Validity of the model

The validity of the model will be tested by comparing the distributions of the number of import and export containers of a barge, and the throughput times of barges at terminal 3, representing the terminal which was observed in reality, with the real data. Before these validity tests are executed, a warm-up period for the simulation needs to be defined, since the simulation will start with a completely empty network, which does not fit reality. Only values that lie outside the warm-up period, when the system reached a steady state, will be used for validity checks and further analysis. The steady state for this system will be defined via the barge total network throughput time. The steady state will be reached when the average throughput time stays relatively stable during the simulation. The validity of the model can only be tested based on the assumption that the system runs stable with all predefined parameters included.

5.5.1 Calculation of the warm-up period

To define the warm-up period, a heuristic method known as the ‘marginal standard error rule’ (MSER) is used. Following Robinson (Robinson, 2014), this method is recommended by Pasupathy and Schmeiser (2010), and Nelson (2013), since its performance on estimating the warm-up period is consistently well, with the benefit that no assumptions or parameters of complex calculations are required. The aim of the MSER is described by Robinson, with reference to White (1997), as “to minimize the width of the confidence interval about the mean of the simulation output data following deletion of the initial transient data.” This means that early observations that are too far away from the mean of all observations are removed. The warm-up period should be chosen for a point in the simulation which minimizes the MSER value (Robinson, 2014).

In the case of this simulation, the MSER is applied to the weekly average total network throughput time of barges, since the simulation handles a periodical of one week. The related graph is shown in Figure 15.

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Figure 12 warm-up period calculation (MSER on average time in system per week)

The minimum MSER value observed is in week 1 with a value of 2042. Week 1 is not suitable for the selection of a warm-up period, since the system is still relatively empty after such a short time. There is another minimum in week three with a MSER value of 2091. Therefore, it is chosen to apply a warm-up period of three weeks.

5.5.2 Validity test: frequency number of barge import and export containers

The first validity test is focused on the observed frequency of number of barge import and export containers, since barges are fully processed by cranes and the number of barge containers have a main impact on the barge throughput times at terminals and for the whole network. Figure 16 shows the histogram of real frequencies, compared to the simulation output with different parameters. “Sim1” stands for a simulation where the initial derived distributions are used.

It could be observed that simulation runs with the original derived distributions for assigning import containers to barges (sim1), results in more observations around the mode and for larger loads. After experimenting with some parameters to reduce the number of containers assigned initially to barges, for example reducing the total amount by 10% by applying a factor of 0,9 (sim 0.9), it is decided to reduce Figure 13 validity test rel. freq. of number of barge import containers

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Looking next at the frequency of number of export containers (Figure 17), it can be seen that the real frequency is of a more uniform nature, where the observations of the simulation runs have the character of a normal-distribution. Since the assignment of container to barge voyages is based on dwell times, like described in Section 5.3.4.3, it is complex to influence the shape of the distributions, representing the frequency of number of export containers, directly. Reasons for the differences between observed and simulated values could be the extreme noise of the input data to calculate pre-voyage dwell times, or the lack of differentiation between different voyages, due to complexity reasons. It is decided to try to shift the mode of the simulation values to the left, thus reduce the value, by reducing the total number of container arrivals at terminals by 30% (factor 0,7; sim0.7). No further action is done, since the throughput times of barges at the terminal seem to have a good fit, which is assumed to be the most important factor of validity (see following section).

5.5.3 Validity test: terminal throughput times of barges

With the adjusted parameters of Section 5.5.2, the throughput times of barges in the simulation fit the values of real observations in an acceptable way (Figure 18). It can be derived that the validity of the model is sufficiently high, also having in mind the reduced complexity of the model compared to the real complexity of the hinterland network, to gain valid results from analysis of forecast scenarios and the test of the hypotheses.

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Figure 15 rel. frequency terminal 3 throughput times barges