# Research on Urban Road Network Evaluation Based on Fractal Analysis

Authors: Wen Wen; Wenhui Zhang; Hongxing Deng
Journal: Journal of Advanced Transportation
 (2023)

---

## Abstract

The structure of the urban road network affects the mode of urban development and the position of urban social and economic activities, families, and employment centers. Therefore, it is necessary to consider the supply inequality of urban road network and its impact on urban development so as to form a sustainable and fair urban development model in cities. Based on the fractal analysis, this paper seeks the evaluation index of urban road network layout and internal structure characteristics to guide the optimization and adjustment of the urban road network, which is of great significance for guiding urban land use, effectively utilizing geospatial space, and promoting sustainable urban development, and attempts to apply the fractal analysis concept to evaluate the urban road network in Harbin, China. It is found that there is a good relationship between the length of the urban road network and the build-up area. Therefore, fractal analysis is used to reasonably determine the spatial demand of incremental road networks, considering the impact of road network increase on development mode. This paper argues that fractal analysis is an auspicious tool for the evaluation of urban road networks, including solving the problem of supply inequality in urban road networks, which is very suitable for the gradual construction of road networks in urban situations, especially in the development environment of road networks with scarce resources.


---

## Body

## 1. Introduction

The relationship between urban development and urban road network development is complementary. On the one hand, the urban road network is the product of urban development [1, 2], and on the other hand, the urban road network is the basis for promoting urbanization [3, 4]. However, with the expansion of the urban scale and the gradual improvement of urban functions, the acceleration of urban development has also increased its requirements for an urban road network [5]. While achieving urban scale expansion, ensuring that the supporting urban road traffic network has scale rationality, structural coordination, and service efficiency is the cornerstone of ensuring the development of high-quality integrated cities. As an integral part of the urban traffic system, the urban road network has formed a complete system to support the operation of the entire urban traffic [6]. In addition, as one of the leading networks for maintaining the regular operation of urban functions, it is also the premise and foundation for the sustainable development of a social economy. It is not only a symbol of the level of urban modernization but also the material basis for ensuring the regular operation of the whole urban lifeline system [7–9]. It is of great significance to improve people’s production and living conditions, promote the rational use and development of land resources, and realize urban modernization [10–13]. Currently, the development speed and demand for urban traffic networks in Heilongjiang Province are not balanced, and there is no standardized method for road network construction. It is observed from the overall planning of cities in Heilongjiang that there is no relevant standard for the circulation pattern of cities, which also seriously restricts the urbanization process, as shown in Table 1.Table 1
Land utilization of cities in Heilongjiang province.
CityPopulation (in lakhs)City area (in sq.km)Road length (km)Road density (km/sq.km)Land utilization rate road length/1 lakh populationHarbin98.854734265.89.0243.15Qiqihar51.65130.96544.164.1610.54Mudanjiang24.4292.68806.598.7033.03Jiamusi51.57188341.211.816.62Daqing27.47327.192252.56.8882.00Yichun8.5121.93628.015.1573.88Jixi16.4780.41474.285.9028.80Hegang8.9185403.64.7545.30Shuangyashan12.09118443.783.7636.71Qitaihe6.967.6539.877.9978.24Suihua61.3492.77189.072.043.08Heihe12.8627.8884.013.016.53Human research on the road network structure can be traced back to 1736 Leonhard Ola’s “seven bridge problem” [14]. Scholars’ research on the road network is roughly from the following three perspectives: First, based on the traditional method and the acquisition of regional road network density, road network connectivity, and other indicators through different data analysis methods such as efficiency analysis and potential energy analysis, the internal structure optimization of the urban road network is proposed [15, 16]. The second is to focus on the impact of regional traffic accessibility on regional economic development, urban system spatial structure, and population distribution [17, 18]. The third is the fundamental representation of a complex road network: how to determine the basic modeling unit of road network research [19, 20]; the fourth is road network spatial analysis and modeling. Representation refers to the processing, storage, and structure of the expression of information [21, 22]. How to systematically and normatively abstract and express spatial objects in the form of direct understanding is an essential and fundamental problem of geographic information science. The results of different road representations on the same road network may be similar or opposite. Therefore, a scientific approach is needed to address the overall structure of the road network and its impact on development patterns and transport quality [23]. In this context, fractal geometry provides an effective and alternative method for evaluating the urban road network’s complex attributes and regional geographical features. Previous studies have shown that fractal theory can be used to analyze the internal structural characteristics of traffic networks such as highways, railways, and urban roads [24]. However, the existing research mainly focuses on a specific road network, and there needs to be a more detailed analysis of its internal hierarchical structure. Research on the hierarchical structure characteristics of the road network is relatively rare. The road network fractal dimension is a reliable index of road network evaluation, so the research on it is of great significance. In addition, previous studies focused on theoretical abstraction and qualitative description. It is difficult to give accurate quantitative analysis results based on the urban road network’s overall situation, making it impossible for different urban studies to compare horizontally on a collaborative research platform [25–27]. At the same time, the qualitative research model also makes the conclusion vague.Therefore, aiming at the research object of the urban road network, the research content can guide the layout and optimization of the urban road network structure more effectively. Based on fractal theory, this study attempts to draw lessons from the experience of previous fractal theories in the structural analysis of network objects such as highways, railways, and urban form and introduces the application of fractal analysis in the evaluation of the Harbin road network in Heilongjiang Province. This study analyzes the problems existing in the practice of transportation network planning and evaluation in Northeast China. Various urban road network evaluation methods were emphatically reviewed, especially the fractal analysis method. According to the density parameter and the rapid development city with a population size of 5–10 million people, the case urban area was selected. By establishing the urban buffer, the relationship between the road network and the development indicators was determined. The fractal dimension of the road network is used to determine the relationship between the fractal dimension, the road network, and the development mode. The road network enhancement strategy was proposed based on the transport network supply imbalance [28]. At the end of the study, new road networks and build-up areas were recommended for general urban areas, especially for case cities, and fractal analysis was used for evaluation.


