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The numerical experiment is developed based on data provided by ProRail. The model is executed based on one day of historical data between the 1st of October 2015 and the 1st of December 2015. As discussed in chapter 4, the input for the model needs to consist of the following element with regards to the inbound trains, and the tracks at the yard.

Table 6.1:Data necessary for the model based on the mathematical model Description

(mk)Length of each trackk∈K. (see section 6.1)

(ai)Original arrival time of traini∈N at the yard at trackk. (pi)Process time that traini∈Nmust remain at the yard. (di)Original departure time of traini∈N from the yard at trackk.

(wi)Delay weighting of each traini∈N indicating the importance of the delay of a train. (li)Length of each traini∈N.

(H)Minimum headway of two trains at the same track.

The following sections explain the data provided by ProRail and shows how the data is used in the model including the assumptions made.

6.2. NUMERICAL INPUT RECEIVED AND ASSUMPTIONS MADE 29

Capacity planning

Capacity on a railway yard for freight transportation is strongly related to the capacity on the net- work. The Rail Infrastructure Manager (RIM) constructs the capacity planning on the network in four different stages:

• Year plan

• Original plan

• Scheduled plan

• Executed

Year plan (±1,5 year in advance): The making of a year plan starts about 1,5 years in advance. The RIM starts with making a capacity planning where it determines where and when trains can perform on the network. After the concept capacity planning is made, all transporters (freight and passengers) can submit their preferred schedule. The RIM then tries to implement it in a concept schedule. The concept plan will be sent back to the transporters where they can decide if adjustments are preferred, or if they concur with the schedule. When all parties agree, a permanent schedule is made for the whole year. During the year changes can still be made and transporters can still request times when they want to drive on the network, however, the transporter that made the request at the concept stage will always have a claim on the time that is given to the transporter.

Original plan (± 3 days in advance): Three days before execution, a so-called original plan is made where the RIM checks if the trains planned in the year-plan will still be executed, if there are some trains that canceled their request, or if there are additional trains that requested a path on the network. Canceling a path requested in advance is no problem, however, if done frequently it could have consequences when requesting paths in the year-plan for the next year.

Scheduled plan (assumed 1,5 hours in advance): A scheduled arrival is communicated 1,5 hours in advance and is needed if a train wants to park at a railway yard. It serves as a final call to the TD to let them know the train is coming. The TD can then determine if the train can still be assigned at the yard. In this study, the scheduled arrival is assumed 1,5 hours before executed

Executed : The executed time is the actual time that a train arrived or departed at or from a yard.

Because a final check on network capacity is determined at the original plan, the schedule of the year plan is not relevant and therefore not considered in this study.

30 CHAPTER6. NUMERICALEXPERIMENT

Selection of one day from two months of data

In order to measure the performance of the model, one arbitrary day will be chosen from the two months data received from ProRail (2015) between the 1st of October 2015 and the 1st of December 2015. To know which day will be normative for the week, the busiest day in a week will be chosen for the experiment. Table 6.2 shows the arrival distribution over two arbitrary weeks. On request of ProRail, the week numbers are not mentioned in this report.

Table 6.2:Arrival distribution over the week (ProRail, 2015)

Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total

week 1 30 44 40 48 42 30 21 255

week 2 34 36 36 41 40 30 30 247

week 1+2 64 80 76 89 82 60 51 502

Percentage 13% 16% 15% 18% 16% 12% 10% 100%

From table 6.2 can be concluded based on these two weeks the Thursdays are the busiest days during the week. For this reason, the Thursday of the first week will be chosen as input data for the case study.

Process times of trains

Because from the received data could not be determined for all trains how long a was spend at the yard, additional data regarding the processes at Whz were required. Based on the documentation received from Keyrail (2014), the total process time needed when arriving at Whz is 1h 35’. The total time needed when departing from Whz is 2h 15’. An extensive description of the assumptions made can be found in appendix E. The process times of each train is visualized in figure 6.2.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Train number 0 30' 1h 1h 30' 2h 2h 30' 3h 3h 30' Process time

6.2. NUMERICAL INPUT RECEIVED AND ASSUMPTIONS MADE 31

Initial train schedule

Including the arrival times and assumed process times of each train, we developed an original train schedule. In this study, we slightly adjusted the data that we received because if we would consider only the input data provided by ProRail, there would always be an empty track at the yard at any time, and therefore never occur a delay. For that reason, we took the 6 busiest tracks and copied the first 3 tracks, giving input of trains 74 and 9 tracks in total. The original train schedule is visualized in appendix E, figure E.2. The adjusted assignment used during the experiments is visualized in figure 6.3. 1 2 3 4 5 6 7 8 9 65 71 25 61 64 67 70 74 46 51 55 57 63 66 69 32 38 72 36 45 47 49 53 56 60 48 52 50 54 58 59 62 68 12 17 29 30 37 42 41 13 26 7 11 15 22 24 35 22 0 1 2 3 4 5 6 7 8 2 44 34 4 8 6 10 39 1 3 5 9 14 19 20 23 28 16 18 21 31 27 33 43 Track nr.

Adjusted original assignment schedule

9 10 11 12 13 14 15 16 17 18 19 20 21 23

Figure 6.3:Visualization of the adjusted original train scheduled used in the experiments

Applied train weighting

In the Netherlands, the RIM (i.e. ProRail) is not allowed to give priorities or weightings to trains. For this reason the train weighting is not considered in these experiments.

Applied delays for the scheduled train plan

As discussed above, three different stages with regards to capacity planning are used. Above we visualized the initial train schedule based on the original data received from ProRail. Based on the data from ProRail, we applied the following delays on top of the original arrival for calculating the scheduled arrival of each trains.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Train number -1h -30' 0 30' 1h 1h 30' 2h 2h 30' 3h 3h 30' 4h 4h 30' 5h Delay

32 CHAPTER6. NUMERICALEXPERIMENT

Applied delays for the executed train plan

Based on the data provided by ProRail, we used the following delays on top of the original arrival for calculating the executed arrival times of each trains.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Train number -1h -30' 0 30' 1h 1h 30' 2h 2h 30' 3h 3h 30' 4h 4h 30' 5h Delay

Figure 6.5:Applied delays from the Original plan to Executed

Headway between trains

The minimum headway(H)of two trains is assumed to be included in the process as discussed in appendix E and is therefore assumed to be 0.

Used train lengths

Because not all train lengths were known from the data provided, we applied our own distribution on the lengths of the trains. An extensive explanation of how the train lengths are determined can be found in appendix F. The used length of each train is visualized in figure 6.6. When a length of 400m is considered, it means that the train can be assigned to every track.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Train number 0 200 400 600 800 Lenght (in m)