# Modeling the Trip Distributions of Tourists Based on Trip Chain and Entropy-Maximizing Theory
## 5 Case Study
### Results and Analysis  
1. Trip chain probability distribution  
Sorting the trip chains obtained by the model in descending order of the calculated probability, we obtained the first 15 trip chains as presented in Table 3. The trip chain code in Table 3 represents the correspondence actual trip chain. For example, trip chain code 93 means the trip chain that starts from traffic zone 9 (see Table 1) to traffic zone 3, and then goes back to traffic zone 9. As shown in Table 3, among the first 15 trip chains that have the maximum probability, the number of trip chains that consist of only one scenic spot is larger than the number of trip chains that involve more than two scenic spots. Specifically, the trip chain with code 93 has the maximum probability. This means tourists have the maximum probability to travel from the road entrance/exit-dominated traffic zone to scenic spot 3, and the number of tourists is also the largest. Moreover, tourists have a larger probability to travel to only one traffic zone. In particular, tourists are more likely to travel to scenic spot 3, other scenic spots, scenic spot 2, scenic spot 4, and scenic spot 5. The detailed distribution of the trip probability of trip chains listed in Table 3 is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline
**Trip Chain Code** & **Actual Trip Chain** & **Trip Chain Code** & **Actual Trip Chain** \\ \hline
93 & RE\({}^{1}\)\(\rightarrow\)SS\({}^{2}\) 3\(\rightarrow\)RE & 95 & RE\(\rightarrow\)SS 5\(\rightarrow\)RE \\
87 & NRS\({}^{3}\)\(\rightarrow\)OSS\({}^{4}\)\(\rightarrow\)NRS & 875 & NRS\(\rightarrow\)OSS\(\rightarrow\)SS 5\(\rightarrow\)NRS \\
97 & RE\(\rightarrow\)OSS\(\rightarrow\)RE & 925 & RE\(\rightarrow\)SS 2\(\rightarrow\)SS 5\(\rightarrow\)RE \\
83 & NRS\(\rightarrow\)SS 3\(\rightarrow\) NRS & 935 & RE\(\rightarrow\)SS 3\(\rightarrow\)SS 5\(\rightarrow\)RE \\
92 & RE\(\rightarrow\)SS 2\(\rightarrow\)RE & 91 & RE\(\rightarrow\)SS 1\(\rightarrow\)RE \\
94 & RE\(\rightarrow\)SS 4\(\rightarrow\)RE & 975 & RE\(\rightarrow\)OSS\(\rightarrow\)SS 5\(\rightarrow\)RE \\
82 & NRS\(\rightarrow\)SS 2\(\rightarrow\)NRS & 937 & RE\(\rightarrow\)SS 3\(\rightarrow\)OSS\(\rightarrow\)RE \\
84 & NRS\(\rightarrow\)SS 4\(\rightarrow\)NRS & \(\cdots\)\(\cdots\) & \(\cdots\) \\ \hline \end{tabular} Note: RE\({}^{1}\) means the road entrance/exit; SS\({}^{2}\) represents the scenic spot; NRS\({}^{3}\) is the north railway station; OSS\({}^{4}\) denotes the other scenic spots.  
\end{table} 
Table 3: Trip chain code and the corresponding actual trip chain. Figure 6: The relation between the residual (\(\varepsilon\)) and the number of iterations. Analysis of the trip chain types  
As described in Section 3.2, this paper classifies trip chains into two types, i.e., simple trip chains and complex trip chains. Here, trip chains were classified according to the value of \(\varphi\). Specifically, a trip chain with \(\varphi=1\) is a simple trip chain and \(\varphi=2\) is a complex trip chain. The proportion of simple and complex trip chains can be calculated according to the model. The trip volume of different trip chain types is shown in Table 4.  
The results presented in Table 4 show that the proportion of tourism activities for simple trip chains is larger than complex trip chains. According to the maximum entropy-based trip distribution model, the maximum proportion of simple trip chains is 77.82%, and the trip volume is 15,120,493. The proportion of complex trip chains is 22.18%, and the trip volume is 4,319,897. The main reason for this might be that, when tourists visit tourism cities, a simple trip chain has a comparatively longer trip distance. This will be further discussed in the next section. Analysis of trip distance  
Each trip chain has a certain distance. Thus, we can classify trip chains according to their distance. By counting the number of trip chains at an interval of 5 km, we can obtain the distribution of trip distances and the corresponding trip probability, as listed in Table 5.