## 2. Data and Methodology

### 2.1. Study Area

Harbin is the capital of Heilongjiang Province in Northeast China and is the political, economic, and cultural center in the north of Northeast China. Harbin has jurisdiction over nine municipal districts, seven counties, and two county-level cities. Due to the build-up areas of counties and county-level cities and the small population, the study area is the municipal area of Harbin. By the end of 2022, the municipal area of Harbin was 10249 km2, the build-up area was 508.7 km2, and the population was 6.9761 million. The total number of buildings and the total area are 105907 and 60965.796 km2, respectively. Figure 1 gives the municipal map of Harbin and the central city of Harbin. The total number of roads in the main urban area is 12800 strips, and the total length of the road network is 9757.934 km.Figure 1
(a) Harbin city map. (b) Harbin municipal area map.
(a)(b)There are a variety of methods for road network evaluation, such as shape grammar rules, graph theory, shortest path matrix, and fractal. Table2 shows the complexity, merits, and limitation of each method.Table 2
Merits and limitations of existing road network evaluation methods.
Evaluating methodsDescriptionComplexityMeritsLimitationShape grammar rulesProvides finite rules on how to add the same or different types of network elementsLong running time but small space requiredStudying the relationship between road density and network loop also guides road network designNot considering the function of urban developmentGraph theoryThe graph is a set of nodes connected by lines or arrowsLong running time and large space requiredMainly used to calculate the road network accessibility between citiesOnly indexes are based on the number of nodes and linksShortest path matrixMinimum generalized cost matrix from arbitrary zonei to arbitrary zone jShort running time but large space requiredIt takes less time to calculate and expenditureDistribution types can be distinguished, but shapes cannot be distinguishedFractalA fractal is a geometric object formed naturally or artificiallyShort running time and small space requiredThere is an intensity method for describing complex forms of transportation networks and urban modelsCannot bear the complexity of the whole system, more sensitive to the data summary


