Equity analysis of bus network balance from the perspective of spatial morphology and service capability

This study obtained the comprehensive indices and influencing factors for 332 bus routes in Xiamen, The seven influencing factors, after being processed using the entropy method as described above, have values ranging between 0 and 1, and the composite index values also fall within the 0 to 1 range. This paper begins by analyzing the maximum population transport capacity of bus routes, spatial structure, network layout balance, and service fairness of the routes.

Analysis of the maximum passenger transport capacity of bus routes

Based on the improved gravity model formula, after standardization and dimension removal, the maximum passenger transport capacity of the bus route is obtained. The larger the value, the greater the number of people that can be transported by the bus route. To better analyze its value, the natural breaks method was used to divide the data into five levels: (a) 98 routes between 0 and 0.11; (b) 87 routes between 0.11 and 0.20; (c) 94 routes between 0.20 and 0.31; (d) 36 routes between 0.31 and 0.47; (e) 17 routes between 0.47 and 1. As shown in Fig. 6, Based on the five levels of maximum passenger transportation, there is a decreasing trend in which the larger the value, the fewer the number of routes, In subsequent analyses, the natural breaks method is consistently used to categorize influencing factors and comprehensive indices into five levels.

Number of bus routes based on the maximum passenger transport capacity.

Combining the spatial distribution of the maximum passenger transport capacity by bus routes(Fig. 7), it is found that routes with a service capacity between 0 and 0.20 are mainly located in the outer areas of the island, characterized by high terrain, low population density, and dense forests, with a few routes located in natural scenic areas within the island. Routes with a service capacity between 0.20 and 0.47 are mostly located in the inner areas of the island, with some routes in the core areas of the outer four districts. Routes with a service capacity between 0.47 and 1 are primarily located in urban village clusters in the non-core areas of Jimei, Tong’an, and Haicang districts.

Spatial distribution of bus routes based on the maximum passenger transport capacity.

The spatial distribution pattern is mainly due to the combined effect of the differences in the number of urban villages and bus routes. The outer four districts (Jimei, Tong’an, Xiang’an, and Haicang) have 637 urban villages, while the inner two districts (Siming and Huli) have only 45 urban villages. The permanent population in the urban villages of the outer districts is much larger than that in the inner districts. Due to economic reasons, the probability of urban village populations choosing public transportation as their mode of travel is higher compared to other options. In the outer island areas, the number of bus routes is fewer than in the inner island areas. As a result, urban village populations with a need for transportation tend to concentrate on a limited number of bus routes, leading to a significant increase in the passenger volume on bus routes passing through urban villages in the three outer island districts. In contrast, the inner island area has a smaller geographic size but more bus routes, with multiple routes serving the same section, offering more transportation options. Consequently, the passenger volume on bus routes in the inner island area becomes more dispersed.

Analysis of network centrality and traversability of bus routes

The integration and choice values of Xiamen’s entire road network were obtained. After standardization and dimensionless processing, these values were assigned to the corresponding spatial locations of the bus routes, resulting in the integration and choice values for each bus route. A higher value of integration and choice indicates greater centrality and traversability of the bus route within the city’s road network.

Integration

The integration values were divided into five levels: (a) 55 routes between 0 and 0.11; (b) 101 routes between 0.11 and 0.20; (c) 103 routes between 0.20 and 0.33; (d) 56 routes between 0.33 and 0.53; (e) 17 routes between 0.53 and 1. As shown in Fig. 8, the number of routes displays a normal distribution trend under the network centrality (integration) classification. This indicates that most bus routes in Xiamen have a good level of centrality, with fewer routes having extreme centrality values, suggesting a relatively even distribution of routes based on centrality.

Number of bus routes based on network centrality.

Figure 9 shows the spatial distribution characteristics of bus route network centrality: Routes with integration values between 0 and 0.11 are mainly located in remote areas away from the district centers. Routes with integration values between 0.11 and 0.53 are mostly located in the core areas of each district, with a few routes in remote areas. The 17 routes with integration values between 0.53 and 1 consist mainly of routes both inside and outside the island. Within the island, these routes pass through major traffic arteries such as Chenggong Avenue, the Island Ring Road, and Jiahe Road, and connect to the outer areas via the Jimei Bridge and Xiang’an Tunnel. The outer routes pass through major roads such as Tongji South Road and Binhai West Avenue in Jimei District; Xiang’an Avenue, Hongzhong Avenue, and Xiang’an South Road in Xiang’an District; and North and South Ring Roads in Tong’an District. The roads covered by these bus routes are the main traffic arteries in the outer districts.

