TreMOla Optimal Timetables for Maintenance of the Gotthard Base Tunnel

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2 TreMOla Optimal Timetables for Maintenance of the Gotthard Base Tunnel Dan Burkolter a, Burkhard Franke a, Sabrina Herrigel a, Thomas Frick b, Peter Hunkeler b a trafit solutions gmbh, Heinrichstrasse 48, 8005 Zurich, Switzerland {burkolter, franke, herrigel}@trafit.ch Phone: +41 (0) b SBB Infrastructure, Berne, Switzerland {thomas.frick, peter.hunkeler2}@sbb.ch Abstract Time reserved for the maintenance of the Gotthard Base Tunnel is scarce, which makes it crucial to calculate timetables that minimize the time trains need to reach their maintenance sites. We present the special situation for maintenance of the tunnel regarding safety procedures, rolling stock, and infrastructure and propose a solution for creating timetables that are optimal regarding available on-site time. Comparisons with basic timetabling strategies show that roughly 5% of additional time for maintenance can be gained, which amounts to about 20 minutes per site and shift. Keywords Maintenance, Timetabling 1 Introduction On 1. June 2016, the Gotthard Base Tunnel was opened after 20 years of construction. With a total length of 57 km, it is to date the longest railway tunnel in the world. Together with the Ceneri Base Tunnel, which is planned to open in 2020, it will reduce travelling time from Zurich to Milano by approximately one hour. However, since day one of operation tunnel maintenance is needed to preserve the tunnel s utility. For each of the two single-track tunnels a night is reserved each week, during which it is closed for normal traffic in order to conduct maintenance work. This is deemed to be very tight making it crucial to efficiently use the allotted time. The Swiss Federal Railways (SBB) has identified the timetable for the maintenance trains into and out of the tunnel as a main parameter for increasing the available time for maintenance, which is why it commissioned a software tool now called TreMOla (as the old Gotthard mountain pass road where TMO stands for Tunnel Maintenance Optimisation ) to calculate optimal maintenance timetables. TreMOla addresses the following problem. For each night a set of maintenance sites is given, each with its position in the tunnel and a minimum time on-site, required vehicles, and whether turning off of the catenary is needed. The target of TreMOla is to calculate train formations for entering and leaving the tunnel along with a timetable that follows all

3 procedures needed when operating ETCS in maintenance mode and maximizes the total on-site time. This paper is structured as follows. In Section 2, an overview of related work is given. The problem tackled by TreMOla is described in detail in Section 3. Here, also the necessary ETCS procedures, the layout of the tunnel infrastructure, and the rolling stock for maintenance is presented. In Section 4, TreMOla s algorithm including its running time calculator as well as two basic scheduling strategies are described. In Section 5, computational results are presented and compared to solutions obtained by the basic strategies. Finally, Section 6 concludes the paper. 2 Literature Review Lidén (2015) surveys the existing literature on railway maintenance optimisation problems and divides them in three categories: strategic, tactical, and operational. Strategic problems consider the dimensioning of the maintenance volumes and allocate them over the infrastructure while taking into account restrictions such as train traffic. As an example, Lévi (2001) looks for an optimal balance between maintenance and renewals for SNCF s railway infrastructure. Tactical problems mostly tackle variants of possession planning, i.e. when and where should parts of the infrastructure be reserved for maintenance. Forsgren et al. (2013) present a MIP model, which allows moving trains and maintenance activities in time such that timetable disruptions are minimal. Budai et al. (2004) consider the problem of scheduling maintenance activities in such a way that track possession times are minimized and propose heuristic solution methods. Finally, papers such as this one concerned with operational problems cover questions that arise from the day-to-day scheduling of maintenance. However, few papers on timetabling of maintenance machines have been published. A noteable exception is Heinicke et al. (2014) who describe a problem of routing machines for corrective tamping of tracks for which they propose several MIP formulations as solution. 3 Problem Description In order to plan maintenance work of the Gotthard Base Tunnel, SBB has built an application called REAL GBT, which manages maintenance activities and shifts. Each activity is attributed with the type of work, the position in the tunnel, its due date and priority, workers, equipment and minimum time needed, and whether the catenary must be turned off. REAL makes an initial assignment of activities and rolling stock to shifts mainly based on priority, which planners then may adapt manually. When all activities for a shift are chosen, they are bundled into so-called maintenance sites, which consist of a segment of the tunnel (typically less than a kilometre), a set of needed maintenance vehicles, and a minimum on-site time. Additionally, some sites require that the catenary section surrounding it to be turned off during maintenance. In order to serve the maintenance sites, a timetable is needed that determines all train formations as well as their departure and arrival times, such that it is guaranteed that all work can be conducted. Since the time needed for an activity is only a guess, the time spent at each maintenance site should be maximized in order to avoid unfinished activities, which would then have to be included in a later shift. In order to calculate this timetable, REAL