### 2.2. Data

The road network data was downloaded from Open Street Map(OSM), as shown in Figure2. We were collecting the road number, road length, build-up area, building number, and building area of 9 districts in Harbin. The detailed data of urban road network is shown in Table 3. The population for the year 2022 was collected from the people’s government of Harbin. The number and area of different areas and buildings were collected from the Heilongjiang Surveying and Mapping Geographic Information Bureau since these data cannot be obtained in the OSM database.Figure 2
Harbin’s road network.Table 3
Detailed data on the urban road network in Harbin.
DistrictsRoad numberRoad length (km)Build up area (km2)Building numberBuilding area (km2)Nangang2279854.1672.42267812843.68Xiangfang22561121.381012833516899.16Songbei19081270.776967393875.67Acheng18861730.5525.970991966.27Daoli14551020.974.8136637961.77Hulan11171516.3350.655553409.21Daowai1108813.6653.81694710822.11Shuangcheng5221107.322.725551294.55Pingfang269322.8838.523361893.37


### 2.3. Data Processing

The urban buffer refers to the planning and establishment of a specific area of a construction project called a “blank area” between two or more functional areas with relatively dense urban areas to alleviate urban traffic pressure and residents’ “sense of urban repression, which is generally planned into a comprehensive road network or a large area of water, forest, and green space. Urban buffer plays an irreplaceable role in alleviating traffic pressure and residents” sense of urban repression in urban intensive functional areas. Even if traffic congestion occurs in intensive functional areas, the congestion time will be significantly shortened due to the existence of the buffer. The buffer radius plays a vital role in understanding the relationship between the built environment and the road network and determining the buffer radius. Thus, the case city was analyzed. Table4 shows the details of buffer intervals at 100 m, 250 m, and 500 m, respectively.Table 4
Identification of buffer interval.
Buffer interval100 m250 m500 mFractal dimension1.6171.5261.506Robust1.251.501.00


### 2.4. Fractal Dimension and Its Features

Mandelbrot first introduced the fractal theory in his French bookFractal: Shape, Opportunity, Dimension in 1975. For some straight lines, if the integer dimension is used to measure, the results are either infinite or zero. Therefore, if we dynamically observe the transformation between points, lines, and surfaces, it will be found that the integer dimension cannot describe some geometric figures. Therefore, it can be seen that the geometric figure composed of fragmented graphics is fractal, and their fractional dimension includes the integer dimension. The integer dimension can only describe the static characteristics of the geometric figure, while the fractional dimension describes the dynamic changes of the geometric figure. Suppose the above understanding is extended to the dynamic behavior or phenomenon of the urban road network. In that case, the fractional dimension describes the behavior of the overall road network system, which consists of the local characteristics of minor roads in the urban road network. The following formula can express the complexity:(1)Dr=lgLRi/lgLRi−1lgRi/Ri−1.Dr = fractal dimension; L (Ri) = length of road network in km in a radius of (i); L (Ri − 1) = length of road network in km in radius of (i − 1); Ri = radius of the buffer; and Ri − 1 = radius of a predecessor buffer zone multiples of the radius.There are three main features of fractal:(1)
Self-similarity: fractal graphics are made up of their scale reduction replication, local and overall similarity;(2)
Scale-free: any local area on a fractal object is enlarged or reduced, but its shape, complexity, and irregularity do not change;(3)
Self-affines: when the transformation ratios of local to global injuries in different directions are different, it is called self-affines transformation, which is a particular case of self-similarity.An urban traffic system is a dynamic, open, complex giant system with typical space-time complex characteristics. Unfortunately, the existing spatial analysis-based methods can only provide some results at a specific scale. They cannot evaluate a system from macro to micro as the fractal analysis does. Suppose the urban traffic network and other subsystems show fractal features named irregular, scale-invariant, and self-similar. In that case, fractal analysis will be an effective tool for evaluation and representation. The urban road network has attracted much attention and research due to its irregular shape and organic growth. The fractal analysis of the urban road network is divided into two categories, aiming to reveal the regularity and self-similarity of the road system. Policymakers and planners need to test the coordination between these subsystems or predict it.