Spatial distribution of bus route network centrality.

The spatial distribution of bus routes aligns with the overall urban road traffic planning. Routes with high integration values are primarily located on major traffic arteries. Since the main traffic arteries form the core of the road network, higher road integration values correspond to higher integration values of the bus routes on these main roads, leading to greater network centrality. The spatial distribution of the bus route network centrality reflects the actual situation.

Choice

Figure 10 shows the division results for the five levels of choice: (a) 130 routes between 0 and 0.08; (b) 121 routes between 0.08 and 0.18; (c) 58 routes between 0.18 and 0.33; (d) 20 routes between 0.33 and 0.60; (e) 3 routes between 0.60 and 1. Unlike the trend observed with integration, the number of routes decreases as the choice value increases, indicating that most bus routes in Xiamen have a low level of traversability. From the perspective of traversability, the route distribution generally covers the road network of Xiamen.

Number of bus routes based on network traversability.

Figure 11 shows the spatial distribution of bus route network traversability. Routes with choice values between 0.33 and 1 overlap with routes that have integration values between 0.53 and 1, primarily located on the main traffic arteries both inside and outside the island. The two routes with the highest choice values are located in Xiang’an District rather than the inner island area.

The spatial distribution can be explained by the definition of choice: Xiang’an District has fewer major traffic roads compared to other areas, offering less route choice and resulting in a higher number of road crossings, which increases the network traversability of bus routes on the main roads. In contrast, the inner island area has a well-developed road network system with multiple options to reach different roads, resulting in lower network traversability for the bus routes within the island.

Spatial distribution of bus route network traversability.

Analysis of the balance of the bus network layout

Entropy is used to determine the randomness of influencing factors. The smaller the entropy, the greater the dispersion of the factor values, the higher the weight of the influencing factor, and the greater the impact on the comprehensive score (comprehensive index) of the route samples (Table 2 and Eq. 8).

From the perspective of analyzing bus route service capacity, the higher the comprehensive index value, the higher the service capacity of the bus route. According to statistics: (a) 72 routes between 0.01 and 0.13; (b) 86 routes between 0.13 and 0.22; (c) 75 routes between 0.22 and 0.31; (d) 56 routes between 0.31 and 0.42; (e) 43 routes between 0.42 and 0.62. As shown in Fig. 12, the number of routes shows an initial increase and then a decrease under the classification of comprehensive index levels. This indicates that bus routes based on the comprehensive index are relatively evenly distributed in Xiamen.

Number of bus routes based on comprehensive index.

Combining the Xiamen DEM map and the spatial morphology of bus routes (Fig. 13), it is found that routes with index values between 0.01 and 0.22 are distributed in the outer four districts’ suburbs with low population and relatively underdeveloped facilities, as well as in the island’s natural scenic areas. The higher the terrain, the sparser the distribution of bus routes. Routes with index values between 0.22 and 0.62 are concentrated in the flat areas of Xiamen Island, the central areas of the outer four districts, and along main traffic arteries. There is a clear spatial difference in bus routes, with index values decreasing from Xiamen Island to the outer areas. From the perspective of bus route service capacity, the bus service capacity in the Siming and Huli districts on Xiamen Island is relatively superior to that of the outer districts. The main reasons are that the two districts on the island have a smaller area, a larger permanent population, complete facility construction, flat terrain, and a higher level of economic development, making them suitable for public transportation system construction. The bus network distribution on the island is relatively balanced and complete. In contrast, the outer districts cover a large area, some parts of which include forest areas not suitable for habitation. The permanent population in the outer districts is larger than that on the island, but except for the densely populated core areas of the outer four districts, the permanent population is relatively scattered in other areas. The outer districts have incomplete facility construction and relatively lagging economic development, leading to an uneven distribution of the bus network in the outer areas.

Spatial distribution of bus routes based on comprehensive index.

In summary, based on the comprehensive index of bus routes, the overall layout of the bus network in Xiamen is relatively balanced on a global scale, with some remote areas being relatively unbalanced. The central areas have a dense layout, while the remote suburbs have a sparse layout.

Analysis of bus routes fairness

Equity means that everyone enjoys equal rights and focuses on the interests of the group³⁴. In this study, route fairness is defined as the ability of a bus route to provide public transportation services to the population within its service area. The comprehensive index of bus routes and the maximum passenger transport capacity are used to measure route fairness. The higher the comprehensive index and the maximum passenger transport capacity, the higher the fairness.

