# Modeling the Trip Distributions of Tourists Based on Trip Chain and Entropy-Maximizing Theory
## 3 Tourist Trip Chain Modeling
### Basic Definitions of Tourist Trip Chain  
A trip refers to the travel of people, goods, or cars as a means of transportation from one place to another [24]. Specifically, the travel of people is called personal or individual trips. Meanwhile, a trip chain is defined as a round trip consisting of people completing one or more activities in chronological order and contains a large amount of information about the time, space, ways, and activities of the trip [25]. The structure of a trip chain generally consists of multiple segments, each of which is recorded as a trip. Thus, a tourist trip chain is a set of sequential trips taken by tourists who participate in one or more tourism activities for tours and sightseeing [26]. Normally, we define the departure point of the trip chain as the starting point, the final destination of the trip chain as the ending point, and the points in the middle of the trip chain as stay points.  
Figure 2: The basic idea for the tourist trip distribution modeling.  
To facilitate the study, this paper divides tourist destinations into different traffic zones. These traffic zones can be further classified into several types, including scenic spot-dominated traffic zones, transportation hub-dominated traffic zones, city entrance/exit-dominated traffic zones, and traffic zones in other areas of the city. These traffic zones have corresponding relationships to the starting point, ending point, and stay points of a trip chain. Generally, the starting point and ending point of the trip chain are the traffic zones dominated by the transportation hub or the entrance/exit of the city, respectively; the stay points are the scenic spot-dominated traffic zones or the traffic zones in other areas of the city. Meanwhile, each traffic zone can either be the starting point or ending point of a trip within a trip chain. To keep things simple, this paper defines the starting point of a trip as the origin zone, and the ending point of a trip as the destination zone.  
Trip chains can be further divided into simple and complex chains according to their complexity. A simple trip chain consists of two consecutive trips and has only one stay point. A complex trip chain consists of more than two consecutive trips and has more than one stay point.  
To analyze the trip types of each tourist, this paper uses \(m\) to represent the origin zone and \(m=\left\{1,\ 2,\ 3,\ldots,M\ \right\}\), \(M\) is the maximum number of origin zones. Similarly, we use \(n\) to represent the destination zone and \(n=\left\{1,\ 2,\ 3,\ldots,M\ \right\}\), N is the maximum number of destination zones. Then, as shown in Figure 3, the trip of a tourist that starts from origin zone \(m\) to a number of destination zones \(\left\{n_{1},n_{2},n_{3},\ldots,n_{\varphi}\ \right\}\) and finally returns to \(m\) again has a chain structure. Here, \(\varphi\) is the maximum number of destination zones that a tourist could visit in a trip chain. Then, we can define the choice set for trips starting from an origin zone as \(H=\left\{d_{1},d_{2},d_{3}\ldots,d_{\varphi}\right\}\). It is a set of trip chains that have selected \(\varphi\) numbers of destination zones and is called the \(\varphi\) dimensional destination zone choice set hereafter.