### 2.5. Methods to Calculate the Fractal Dimension

There are many methods for calculating fractal dimensions in fractal geometry. Some of them are classical calculation methods, such as self-similarity and box-counting dimensions. Other calculation methods are evolved from classical algorithms according to the actual situation and the needs of calculation and research, such as the fractal method, area-perimetric method, root-mean-square method, and structural function method. This study uses the mass-radius method to calculate the fractal dimension. There are two main reasons. First, urban roads and build-up areas have similar spatial distributions. Namely, they have self-similar properties. Secondly, more quantitative spatial information can be obtained by fractal analysis to describe the relationship between them.There are four aspects to using fractal analysis: Firstly, a city as a fractal and the fractal nature of a city’s growth, or the “space-contour” process; Secondly, the fractal analysis moves towards a larger spatial scale to examine the fractal nature of the urban system and human settlement pattern; Thirdly, pay attention to some subsystems of the city, such as the land use pattern, build-up area distribution, or traffic network; last but not least, the pattern is closely related to urban growth and build-up area increase. The fractal dimension tool is used to analyze this relationship.(2)L1∝S1/2∝V1/3∝M1/D,L is geographical entity length, S is an area, V is volume, M is an arbitrary dimension, and D is fractal geometry.


## 2.1. Study Area

Harbin is the capital of Heilongjiang Province in Northeast China and is the political, economic, and cultural center in the north of Northeast China. Harbin has jurisdiction over nine municipal districts, seven counties, and two county-level cities. Due to the build-up areas of counties and county-level cities and the small population, the study area is the municipal area of Harbin. By the end of 2022, the municipal area of Harbin was 10249 km2, the build-up area was 508.7 km2, and the population was 6.9761 million. The total number of buildings and the total area are 105907 and 60965.796 km2, respectively. Figure 1 gives the municipal map of Harbin and the central city of Harbin. The total number of roads in the main urban area is 12800 strips, and the total length of the road network is 9757.934 km.Figure 1
(a) Harbin city map. (b) Harbin municipal area map.
(a)(b)There are a variety of methods for road network evaluation, such as shape grammar rules, graph theory, shortest path matrix, and fractal. Table2 shows the complexity, merits, and limitation of each method.Table 2
Merits and limitations of existing road network evaluation methods.
Evaluating methodsDescriptionComplexityMeritsLimitationShape grammar rulesProvides finite rules on how to add the same or different types of network elementsLong running time but small space requiredStudying the relationship between road density and network loop also guides road network designNot considering the function of urban developmentGraph theoryThe graph is a set of nodes connected by lines or arrowsLong running time and large space requiredMainly used to calculate the road network accessibility between citiesOnly indexes are based on the number of nodes and linksShortest path matrixMinimum generalized cost matrix from arbitrary zonei to arbitrary zone jShort running time but large space requiredIt takes less time to calculate and expenditureDistribution types can be distinguished, but shapes cannot be distinguishedFractalA fractal is a geometric object formed naturally or artificiallyShort running time and small space requiredThere is an intensity method for describing complex forms of transportation networks and urban modelsCannot bear the complexity of the whole system, more sensitive to the data summary


## 2.2. Data

The road network data was downloaded from Open Street Map(OSM), as shown in Figure2. We were collecting the road number, road length, build-up area, building number, and building area of 9 districts in Harbin. The detailed data of urban road network is shown in Table 3. The population for the year 2022 was collected from the people’s government of Harbin. The number and area of different areas and buildings were collected from the Heilongjiang Surveying and Mapping Geographic Information Bureau since these data cannot be obtained in the OSM database.Figure 2
Harbin’s road network.Table 3
Detailed data on the urban road network in Harbin.
DistrictsRoad numberRoad length (km)Build up area (km2)Building numberBuilding area (km2)Nangang2279854.1672.42267812843.68Xiangfang22561121.381012833516899.16Songbei19081270.776967393875.67Acheng18861730.5525.970991966.27Daoli14551020.974.8136637961.77Hulan11171516.3350.655553409.21Daowai1108813.6653.81694710822.11Shuangcheng5221107.322.725551294.55Pingfang269322.8838.523361893.37