Based on the construction of the comprehensive index system for bus routes, the specific values of the comprehensive index and influencing factors for 332 bus routes in Xiamen were obtained. To highlight the characteristics of the comprehensive index and spatial morphology of the bus routes, this study selected the top 10% and bottom 10% of bus routes based on the comprehensive index values, resulting in a total of 60 bus routes. These routes include those within the administrative districts of Xiamen Island, routes connecting the island with outer areas, and routes crossing administrative districts. The comprehensive index and factor values for these 60 bus routes are shown in Figs. 14 and 15. Based on the comprehensive index and the values of the 7 influencing factors, the top 10% and bottom 10% of bus routes were ranked, and semantic information was assigned to the ranking values to construct a semantic information table corresponding to the route rankings for the subsequent analysis of route fairness, as shown in Table 3.

Comprehensive index and factor values of the top 30 bus routes.

Comprehensive index and factor values of the bottom 30 bus routes.

Top 10% of bus routes

The top 30 bus routes have comprehensive index values greater than 0.5, with intervals between values less than 0.1. Among the 7 influencing factors, the maximum value of the maximum passenger transport capacity tends towards 0.9, and the minimum value is less than 0.15, specifically for routes 641 and 86, respectively. There is a significant difference in extreme values between routes, but the difference in values between adjacent routes is small, except for a few routes. The number of bus routes available for transfer has generally high values, with the maximum at 1 and the minimum near 0.5, specifically for routes 655 and 30, respectively, with small differences between adjacent routes. The values for network centrality and traversability are similar in structure, characterized by large differences in extreme values and most routes having centrality and traversability values below 0.4. The number of commercial and industrial facilities, public infrastructure, and cultural, tourism, and leisure facilities are generally high, with maximum values of 1, and small differences between adjacent routes except for a few outliers.

The top 30 bus routes are mainly distributed within Xiamen Island (Fig. 16), with a few routes passing through major traffic arteries connecting the island with the outer areas, such as Jimei Bridge, Xinglin Bridge, and Xiamen Bridge. The bus routes in Huli and Siming districts (on the island) cover the main roads of these two districts, exhibiting various spatial distribution structures such as intersections, adjacencies, and overlaps between routes. Based on the characteristics of the top 30 routes, such as different administrative districts, cross-district routes, spatial morphology, and comprehensive index values, 5 routes are selected for detailed analysis:

Spatial distribution structure of the 60 bus routes.

1. (a)

   Route 655 spans four administrative districts: Huli, Siming, Jimei, and Tong’an. It passes through the Xiamen Bridge (connecting the island and the mainland), with the island section located on the west side, surrounded by various facilities and buildings. According to Table 3 (all subsequent analysis ranks are based on Table 3), Route 655 ranks first in the comprehensive index among the top 30 bus routes and is in the top 5 for the daily passenger served, both at the ’High’ level. The indicator value for the number of bus routes available for transfer is 1, with a significant range compared to other routes. The main reason is that Route 655 spans four districts, has a long route, and has many stops, providing passengers with more opportunities to transfer to other routes. Overall, its route fairness is high.

2. (b)

   Route 641, similar to Route 655, spans the Huli, Siming, Jimei, and Tong’an districts, passing through the Jimei Bridge (connecting the island and the mainland). The comprehensive index is at the ’Average’ level, while the daily passenger served ranks first, at the ’High’ level. The island section of the route is on the east side, with fewer facilities compared to the other 30 routes. The main reason is that the island section of Route 641 passes through many natural scenic areas, which have relatively fewer facilities. Overall, its route fairness is above average.

3. (c)

   Route 951 spans three districts: Siming, Huli, and Jimei, passing through the Xinglin Bridge (connecting the island and the mainland). The comprehensive index is at the ’Low’ level, and the maximum passenger transport capacity is ’Below Average.’ The values for the maximum passenger transport capacity and the number of bus routes available for transfer are opposite, mainly because Route 951 on the island overlaps significantly with other bus routes, leading to a dispersion of the nearby passenger population. In contrast, the section in Jimei has a long route with few stops, resulting in a relatively small population served. Overall, its route fairness is low.