4 Figure 1: Gotthard Base Tunnel northern portal. Tunnel starts on the two tracks to the right. The maintenance trains depart from the four central tracks belonging to Rynächt. Figure 2: Gotthard Base Tunnel southern portal. Tunnel starts on the two tracks to the left. The single central track leads to the station of Biasca where the maintenance trains depart. GBT calls the application TreMOla, which must solve the following scheduling problem. Find a timetable including the train formations within the time frame of the shift to reach a given set of maintenance sites such that on-site time is maximized. Additionally, since the Gotthard Base Tunnel is operated under ETCS Level 2, the timetable must follow the special driving and safety procedures required for ETCS in maintenance mode. In the following the infrastructure, rolling stock, and ETCS procedures are described. 3.1 Infrastructure The Gotthard Base Tunnel consists of two single-track tunnels of 57 km each. The tunnels are very homogeneous with no speed changes and constant gradients (4 from northern portal to culmination point then 6.75 to southern portal). Though two crossovers exist within the tunnels, they cannot be used for maintenance since only one tunnel is closed in each shift. Thus, maintenance takes place on single track implying that trains cannot overtake and the order of all rolling stock entering the tunnel is effectively predetermined by the position of the maintenance sites. However, how the rolling stock is grouped to trains remains open and can be exploited to create better schedules, see Section 3.2. Maintenance trains either depart in Rynächt and enter the tunnel from the northern portal or depart in Biasca and enter in the south (see Figures 1 and 2 for the track layouts). Within the current railway timetable for Switzerland four train paths are reserved for maintenance trains to enter the tunnel from each end, though not all are necessarily used. These paths fully determine both departure times and routes to the portals. Similarly, four train paths exist for both tunnel ends to leave the tunnel at the end of the shift. By only using the reserved paths, maintenance trains are guaranteed to not disrupt other train runs and as a consequence normal traffic can be neglected when calculating maintenance timetables. The initially entering train formations are decoupled inside the tunnel, such that each unit may reach its designated site. When leaving the vehicles are coupled inside the tunnel such that at most four train formations leave the tunnel using the reserved paths. It is

5 possible and quite often advantageous to create different train formations for entering and leaving the tunnel. 3.2 Rolling Stock The maintenance vehicles used are specifically developed for the Gotthard Base Tunnel. The dual-mode vehicles have both an electrical and a thermal propulsion and are suitable for push-pull action. Their maximum speed of 100 km/h however can only be utilised with the main driver s cab leading. Maximum speed is reduced to 60 km/h for safety reasons if running backwards using an auxiliary driver s cab. Consequently, running times can be greatly reduced by optimally combining and orienting the vehicles in a train set and, thus, ensuring that trains can run at 100 km/h both when entering and leaving the tunnel. The values listed in Table 1 are used for running time calculation. Parameter Value Electrical Propulsion 1080 kw Thermal Propulsion 550 kw Tractive Effort 150 kn Weight 80 t Brake Percentage 73% Table 1: Maintenance vehicles for Gotthard Base Tunnel 3.3 ETCS in Maintenance Mode When ETCS is used in maintenance mode some rather tedious time-consuming procedures exist, which must be observed in order to construct realistic schedules. Simply put, trains may run under full supervision allowing a speed of 100 km/h, but on-site trains run unsupervised within a blocked sector with a maximum allowed speed of 40 km/h. In the following the most important procedures are described. Creating and entering a blocked section In order to reach its maintenance site, a train must run to the last balise before the site and stop there. Now, the blocking of the section can be requested from the control centre. Finally, the train may enter the blocked section in unsupervised mode, i.e. at at most 40 km/h. Releasing and leaving a blocked section In order to leave its site, a train must request the release of the blocked section from the control centre. Then the train may run unsupervised to the next balise, where supervision starts and the speed can be increased to 100 km/h. However, if the blocked section contains axle counters, these must first be reset, which necessitates that the train must drive through the whole blocked section at slow speed. Coupling trains Coupling can only take place within a blocked sector, where one train is already waiting. The second train must run to the last balise before the blocked section, stop there, and then request permission to enter the blocked section. Afterwards,