## 2.3. Data Processing

The urban buffer refers to the planning and establishment of a specific area of a construction project called a “blank area” between two or more functional areas with relatively dense urban areas to alleviate urban traffic pressure and residents’ “sense of urban repression, which is generally planned into a comprehensive road network or a large area of water, forest, and green space. Urban buffer plays an irreplaceable role in alleviating traffic pressure and residents” sense of urban repression in urban intensive functional areas. Even if traffic congestion occurs in intensive functional areas, the congestion time will be significantly shortened due to the existence of the buffer. The buffer radius plays a vital role in understanding the relationship between the built environment and the road network and determining the buffer radius. Thus, the case city was analyzed. Table4 shows the details of buffer intervals at 100 m, 250 m, and 500 m, respectively.Table 4
Identification of buffer interval.
Buffer interval100 m250 m500 mFractal dimension1.6171.5261.506Robust1.251.501.00


## 2.4. Fractal Dimension and Its Features

Mandelbrot first introduced the fractal theory in his French bookFractal: Shape, Opportunity, Dimension in 1975. For some straight lines, if the integer dimension is used to measure, the results are either infinite or zero. Therefore, if we dynamically observe the transformation between points, lines, and surfaces, it will be found that the integer dimension cannot describe some geometric figures. Therefore, it can be seen that the geometric figure composed of fragmented graphics is fractal, and their fractional dimension includes the integer dimension. The integer dimension can only describe the static characteristics of the geometric figure, while the fractional dimension describes the dynamic changes of the geometric figure. Suppose the above understanding is extended to the dynamic behavior or phenomenon of the urban road network. In that case, the fractional dimension describes the behavior of the overall road network system, which consists of the local characteristics of minor roads in the urban road network. The following formula can express the complexity:(1)Dr=lgLRi/lgLRi−1lgRi/Ri−1.Dr = fractal dimension; L (Ri) = length of road network in km in a radius of (i); L (Ri − 1) = length of road network in km in radius of (i − 1); Ri = radius of the buffer; and Ri − 1 = radius of a predecessor buffer zone multiples of the radius.There are three main features of fractal:(1)
Self-similarity: fractal graphics are made up of their scale reduction replication, local and overall similarity;(2)
Scale-free: any local area on a fractal object is enlarged or reduced, but its shape, complexity, and irregularity do not change;(3)
Self-affines: when the transformation ratios of local to global injuries in different directions are different, it is called self-affines transformation, which is a particular case of self-similarity.An urban traffic system is a dynamic, open, complex giant system with typical space-time complex characteristics. Unfortunately, the existing spatial analysis-based methods can only provide some results at a specific scale. They cannot evaluate a system from macro to micro as the fractal analysis does. Suppose the urban traffic network and other subsystems show fractal features named irregular, scale-invariant, and self-similar. In that case, fractal analysis will be an effective tool for evaluation and representation. The urban road network has attracted much attention and research due to its irregular shape and organic growth. The fractal analysis of the urban road network is divided into two categories, aiming to reveal the regularity and self-similarity of the road system. Policymakers and planners need to test the coordination between these subsystems or predict it.


## 2.5. Methods to Calculate the Fractal Dimension

There are many methods for calculating fractal dimensions in fractal geometry. Some of them are classical calculation methods, such as self-similarity and box-counting dimensions. Other calculation methods are evolved from classical algorithms according to the actual situation and the needs of calculation and research, such as the fractal method, area-perimetric method, root-mean-square method, and structural function method. This study uses the mass-radius method to calculate the fractal dimension. There are two main reasons. First, urban roads and build-up areas have similar spatial distributions. Namely, they have self-similar properties. Secondly, more quantitative spatial information can be obtained by fractal analysis to describe the relationship between them.There are four aspects to using fractal analysis: Firstly, a city as a fractal and the fractal nature of a city’s growth, or the “space-contour” process; Secondly, the fractal analysis moves towards a larger spatial scale to examine the fractal nature of the urban system and human settlement pattern; Thirdly, pay attention to some subsystems of the city, such as the land use pattern, build-up area distribution, or traffic network; last but not least, the pattern is closely related to urban growth and build-up area increase. The fractal dimension tool is used to analyze this relationship.(2)L1∝S1/2∝V1/3∝M1/D,L is geographical entity length, S is an area, V is volume, M is an arbitrary dimension, and D is fractal geometry.