4. (d)

   Route 86 is located on Xiamen Island, spanning Siming and Huli districts, characterized by a short route with few stops. Route 86 has the lowest comprehensive index and daily passenger served among the top 30 routes, at the ’Low’ level. The main reason is that half of Route 86 is on the southern part of the island, passing through areas with few residential points and many natural scenic spots, such as Daxue Road, Yanwu Road, Siming South Road, and Fengchaoshan Road. It does not pass through the central roads of the island, resulting in low values for the maximum passenger transport capacity, network centrality, and traversability. Overall, its route fairness is low.

5. (e)

   Route 755 spans Huli, Jimei, and Xiang’an districts, with half of the route passing through the Jimei Bridge and Binhai West Avenue (G228). The comprehensive index is at the ’Average’ level, while the maximum passenger transport capacity is at the ’High’ level. The values for Route 755’s indicators and factors are relatively high, but the number of nearby facilities is ’Below Average.’ The main reason is that the routes passing through national roads and bridges have relatively fewer facilities, residential points, and stops. Overall, its route fairness is above average.

Bottom 10% of bus routes

The bottom 30 bus routes have comprehensive index values less than 0.08, with intervals between values less than 0.01. Among the 7 influencing factors, the maximum daily passenger served is greater than 0.2, and the minimum is close to 0, specifically for routes 607 and 361 [peak school days]. The difference in extreme values between routes approaches 0.2, with significant differences in values between adjacent routes. The number of bus routes available for transfer has a maximum value greater than 0.2 and a minimum close to 0, specifically for routes 823 and 605, respectively, with significant differences between adjacent routes. The maximum values for network centrality and traversability are close to 0.15, with the minimum values close to 0; both have significant differences between adjacent routes, and the values for network traversability are generally lower than those for centrality. The values for the number of commercial and industrial facilities, public infrastructure, and cultural, tourism, and leisure facilities are all around \(0.12 \pm 0.01\), with minimum values close to 0, and significant differences between adjacent routes except for a few outliers.

The bottom 30 bus routes are mainly distributed outside Xiamen Island (Fig. 16), with a few routes located in natural scenic areas within the island. Haicang, Jimei, Tong’an, and Xiang’an districts have multiple bus routes, primarily in suburban areas. In Tong’an District, the bus routes exhibit spatial distribution structures such as overlaps and intersections. Based on the characteristics of the bottom 30 routes, such as different administrative districts, cross-district routes, spatial morphology, and comprehensive index values, 5 routes are selected for detailed analysis:

1. (a)

   Route B1 [Holiday], located in Siming District, runs mostly along the southern end of the island on Huandao South Road. Its comprehensive index is ranked ’Below Average,’ and its maximum passenger transport capacity is ’Low.’ The main reason is that this route operates only on weekends and holidays, and Huandao South Road is primarily a tourist area. Therefore, the surrounding area has few residential points and commercial facilities, with slightly more tourist service facilities. Overall, its route fairness is below average.

2. (b)

   Route 823, located in Haicang District, has a long route with few stops. Its comprehensive index and daily passenger served are both at ’Average’ levels, while other factor values are ’Above Average.’ The main reason is that there are relatively few residential points nearby, and the route’s characteristics of having few stops result in fewer passengers served. Overall, its route fairness is average.

3. (c)

   Route 383 [Night], located in Jimei District at the westernmost end of Xiamen, near the Zhangzhou border. Its comprehensive index and the maximum passenger transport capacity are both at ’Low’ levels. Most of the route is along Dongfu Avenue, which has many urban villages and commercial and industrial facilities. Thus, the route’s maximum passenger transport capacity and the number of commercial and industrial facilities are at ’Average’ levels. However, because it is a night route with limited operating hours, the population it can serve is limited. Overall, its route fairness is low.

4. (d)

   Route 600, located in Tong’an District, has a comprehensive index of ’Below Average’ and the maximum passenger transport capacity of ’High.’ This route is mostly in the suburban areas of Tong’an, with only a small part in the center of Tong’an. The residential points and various facilities are concentrated in the central area of Tong’an, so the population served by this route is high in the center and low in the suburbs. Overall, its route fairness is average.

5. (e)

   Route 733, located in Xiang’an District, is one of the easternmost routes in Xiamen, passing through Xiang’an East Road, which connects Xiang’an District and Dadeng Island. Among the bottom 30 routes, Route 733 has a ’High’ comprehensive index and the maximum passenger transport capacity, and other factors are also ranked highly. Overall, its route fairness is high, making it a relatively important route.