# An Arch-Bridge Topology-Based Expressway Network Structure and Automatic Generation
## 3 Methodology  
### Arch-Bridge Topology  
In the ETC system, OBUs (onboard units) are mounted onto vehicles and RSUs (road-side units) are mounted onto the roadside. Through DSRC (dedicated short-range communication) technology, they communicate with each other to collect all relevant information about passing vehicles. In other words, the expressway network uses ETC gantries as key nodes that can collect information from all vehicles in the entire area and all samples. However, according to the \"ETC gantry system technical requirements for expressways\" issued by the Ministry of Transport in 2019 [59], ETC gantries are deployed not only at the entrances and exits of each toll station but also on road sections before changes in traffic flow occur, such as entrance/exit ramps and interchanges. Of course, this is significantly different from the traditional expressway road network structure, i.e., intersections as nodes. As shown in Figure 1, red triangles are used to mark expressway intersections. However, in the current practical situation, the expressway intersection as a node cannot obtain all passing vehicle information, which makes it difficult to realize the fine management of the expressway. Therefore, we propose a new type of expressway network structure based on the ETC system. The road network is composed of a set of ETC gantry nodes deployed on sections of the road with two-way traffic, denoted as \(G_{r}=\left\{s_{1}^{ur},s_{1}^{dr},s_{2}^{ur},s_{2}^{dr},\ldots,s_{n1}^{ur},s_{ n1}^{dr}\right\},\)  
Figure 1: A simple road network. a set of gantry entrance station (including cross-provincial entrances) nodes denoted as \(G_{en}=\left\{g_{1}^{en},g_{2}^{en},\ldots,g_{n2}^{en}\right\}\), and a set of gantry exit station (including cross-provincial exits) nodes denoted as \(G_{ex}=\left\{g_{1}^{ex},g_{2}^{ex},\ldots,g_{n2}^{ex}\right\}\), etc., forming a key node set \(G=G_{r}\cup G_{en}\cup G_{ex}\) (the total number of nodes \(n=2\times(n1+n2)\)) and a set of road sections \(S=\left\{s_{1},s_{2},\ldots,s_{m}\right\}\) formed by the nodes. Each road section is represented as \(s_{i}=\left\langle g_{start},g_{end}\right\rangle\in S,i=1,2,3\ldots,m\), where \(g_{start}\in\left\{G_{r}\cup G_{en}\right\}\) and \(g_{end}\in\left\{G_{r}\cup G_{ex}\right\}\) are the two key nodes of the road network, representing the starting and ending nodes of the road section \(s_{i}\), respectively. Figure 1 shows a simple expressway network, where there are four entrance/exit gantry station nodes \(\left\{g_{1}^{en},g_{2}^{en},g_{1}^{ex},g_{2}^{ext}\right\}\) and six ETC gantry nodes \(\left\{g_{1}^{sur},g_{1}^{dr},g_{2}^{sur},g_{2}^{dr},g_{3}^{dr},g_{3}^{dr} \right\}\), forming a total of 12 road sections \(\left\{s_{1},s_{2},\ldots,s_{12}\right\}\). From Figure 1, it can be observed that the expressway is a fully enclosed, multi-lane road that controls all entrances and exits and is divided into upline and downline lanes. The ETC gantries are deployed on adjacent (>30 m) upline and downline lanes. Of course, compared with the complex urban road network, the expressway network relying on the ETC system is more structured and organized. Therefore, based on the network topology construction method in complex network analysis, the roadside gantries and station entrance and exit gantries are abstracted as nodes, road sections are abstracted as edges, and a new type of arch-bridge topology structure is defined as follows:  
**Definition 1**. : _Arch-bridge Topology: When an \(n\)-order graph \(\boldsymbol{\hat{S}}=\left.<G,\ E>\right.\) meets the following conditions, the graph \(\boldsymbol{\hat{S}}\) is defined as an arch-bridge topology:_  
1. \(\boldsymbol{\hat{S}}\) _is a directed graph, with the starting node_ \(G_{en}\)_, the middle node_ \(G_{r}\)_, and the ending node_ \(G_{ex}\)_;_
2.