## 3. Analysis and Results

### 3.1. Impact of Buffer Interval on the Road Network and Development Patterns

It was observed from the analysis that the increase in buffer spacing resulted in a decrease in living areas. With the migration away from the city center, the city’s built-up area will decrease because, compared with the internal region, the living population in the outer region will decrease as shown in Figure3.Figure 3
Rate of change in build-up area.This study divided the build-up area into three main land use types for detailed segregation analysis. It is observed that with the increase in buffer interval, the residential slope gradually decreased, and the commercial residential area appeared to have a negative slope.The parameter of road network length presents a negative slope with the increase of buffer interval. It is generally observed in small cities that with the outward movement from the city center, the length of the urban road network will decrease due to the decrease in the length of local roads and collector roads as shown in Figure4.Figure 4
Rate of change in road length.The number of intersections harms the increase of buffer interval. This shows that compared with the internal areas, the intersection of external areas will decrease, which is also a general phenomenon that Chinese cities will observe.With the increase in buffer interval, the average distance between the two junctions will increase. There is a good correlation (avg 0.96) between various road widths (below 3.5, 3.5–7.0, 7.0–12.0, and above 12 m) and buffer intervals. With the increase in buffer interval, in addition to the local roads, the width of various roads will increase, which is generally observed in any city in Heilongjiang in China.


### 3.2. Impact of the Road Network and Development Patterns

It can be seen from the analysis of internal relations that the road network length is directly related to the build-up area. As observed, increasing the length of roads will increase the build-up area in the city to a certain point, which will have a negative impact afterward. Good interlinkages between build-up areas and various land uses (residential, commercial, and others) were also identified. With the increase of the build-up area, the residential area also increased at the same level (slope), while commercial and other land uses showed a constant slope after a certain point and even increased in the build-up area. There is a good relationship between road length and road width (below 3.5, 3.5∼7.0, 7.0∼12.0, and above 12 m). When the road length increases above 12 m and 7.0 m, the road length under the same slope also increases, but the road lengths below 3.5–7.0 m and 3.5 m appear to have a negative slope after the road network length increases to a certain point. The increase in road network length will reduce the traffic congestion index. With the increase of the build-up area, the speed also increases to the break-even point, and then there will be a negative impact from the decline in the speed level. The road network density positively affects the weighted average speed of the city. There is a good correlation between road network density and weighted average speed, and the coefficient is 0.946. The desired speed of Harbin is calculated to be 26 km/h, as shown in Figures5–9.Figure 5
Relation with road density and build-up area.Figure 6
Various land use in build-up areas.Figure 7
Relationship between road widths and lengths in each buffer.Figure 8
Relationship between road density and weighted speed.Figure 9
Desired speed at peak hour in Harbin.


## 3.1. Impact of Buffer Interval on the Road Network and Development Patterns

It was observed from the analysis that the increase in buffer spacing resulted in a decrease in living areas. With the migration away from the city center, the city’s built-up area will decrease because, compared with the internal region, the living population in the outer region will decrease as shown in Figure3.Figure 3
Rate of change in build-up area.This study divided the build-up area into three main land use types for detailed segregation analysis. It is observed that with the increase in buffer interval, the residential slope gradually decreased, and the commercial residential area appeared to have a negative slope.The parameter of road network length presents a negative slope with the increase of buffer interval. It is generally observed in small cities that with the outward movement from the city center, the length of the urban road network will decrease due to the decrease in the length of local roads and collector roads as shown in Figure4.Figure 4
Rate of change in road length.The number of intersections harms the increase of buffer interval. This shows that compared with the internal areas, the intersection of external areas will decrease, which is also a general phenomenon that Chinese cities will observe.With the increase in buffer interval, the average distance between the two junctions will increase. There is a good correlation (avg 0.96) between various road widths (below 3.5, 3.5–7.0, 7.0–12.0, and above 12 m) and buffer intervals. With the increase in buffer interval, in addition to the local roads, the width of various roads will increase, which is generally observed in any city in Heilongjiang in China.


