager, to which we refer simply as MAs. In the practice, the required timetable rearrangements are usually made either by hand, based on the experience of the dispatchers, or by resorting to some optimization tool, based on macroscopic aspects of the infrastructure.
The objective of this work is, first, to propose a formulation that allows the insertion of unplanned MAs into an existing timetable while guaranteeing its feasibility. More specifically, we present RECIFE-MAINT: a mixed integer linear programming (MILP) formulation to perform rearrangements on planned train circulations while minimizing the scheduled time deviations with respect to the existing timetable. RECIFE-MAINT has been developed as part of the decision support tool named RECIFE (REcherche sur la Capacité des Infrastructures FErroviaires) (Rodriguez et al., 2007). Thanks to the microscopic representation of the infrastructure and rolling stock, a number of specific circulation constraints can be defined in RECIFE-MAINT thus, ensuring the feasibility of the resulting timetable while optimizing the railway capacity utilisation. Additionally, RECIFE-MAINT takes into account specific aspects related to MAs that are often disregarded in the literature, such as temporary speed limitations and planning of MTs.
Moreover, we present three algorithms founded in RECIFE-MAINT to solve the problem of rearranging a timetable to cope with MAs. We use these algorithms in the experimental phase to solve instances based on a case study of the French railway network. Furthermore, we compare the performance of these algorithms with an emulation of the current practice.
The rest of the paper is organized as follows. Section 2 describes the railway infrastructure representation considered in this paper. Section 3 reviews the related scientific literature. Section 4 details the problem addressed in this paper. Section 5 presents the complete formulation of RECIFE-MAINT. Section 6 describes the algorithms we propose. Section 7 introduces a real world case study, which is then used to perform experiments; results are presented and discussed. Finally, Section 8 enlists our conclusions and perspectives.
Section snippets
Railway infrastructure representation
The railway infrastructure can be represented in multiple ways. They can be classed into two main groups: macroscopic and microscopic.
On the one hand, macroscopic representations are based on the abstraction of large elements existing in the infrastructure, e.g., stations and lines connecting them. Commonly, they use approximations to define circulation and capacity constraints, e.g., the minimum headway time between two trains on the same track segment, the maximum number of trains that a
Literature review
A large number of works in the scientific literature deal with the timetabling problem. For a comprehensive review, we refer the reader to Cacchiani and Toth (2012) and Siebert and Goerigk (2013).
However, only few contributions deal with the unavailability periods of track segments caused by MAs. We classify them into three categories according to the manner in which they deal with MAs:
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Fixed Timetables, Variable Maintenances (FTVM),
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Variable Timetables, Fixed Maintenances (VTFM) and
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Variable
Detailed problem description
As mentioned, the maintenance needs of the infrastructure are commonly defined before the conception of train timetables. Then, the timetables are conceived taking into account the temporal unavailability of track segments caused by MAs. This is often done considering a macroscopic representation of the infrastructure, hence, the separation between pairs of trains is constrained by an estimation of a minimum separation time. This value ought to be the highest possible one considering the routes
Problem formulation
In this section we present RECIFE-MAINT, a MILP formulation to tackle the problem described in Section 4. It is based on the RECIFE-MILP formulation, presented by Pellegrini et al. (2015). The novel features of RECIFE-MAINT include the introduction of new variables and constraints for the implementation of the green wave policy for OTs, the model of MAs, the planning of MTs and the observance of TSLs. Additional information concerning these new features is given below.
Since we use a microscopic
Solution algorithms
In this section, we present the algorithms that we propose in this paper and that we test in the experiments reported in Section 7. We establish a whole time limit for each algorithm. This is the total wall clock time available for an execution. After this time, the best feasible solution (if any) is returned. Note that a solution is considered optimal only if the algorithm completes its optimality proof. Moreover, some of the proposed algorithms are two-phase algorithms, in these cases, a
Experiments and results
We set up two rounds of experiments using the case study described in Section 7.1. The objectives of the first round of experiments are: Initially, to evaluate the capacity of RECIFE-MAINT and the proposed algorithms to obtain solutions to instances of the problem with different characteristics. Then, to assess the solutions improvement with respect to the solutions applied in current practice, i.e., the solutions obtained by RM-B. Finally, to obtain insights about the features of difficult
Conclusion
In this paper, we presented RECIFE-MAINT: a MILP formulation to solve the problem of rearranging a timetable to cope with maintenance activities while considering specific aspects such as maintenance trains and temporary speed limitations.
There is a limited number of approaches proposed in the literature to deal with this problem. All of them are based on macroscopic representations of the infrastructure, which often use time overestimations to guarantee feasibility, thus reducing the available
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