Equity in Urban Parking Distribution: A Spatial Statistical Framework for Sustainable Transport Planning

Abstract

Rapid urbanization has increased private vehicle usage, generating intense parking demand in congested cities like Shiraz, Iran. The spatial distribution of parking is thus critical to sustainable urban transport, as a misalignment with local demand leads to prolonged travel times, higher fuel consumption costs, and elevated pollution, thereby impeding sustainable transportation planning. In this study, we aim to develop a statistical framework to assess equity in parking distribution in an urban context and address two core questions: how parking supply correlates with local demand and what the equity implications of this distribution are. To achieve this, we employ spatial statistical methods (ANNI, Kernel Density, and Moran’s I) and correlation analysis to examine parking supply and demand across 56 districts of Shiraz. Our analysis reveals statistically significant yet weak correlations between parking capacity and demand, indicating supply-demand mismatches across city zones that result in extended search times, increased congestion, higher fuel consumption, and amplified environmental impacts, thereby perpetuating socio-economic inequities. Overall, the innovation of this article lies in integrating spatial statistical methods with supplementary analyses as a framework to evaluate parking distribution, bridging the gap between quantitative descriptive analysis and justice-based assessments in the context of parking planning in an Iranian city.

1. Introduction

1.1. From Urbanization to Transport and Spatial Equity

Rapid urbanization has been especially intense in developing countries. Consequently, the provision of essential services has failed to keep pace with this growth, leading to an uneven distribution of urban amenities with significant implications for social equity and sustainability [1,2]. Transport equity, a principle of sustainable planning, concerns the fair distribution of a transportation system’s benefits and burdens [3]. Within this, equitable urban parking distribution interrogates the fairness and socio-economic consequences of how parking resources are allocated [4]. Parking infrastructure significantly influences traffic congestion, land use, and mobility; studies show parking searches can account for 25–40% of traffic volume in congested centers [5]. Furthermore, inequitable parking provision often favors central or high-income areas, exacerbating social inequities for peripheral and low-income neighborhoods by increasing commute times and reducing access to opportunities [6,7]. Equity, the principle of fairness and justice that aims for equal outcomes by addressing need, is key here [8,9]. In urban transportation, an inequitable system disadvantages marginalized groups. Applied to parking, a mismatched supply creates congestion and pollution, disproportionately burdening vulnerable communities. Prioritizing equity ensures parking infrastructure supports a low-carbon transition and distributes benefits broadly [10]. The framework of spatial justice emphasizes the fair distribution of resources across geographic space to rectify unjust inequities [11]. Foundational works argue that space is shaped by social relations and power dynamics [12,13] and that planning must embrace equity to ensure access to essential services [14]. Thus, equitable parking distribution in an urban context is the foundation of the present research, and it is a matter of social justice impacting congestion, land use, and economic opportunity.

1.2. Knowledge Gaps and Previous Approaches to Equity in Urban Parking Distribution

A review of equity in urban parking distribution in recent studies reveals that when addressing equity in the context of urban parking, none of the existing literature has employed a combination of statistical methods to develop a spatial statistical framework. Some studies have focused on economic aspects; in these studies, the primary factor for measuring equality among social groups is the price and fee that each individual must pay for parking. They typically use databases related to large, complex parking facilities across the city [15,16].

While others have examined social aspects, this category of research examines social factors such as the level and manner of access to parking for different racial, ethnic, and gender groups. These dimensions serve as a factor for measuring justice in the distribution of parking [17]. Another segment of the literature has addressed the physical aspects of parking spaces; in this category, the design of the parking facility itself, specifically the number and layout of its entrances and exits, as well as the topography of the land on which it is built, serves as a factor for examining spatial justice in parking [18,19]. In many studies, parking is not the central theme but is treated as a subset of street space [20]. The methodologies employed across these studies range from statistical to descriptive approaches. Since most of these studies remain at a descriptive level and do not engage in a profound analysis of parking, and furthermore, do not provide a comprehensive model for evaluating parking distribution, the present article aims to combine statistical methods to develop a conceptual model for assessing parking distribution at the city level, thereby filling a research gap in this field.

Table 1. Overview of Recent Studies on Equity in Urban Parking Distribution.