## 3.2. Impact of the Road Network and Development Patterns

It can be seen from the analysis of internal relations that the road network length is directly related to the build-up area. As observed, increasing the length of roads will increase the build-up area in the city to a certain point, which will have a negative impact afterward. Good interlinkages between build-up areas and various land uses (residential, commercial, and others) were also identified. With the increase of the build-up area, the residential area also increased at the same level (slope), while commercial and other land uses showed a constant slope after a certain point and even increased in the build-up area. There is a good relationship between road length and road width (below 3.5, 3.5∼7.0, 7.0∼12.0, and above 12 m). When the road length increases above 12 m and 7.0 m, the road length under the same slope also increases, but the road lengths below 3.5–7.0 m and 3.5 m appear to have a negative slope after the road network length increases to a certain point. The increase in road network length will reduce the traffic congestion index. With the increase of the build-up area, the speed also increases to the break-even point, and then there will be a negative impact from the decline in the speed level. The road network density positively affects the weighted average speed of the city. There is a good correlation between road network density and weighted average speed, and the coefficient is 0.946. The desired speed of Harbin is calculated to be 26 km/h, as shown in Figures5–9.Figure 5
Relation with road density and build-up area.Figure 6
Various land use in build-up areas.Figure 7
Relationship between road widths and lengths in each buffer.Figure 8
Relationship between road density and weighted speed.Figure 9
Desired speed at peak hour in Harbin.


## 4. Discussions

The analysis shows that the proper fractal dimension of the Harbin road network is 1.637. The identification of proper fractal dimensions is mainly based on two criteria. First, the city is a two-dimensional element with two directions for growth. Therefore, the proper buffer will be in the range of 1-2; this condition considers the values more significant than one and less than two. Secondly, each buffer interval and its corresponding index fractal dimension are calculated using the concept of actual fractal dimension modal values, where all indexes of a buffer are in the same fractal dimension. When a buffer of fewer than 1.5 dimensions needs to be augmented and the need for more than 1.5 is limited, a green field system model is established between the fractal road length and population/1000 to increase the network in the inequality buffer. As shown in Figure10. Thirdly, there is a good relationship between fractal dimension and road network length, and build-up area. We develop a model to increase the road network length and estimate the build-up area to determine the fractal dimension. Fourthly, the model is used to identify the required build-up area and road network. The mutual relationship model evaluates the width and length of various roads under various land uses and road network lengths in the build-up area as shown in Tables 5 and 6.Figure 10
FD of road length with per 1000 population.Table 5
Relationship between buffer interval and land use.
Buffer radiusFD of road lengthLand use0.501.592No more development0.751.761Restricted1.001.707No more development1.251.563No more development1.501.862Restricted1.751.574No more development2.001.381Promote2.251.349PromoteTable 6
Relationship between buffer interval and development indicators.
Development indicatorsBuffer interval2.002.25ExistAdditionalExistAdditionalRoad length18.793.4916.845.66Road width5.921.236.432.17Build up area0.310.180.350.23Land use0.190.110.300.15ExistImpactExistImpactSpeed3225.913426.22Congestion index−0.1670.108−0.6840.828


## 5. Conclusions

This paper measured the fractal dimension of the urban road network using the mass-radius method. It is observed that there is a strong correlation between the road network index and the fractal dimension as well as between the road network index and the build-up area index. In the absence of development opportunities in urban core areas, a brown regional model was established, with only development space in remote areas. According to the length of the existing road network and the characteristics of the build-up area, additional requirements are put forward for the urban road network by keeping the attenuation curve of road network density corresponding to the population density per square kilometer in each buffer zone.The main advantage of fractal analysis is that it is an intuitive model with less time and cost. In addition, it is also helpful in preparing overall planning (network expansion). This model is very beneficial for cities with relatively small scales in developing countries.The analysis results confirm the need to identify commonalities in road networks, intersections, and build-up areas. In this case, the observed urban deficiencies are also highlighted in the high-order road function system. Based on the actual fractal dimension, the analysis has been used as a standard for promoting/reducing land use in urban buffer zones. Therefore, the rapid change of peripheral urban areas can be investigated through fractal dimension estimation and its value change over time. The conclusion shows that this method is beneficial for evaluating the road network of nonlarge cities.



---

*Source: 9938001-2023-01-18.xml*