6 Figure 3: Blocked sections when a catenary is turned off. it may enter the section unsupervised. Depending on the vehicles coupling is done automatically or must be conducted manually. Decoupling trains Decoupling can only take place within a blocked sector, and again can be done automatically or must be done manually. Then, a train must request permission to leave the section and run unsupervised to the next balise before supervision begins and speed can be increased. Catenary switch-off Many maintenance activities require the catenary to be switched off. In this case, additionally to the section where the maintenance work is conducted, the two sections at the end of the catenary section must also be blocked, see Figure 3. This is due to safety reasons. An additional rule is enforced in the Gotthard Base Tunnel, which requires maintenance vehicles to always use thermal propulsion within blocked sections. Thus, setting up a blocked sector will guarantee that no train will accidentally create a short-circuit. A train incurs a big time loss should it need to enter a switched-off catenary section since the procedures for entering and leaving blocked sections apply. Process times for all mentioned procedures vary. Assumed times for calculating timetables are given in Section 5. 4 TreMOla The scheduling problem for TreMOla to solve can be stated as follows. Find a timetable with associated train formations such that each maintenance site is reached by its designated rolling stock, required procedures are properly conducted, minimum on-site times are kept, and overall on-site time is maximised. Notice that it is possible to enumerate all possible solutions: Overtaking in the tunnel is not possible hence the positions and required rolling stock of the maintenance sites determine the order of the vehicles for each tunnel portal. What remains to be done is to divide this order of vehicles into at most four trains (since four train paths for entering the tunnel are reserved). The number of possible entering train formations is thus ( ) ( ) ( ) ( ) n 1 n 1 n 1 n which is O(n 3 ) (1) where n is the number of maintenance sites. Building trains for leaving the tunnel at the end of the shift is analogous.

7 Each train runs to the maintenance site of one of its train parts where it is decoupled. The individual train parts again run to the site of one of its sub-parts and is again decoupled. This continues until all vehicles have reached their site. In the worst case, the resulting number of possibilities grows exponentially in the length of the train. However, this is in reality not a problem as the number of maintenance sites and hence the length of the train is small. Again, the process for leaving is analogous. As calculations with realistic test instances showed that a complete enumeration of all possible solutions is feasible within short time (see Section 5), we decided to forgo any pruning strategies to reduce the solution space. TreMOla s algorithm for calculating the entering timetable is shown as pseudo-code in Algorithm 1. The algorithm for leaving is analogous, however calculation runs backwards starting at the arrival at the portal. Complete timetables are created by combining an entry and a departing timetable and the optimal solution is the combination, which fulfils all minimal on-site times and has the largest sum of on-site time. Algorithm 1 TreMOla s enumeration of all entering timetables 1: for all Possible entering train divisions t do 2: for all Maintenance sites s served by train t do 3: Calculate running time to site s 4: parttrainruns(t) 5: end for 6: end for 7: 8: procedure PARTTRAINRUNS(t) 9: for all Possible train parts p of train t do 10: for all Maintenance sites s served by train part p do 11: Calculate running time to site s 12: if p still has sites to reach then 13: parttrainruns(p) 14: end if 15: end for 16: end for 17: end procedure Figure 4 shows the graphical timetable of an example of TreMOla s solution. 4.1 Running Time Calculation Since TreMOla must calculate running times of a large number of train runs, achieving very short computation times is paramount. On the other hand, obtaining realistic running times is necessary to create practical timetables. However, since the needed time for many ETCS procedures such as obtaining permission to enter or leave a blocked section may vary a lot, a very detailed running time calculation has no added value the uncertainty of the duration of ETCS procedures would be larger. TreMOla s running time calculation considers tractive effort including adhesion limit, vehicle resistance, gradient resistance, and rotating masses as described in Brünger and Dahlhaus (2008). The formula of Strahl (Strahl (1913)) is used for vehicle resistance since

8 Figure 4: Graphical timetable of a solution for a shift of 11 maintenance sites maintenance vehicles are more similar to freight trains. Curve resistance having very little effect on running times is neglected. In order to achieve very short computation times, TreMOla exploits the homogeneity of the Gotthard Base Tunnel. Whenever a train has reached maximum speed, running time to the next braking position is computed in one single step by dividing distance by speed. As a consequence, running time calculation consists of an acceleration and a braking phase computed in steps of one second and a single computation step in between (except for the short train runs outside of the tunnel where due to speed and gradient changes several acceleration and braking phases take place). 4.2 Basic strategies In order to be able to compare the quality of solutions obtained by TreMOla, two strategies often employed when constructing timetables manually were identified and implemented. Train bundle The strategy builds up to four formations of all vehicles destined for neighbouring maintenance sites. Each formation first runs to the central destination site where it is decoupled and part formations then run to the neighbouring sites. At the end of the maintenance shift, the part formations again first run to the central site where they are coupled and leave the tunnel as one formation. The strategy has the advantage that all coupling and decoupling procedures are conducted at one place. On the other hand, some vehicles must first pass their intended site only to retract later. Train cascade Again, the strategy builds up to four formations of all vehicles destined for neighbouring maintenance sites. However, each formation stops at every site to decouple and continues without the vehicles that have reached their intended destination until all reach their site. Similarly, the formation picks up all vehicles at each site to leave the tunnel. This strategy avoids that some vehicles must first pass by their intended site only to retract later, but more (de-)coupling procedures are needed.

