Research on Regional Traffic and Economic Linkage Based on Accessibility and Gravity Model--Taking Hengyang, China as an example

Regional urban connection is mainly reflected in the connection between transportation and economy. Using accessibility and improved gravity model, this paper studies the traffic and economic relations and spatial pattern analysis among districts and counties in Hengyang based on the shortest travel time data and socio-economic data of 12 districts and counties in Hengyang, China. The results show that: firstly, in terms of traffic accessibility, there are 8 districts and counties in Hengyang that have higher accessibility than the average level of the city, and 4 districts and counties that have lower accessibility than the average level. Secondly, the accessibility of districts and counties in Hengyang generally presents an irregular circular distribution pattern, forming a core edge distribution feature with five districts in Hengyang as the core and gradually decreasing outward enclosure. Thirdly, from the perspective of economic connection, the 12 districts and counties in Hengyang are divided into five levels. The first level is the connection between Shigu District and Yanfeng District in the central city. The second level connection intensity is between Shigu District and Zhengxiang District in the central city and between Zhengxiang District and Hengyang County. The intensity of the three-level connection is the connection between the counties near the central urban area and the districts in the central urban area, as well as the connection between the counties near the central urban area and the neighboring counties. The fourth level connection refers to the connection between districts and counties far away from the central urban area and counties near the central urban area. The fifth level connection refers to the connection between districts and counties far away from the central urban area. Last but not least, the economic connection of Hengyang District and county forms the center-peripheral radiation pattern which diffuses from the area with the core of Shigu District, steamed Xiang District, Yanfeng District and Zhuhui District as the core, which presents the pattern of “one core and two centers” in space.


Introduction
The regional connection is manifested as the interaction and connection between economic entities and regions. In the regional space, it is manifested in various forms such as people flow, logistics, capital flow and information flow. The size of the regional economic connection is the strength of the interaction. Through the quantitative study of its size, the strength and spatial orientation of the regional connection can be quantitatively discussed [1] . By quantifying the strength and spatial orientation of regional traffic accessibility and economic ties, the status and role of each city in the region can be 2020 4th International Workshop on Renewable Energy and Development (IWRED 2020) IOP Conf. Series: Earth and Environmental Science 510 (2020) 062005 IOP Publishing doi: 10.1088/1755-1315/510/6/062005 2 clarified, and the relevant theoretical basis and decision support can be provided for the rational development and functional positioning of the cities in the region. In this study, the accessibility and improved gravity model are used to analyze the traffic and economic relations and spatial pattern among 12 districts and counties in Hengyang, China.

Research area
, is a prefecture level city under the jurisdiction of Hunan Province, China. It is a sub-central city, central city of southern Hunanin in Hunan Province, and one of the important transportation hubs in Hunan Province and Central South China. Besides, many railway trunk lines and important highways meet here. Hengyang has jurisdiction over 5 counties of Hengnan, Hengyang, Hengshan, Hengdong and Qidong, 2 cities of Changning and Leiyang, 5 districts of Nanyue, Yanfeng, Shigu, Zhuhui and Zhengxiang, with a total area of 15310 square kilometers. In 2018, there were 7.2434 million permanent residents, including 3.8832 million urban residents, with a urbanization rate of 53.61%. The gross regional product reached 304.603 billion yuan.

Research methods
3.1.1. Traffic accessibility analysis. The concept of accessibility was first proposed by Hansen in 1959 [2], that is, the interaction opportunity of each node in the traffic network. In the regional scope, accessibility reflects the difficulty of spatial interaction and connection between a city or region and other cities or regions [3][4][5]. Considering the influence of node scale and economic development level on accessibility, weighted average travel time distance index is used to measure, and its expression is as follows: In the formula, T ij is the shortest travel time distance from node i to node j; M j is the weight of node j, which can be population scale or GDP, reflecting the impact of node scale on people's willingness to move. M j = j jG P In the formula, P j is the population scale of j area, G j is the total GDP of j area; n is the total number of nodes except i point; A i is the weighted average travel time of node city i, which represents the accessibility level of i point in the traffic network. The smaller the value of A i is , the better the accessibility of node is. Otherwise, the worse the accessibility of node is.
In order to further reveal the status and changing trend of each node in the whole traffic network, the accessibility coefficient is used to reflect the relative level of each node's accessibility level [6,7] . The accessibility coefficient is the ratio of the node's accessibility value and the average accessibility value of all nodes in the network, and its expression is: In the formula, S i is the accessibility coefficient of node i, A i is the accessibility value of node i, and n is the number of nodes. The higher the S i value, the worse the accessibility of the node. A value greater than 1 indicates that the accessibility level of the node is lower than the regional average level, and a value less than 1 indicates that the accessibility of the node is better than the regional average level.
(1)  [8] is commonly used to calculate the strength of economic ties, which is calculated by the shortest actual traffic distance between two cities [9,10] . This study uses time-distance improved gravity model to improve the gravity model, and its expression is as follows: In the formula, R ij is the intensity of economic ties between regions i and j; P i and P j are the population of regions i and j; G i and G j are the GDP of regions i and j; D ij is the travel time based on the shortest path of road network between regions i and j.
On the basis of gravity model, calculate the sum of economic ties between each region and all other regions, that is, the total amount of external economic ties of the region, expressed as: In the formula: R i is the total amount of external economic ties in region i, reflecting the density of economic ties between the region and other regions.

Data source
The data used in the study mainly include traffic data and economic data. The traffic data comes from the shortest travel time between different regions of the city under the self driving mode of Gould map. The research unit is abstracted as a node in the transportation network, and the specific location is the district and county government of the research area, that is, taking the district and county government as the starting or destination, the shortest travel time matrix is finally obtained. Economic data comes from Hunan statistical yearbook and Hengyang statistical yearbook.

Regional traffic accessibility calculation
Based on the comprehensive strength of each district and county and the shortest travel time data of highway transportation network, the weighted average travel time of each county unit in Hengyang is calculated as shown in Table 3 and the accessibility coefficient as shown in Table 4.

Spatial pattern of regional transport connection
In order to understand the spatial differentiation characteristics of regional traffic links more intuitively, the weighted average traffic time of 12 districts and counties in Hengyang City is interpolated by using Arc GIS statistical module. It can be seen that the core area of traffic accessibility is composed of five areas: Zhengxiang, Shigu, Zhuhui, Yanfeng and Nanyue, accounting for about 1 / 4 of the whole Hengyang City, with a weighted average traffic time of 0.91-1.11h. The areas with higher accessibility than the average level are located in Hengyang County, Hengnan County, Hengshan County and Hengdong County in the northeast of the core area. The weighted average travel time isoline of Changning City in Southwest China is sparse compared with other parts, and the accessibility level is slightly lower than the average level. The worst accessibility is Leiyang City in the southeast and Qidong County in the West. The weighted average travel time is 2.75-2.95 h and 2.55-2.75 h respectively. As a whole, the weighted average travel time of each district and county in Hengyang City gradually increases from the Northeast core area to the surrounding area, presenting an irregular circular distribution pattern on the whole, forming a core edge distribution feature with five districts in Hengyang City as the core and gradually decreasing outward enclosure.

Analysis of differences in regional economic ties
According to the gravity model of time distance correction, the strength and total amount of economic ties of each district and county are calculated by using the time distance of the resident population, GDP and the time distance of each region of Hengyang City in 2018, as is shown in Table 6 and Table 7.