2. Literature Review
3. Materials and Methods
3.1. Case Study
3.2. Data Sources
3.2.1. Geographic Zones and Population
- Neighbourhoods—The division into neighbourhoods in Palma city was provided by the Population Service of Palma City Council. A total of 88 areas of heterogeneous dimensions were recorded.
- Census sections—The National Institute of Statistics is responsible for carrying out the population census in Spain, which it does every 10 years. A total of 245 census sections were recorded.
- Cadastral blocks—From Palma City Council, through its Department of Population. The municipality of Palma comprises a total of 3012 cadastral blocks.
- 400 × 400 m mesh—A mesh of homogeneous square polygonal units of dimensions 400 × 400 m was created. The municipality comprises a total of 1381 units. Its population was obtained from census sections.
3.2.2. Bus Stops, Bus Lines, and Frequencies
3.3.1. Calculation of the Bus Service Level and the Horizontal Equity Using the Current Bus Frequencies
- GIS database creation—Importation of geographical transport files (GTFC), bus stops, and routes (Figure 3a).
- Calculation of the Bus Service Level by Bus Stop—The level of service provided by each bus stop was calculated based on the number of buses that pass through it over the course of 12 h, according to the following expression:
- Calculation of the Bus Service Level (BSL) for each geographic unit—Using the DelBosc method , a buffer of 400 m was generated for each bus stop (Figure 3b) and the number of buses passing through this stop was counted. The buffer layer was then overlapped on each of the zonings carried out, obtaining a level of service for each geographical unit, according to the following expression (Figure 3c):
- Analysis of population concentration and bus service—An analysis of the spatial autocorrelation of the service level and population was carried out by calculating the Moran’s Global and Local indices [55,56,57]. The Moran’s Global index provides information on the spatial autocorrelation of the variable and its degree of concentration:
- Mapping of territorial imbalances (Figure 3g)—A cartographic analysis was performed for each type of zoning, in order to represent the relationship between the population and level of service. For this purpose, the mapping of the level of service normalized by resident population was presented and deficit zones were identified. The process is carried out by classifying the population and the level of service in three categories (33 and 66 percentile), and represented by a map showing all the categories.
- Lorenz Curves generation (Figure 3h)—A Lorenz curve shows a cumulative distribution of the level of service and population for geographic units, as well as the straight line that would represent perfect equality in distribution [26,27]. A Lorenz curve was constructed for each of the zonings, based on the information corresponding to the population of each geographic unit and its level of service, in which the level of horizontal equity can be observed.
- Gini coefficient calculation—The Gini coefficient [26,58,59] was developed in the field of economics, in order to measure the degree of inequality of an economic variable (income) in relation to the population. The index is based on an analysis of the deviation from the Lorenz curve. The calculation of the Gini coefficient was carried out using accumulated population and service level data for each of the zonings used, according to the following expression (Figure 3i):
3.3.2. Sensibility Analysis of Bus Service Level and Horizontal Equity by Simulation of the Change of Bus Frequencies (±5 min)
3.3.3. Optimization of Bus Fleet Frequencies
- Maximising the Global Service Level;
- Minimisation of the Gini coefficient; and
- Minimisation of population not covered by the Bus Service.
4. Results and Discussion
4.1. Service Level and Equity for Each Zoning with the Current Bus Frequencies
4.2. The Role of Bus Lines in Service Level and Horizontal Equity
4.3. Bus Frequencies Optimization to Improve Service Level and Horizontal Equity
- Small unit zoning is much more accurate for service-level analysis. Small units are also more sensitive to detecting imbalances between bus service supply and resident population levels.
- The range of variability of global indicators of concentration (Moran’s Global) did not undergo very significant changes, concerning the use of various zonings; in other words, service level concentrations were detected in all cases. However, the identification of the high bus service level areas (Moran’s Local) was more precise when using small unit zoning. The use of large units can hide significant areas of concentration.
- Orthogonal zoning (mesh) proved to be particularly sensitive for concentration detection, regardless of unit size. It has a tendency to soften the values of BSL improvement and equity, compared to the other zonings. At the same time, it provides a broader view of the municipality.
- The horizontal equity analysis showed that the Gini coefficient increases as the size of the geographical units decreases. This implies that the smaller the geographical unit used, the greater the sensitivity in detecting imbalances. In other words, many imbalances could go undetected if large geographical units are used.
- The sensitivity analysis of bus service level and equity derived from the variation of route frequencies showed the strong dependence of service level on a series of long-distance routes that radially cross the city. This bus transportation system demonstrates rigidity.
- There were significant variations in the roles of bus lines, depending on the type of zoning used. In general, there was a coincidence in the zoning systems, in terms of identifying the lines that improve the level of service. However, there were significant divergences for the maintenance of equity; these issues are unclear.
- In optimizing the level of service and horizontal equity by changing the frequencies of bus lines, it became clear that fundamental changes must be made to the city’s key lines. The variations to the original service level values are significant and can lead to improvements in many areas.
Conflicts of Interest
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|Indicators||Neighbourhoods||Census Sections||Cadastral Blocks||400 × 400 m Mesh|
|Standard deviation population||4759.25||622.60||186.48||1050.72|
|Minimum population density||0||0||0||0|
|Mean population density|
|Maximum population density|
|Standard deviation Population density||118.78||241.64||391.26||65.67|
|Neighbourhoods||Census Sections||Cadastral Blocks||400 × 400 m Mesh|
|Bus Service Level||0.669||0.820||0.829||0.809|
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