Calculating the TD-TT using the CH-algorithm

In this section, we give an example how the CH-algorithm retrieves a time dependent travel time using the precalculated congestion factors. Say, the CH-algorithm needs to calculate the time dependent travel time from node 1.986.221 to node 1.986.222 at a Monday at 00:48. The free ow travel time is already known, and is in this case 60 minutes. First, the algorithm checks at the lowest level if area ID 99 and 100 have representatives and are neighbours (see Figure 5.6). We know that they are neighbours at the lowest level (area ID 99 and 100), but in this example we assume both areas do not have a representative on this level (Figure 5.7a does not show this level). Therefore, the algorithm moves up one layer and checks

Chapter 5. Congestion Hierarchy Algorithm 53

the same for area ID 25 and 26. These two areas are neighbours as well, and both have a representative as well (see Figure 5.7a). Therefore, it is possible to retrieve the congestion factors.

Let us assume that the index and oset values of area ID 25 to area ID 26 are the same as area 1 to area 3, we use the same information as shown in Figure 5.7b. The Monday congestion factors are stored in row 48 of the congestion factor data structure. The congestion factors consist of 96 bytes of information, but only 12 bytes are shown in Figure 5.7. Because the departure time is at 00:48, we need the third and fourth congestion factor within the congestion factor array. In this example this is 9 and 8, and with the increasing of these factors by the oset, we get 98 and 97. Using interpolation, the nal congestion factor at 00:48 is98 + 00:48_00:15−00:45 ∗(97−98) = 97.8. If in this example, the free ow travel time would

Chapter 6

Experiments & Results

This chapter describes the experiments to test our algorithm and evaluate its results. In Chapter 4, we already described the benchmark experiments to test the current algorithm. In this chapter we use the same datasets and performance indicators, but we conduct dierent experiments. We describe the data and the evaluation criteria in respectively Section 6.1 an Section 6.2. Section 6.3 describes the experiments to test our solution method. In Section 6.4 we analyse and discuss the results of the experiments.

6.1 Data

In this section, we discuss the three dierent types of data we need to conduct the experiments. These three data types are similar to the types we discussed in Section 4.1. First, we have the map data for which we use the same BeNeLux map as during the benchmarking experiments. We refer the reader back to Section 4.1.1 for a detailed description of the map data. Second, we use test data that contain a large number of dierent random origin and destination pairs that we use to test the TTC and the CH-algorithm. From the three test groups described in Section 4.1.2, we use test group 1 (path lengths) and test group 3 (congested areas) in this chapter as well. Test group 2 contains O-D pairs with dierent lengths towards their representatives. The representatives of this test group are in a 20x20 grid formation. Because the CH-algorithm uses a dierent set of representatives, each of the four test sets in the test group does not hold the property anymore that all origin and destination nodes are located at the same distance from their representative. Therefore, this test group becomes useless in the following experiments. Last, we use the congestion data that is created during the preprocessing stage of the CH-algorithm. We refer the reader back to Section 5.3.1 for the full explanation of this preprocessing stage. In that section, we explained that we have three parameters we can adjust during the preprocessing stage. These three parameters are the threshold to accept an area to get a representative (α), the number of neighbours

around a representative (inclusion width), and the number of layers of representative areas. We split the latter parameter in two dierent parameters, namely the rst layer and the number of layers. Preliminary results show that several longer paths tend to only share congestion factors at the 2x2 and the 4x4 layers. However, these layers produce inaccurate results as the representatives represent a too large area to be accurate. Therefore, we decide to add a parameter known as the rst layer, which is

Chapter 6. Experiments & Results 55

the rst layer in the congestion hierarchies where the congestion factors for each representative to all other representatives are calculated. Essentially, in this layer we compute the congestion factors as in the current algorithm. In this way, we force the algorithm to always nd the congestion factors in this rst layer. The preliminary results also show that calculating all congestion factors in the 16x16 layer, did not signicantly improve the accuracy compared to doing the same for the 8x8 layer. As calculating all congestion factors in 8x8 layer uses less memory that in the 16x16 layer, we chose the 8x8 layer as the rst layer. The number of layers is the number of times we split an area into four equal areas. If we have 9 layers, the bottom layer consist of29_{= 512 =>512∗512 = 262.144 areas.}

Table 6.1 shows three dierent datasets with preprocessed congestion data of the CH-algorithm. The four columns of the table show the values of the parameters used to compute that congestion dataset. The rst two columns contain the parameters that are xed, and cannot be altered. Preliminary experiments show that it is enough to xate the rst layer value to 8x8, and to only dierentiate among the value of

α. The 4x4 layer and 16x16 layer were respectively not accurate enough or equally accurate compared to

the 8x8 layer. The last two columns contain the parameters, for which dierent values can be simulated. Although more layers and a larger inclusion is available, it is possible to restrict these numbers during the experiments. Therefore, the values in these columns can be considered as the maximum values of the dataset.

α First layer Number of layers Inclusion width

Set 1 0.5 3 (8x8) 9 (512x512) 5 Set 2 1 3 (8x8) 9 (512x512) 5 Set 3 2 3 (8x8) 9 (512x512) 5 Set 4 1 3 (8x8) 8 (256x256) 9

Table 6.1: Overview of the parameter values of the three congestion datasets we use for the experiments.