9 (a) Train bundle (b) Train cascade Figure 5: Basic strategies for creating maintenance timetables Figure 5 shows graphic timetables of solutions obtained by the basic strategies for the same instance as the solution depicted in Figure 4. While the cascade solution must (de-)couple at seven different places, the bundle solution only needs four. On the other hand in the bundle solution vehicles must retract at three places before reaching their destination. 5 Results To test TreMOla, we have created 20 test instances. Instance sizes ranged from 5 to 13 maintenance sites during one shift. In some instances all sites are reached from one portal while in others from both. Correspondingly a solution consisted of at most four or eight initial train formations for entering the tunnel. Assumed times for maintenance procedures are given in Table 2. Procedure Time needed [min] Request section blocking 2 Release section blocking 3 Axle counter reset 10 Catenary switch-off 10 Catenary switch-on 5 Automatic (de-)coupling 2 Manual (de-)coupling 4 Table 2: Time needed for maintenance procedures. For all instances, we compared the average and the sum of on-site time of the optimal solution with the time obtained by the basic strategies. All computations were conducted on a computer with a 2.8 GHz quad-core processor with 16 GB of RAM running Windows 10. Average computation time was 1.1s where the longest instance took 2.9s.

10 Table 3 shows that TreMOla is able to increase productive time at maintenance sites by about 5%, which is about 20 minutes per site. Average on-site time [h:mm] Sum of on-site time Optimum 7:13 100% Train bundle 6: % Train cascade 6: % Table 3: Comparison of optimal solution with basic strategies. SBB is concerned that too complicated timetables could lead to mistakes during maintenance shifts. Therefore, we examined how much on-site time is lost, if two additional restrictions for simplifying the generated timetables are added. The first restriction requires that entering and leaving processes are symmetric in the sense that trains should be coupled the same way for entering and leaving, i.e. all vehicles are (de-)coupled in the same formation in the same order. The second restriction requires that all coupling and decoupling procedures of train formations are conducted at one place as in the train bundle strategy. Table 4 shows that these restrictions can be added with little loss in on-site time. Average on-site time [h:mm] Sum of on-site time Optimum 7:13 100% Symmetry 7: % Single (de-)coupling 7: % Both 7: % Table 4: Loss of on-site time when simplifying restrictions are added. 6 Conclusions Due to the success of the solutions created by TreMOla, it was integrated into SBB s maintenance planning software for the Gotthard Base Tunnel and is now used to create the actual maintenance timetables. Due to the automatisation of the timetable generation, SBB not only gains additional maintenance time but also and maybe even more importantly speeds up the generation of timetables. This not only reduces needed workforce but also makes it possible to rapidly change timetables for urgent maintenance work, which would not be possible when constructing timetables manually. An interesting question to tackle in future work would be to plan several maintenance shifts simultaneously. Currently, maintenance activities are allocated manually to individual shifts. If instead activities for e.g. several weeks were to be scheduled simultaneously, an additional potential for increasing available maintenance time could be tapped.

11 References Brünger, O., Dahlhaus, E., Running Time Estimation, In: Hansen, I.A., Pachl, J. (eds.), Railway Timetable & Traffic, pp , Eurailpress, Hamburg. Budai, G., Huisman, D., Dekker, R., Scheduling preventive railway maintenance activities, Journal of the Operational Research Society, vol. 57, pp Forsgren, M., Aronsson, M., Gestrelius, S., Maintaining tracks and traffic flow at the same time, Journal of Rail Transport Planning & Management, vol. 3(3), pp Heinicke, F., Simroth, A., Scheithauer, G., Fischer, A., On a Railway Maintenance Scheduling Problem with Customer Costs and Multi-Depots, Technical Report MATH- NM , TU-Dresden, Dresden, Germany. Lévi, D., Optimization of track renewal policy, In: World Congress on Railway Research, Cologne, Germany. Lidén, T., Railway infrastructure maintenance a survey of planning problems and conducted research, In: 18th Euro Working Group on Transportation, EWGT 2015, Delft, Netherlands. Strahl, Die Berechnung der Fahrzeiten und Geschwindigkeiten von Eisenbahnzügen aus den Belastungsgrenzen der Lokomotiven, Glasers Annalen für Gewerbe- und Bauwesen, vol. 73, pp View publication stats