No.	Authors (Year)	Study Title	Methodological Approach	Key Findings
1	Katharina Goetting Ulf Liebe Sophia Becker [17] (2025)	From parking place to public space: a factorial survey experiment on the public’s acceptability of parking space reallocation in Germany.	Use FSE method (Factorial survey experiments) 2798 participants were evaluated.	Social aspects, This article found that, contrary to expectations, the German public showed a greater preference for the equality principle for distributing parking and its reallocation.
2	Simona De Bartolomeo Michele Ottomanelli Leonardo Caggiani [18] 2025	An equity parking area location model for transition from dockless to docked shared micromobility systems	Using the Gini index, developed a bi-objective optimization model using a genetic algorithm to locate shared micromobility parking stations by minimizing both total walking distance and inequality	physical aspects, It provided a mathematical framework to ensure that the burden of walking to newly created micromobility parking stations is distributed more fairly across different population zones.
3	Elena Savignano [16] 2023	Change for the Meter: Exploring the Equity Implications of Market-Priced Parking	Mixed-methods (including literature review, secondary data analysis, field observations, and an in-person survey)	Economic aspects, This article identified that market-priced parking has disparate impacts based on gender and race and provided policy recommendations.
4	Gabriel Ropars Lefebvre et al. [12] 2021	Toward a framework for assessing the fair distribution of space in urban streets	This paper proposes a method to assess the balance between the three fundamental dimensions of the street.	Parking as a subset of urban space, The paper tries to integrate three aspects of a public space, including a parking lot. the link, the place, and the environment to approach the fair distribution of street space in an urban context.
5	Noli Brazil [15] 2020	The unequal spatial distribution of city government fines: The case of parking tickets in Los Angeles	The Getis-Ord Gi method (the analysis of spatial association by using distance statistics) is based on binomial regression models.	Economic aspects, This article showed that neighborhoods with a higher concentration of renters, young adults, and Black people in Los Angeles disproportionately issued parking tickets.
6	Jan Brueckner Sofia Franco [19] 2017	Parking and urban form	The study used a theoretical monocentric urban model with specific Cobb–Douglas functional forms.	Physical aspects, It demonstrated that a universal minimum parking requirement, rather than systematically addressing spatial equity, is a crude policy tool that can reduce social welfare and distort urban form.

summarizes the findings of this review. This study identifies and addresses this research gap (the lack of a comprehensive perspective and an integrated framework, especially for the cities of Iran); hence, its primary contribution lies in developing a spatial statistical conceptual framework for urban parking distribution. Furthermore, this conceptual model has been empirically applied to the city of Shiraz; this effort has led to filling and addressing the research gap. The corresponding results are reported.

1.3. Research Objectives and Conceptual Framework Contribution

This study is the first of its kind to measure spatial justice in urban parking distribution by integrating established statistical methods for spatial justice analysis with linear regression. Previous research has not achieved this methodological synthesis; its attempts have failed to produce a coherent conceptual model for assessing parking distribution. Therefore, it aims to quantify the spatial distribution of parking using ANNI, kernel density, and Moran’s I; examine the correlation between parking supply and demand at the zone level; and analyze the equity implications within a spatial justice framework. It addresses the research question: How does the spatial distribution of parking lots correlate with local parking demand in Shiraz? What are the equity implications of these patterns? This research contributes to the understanding of urban mobility in Shiraz and the international debate on parking equity [7,21,22]. While previous studies have analyzed parking efficiency, a significant gap persists regarding equity [23]. This study addresses this by integrating spatial justice into a conceptual framework, moving beyond supply-demand metrics to evaluate the fairness of distribution and its socio-spatial impact. Figure 1 illustrates the structure of this article.

2. Literature Review

This section reviews the literature on spatial justice and urban equity, with a particular focus on studies that use spatial statistics to analyze facility distribution and those that explicitly consider equity in parking provision.

2.1. Theoretical Foundations of Spatial Justice and Urban Equity

The concept of spatial justice emerged as a critical lens to examine how the distribution of urban resources and services affects social outcomes. A review of the literature in this field revealed that creating a statistical framework for assessing equity in urban parking distribution and empirically applying it to a case study highlights a weakness in the area of empirical application, which this paper addresses.

Soja [11] argues that space is not a neutral backdrop for social processes; rather, it is actively produced and reproduced through power dynamics and planning decisions. Seminal works by Lefebvre [12] and Harvey [13] further elaborate on the “right to the city” and the idea that urban space is a site of struggle over resource allocation and social justice. These foundational texts highlight that inequalities in spatial distribution are not accidental but are embedded in the very structure of urban planning and policy.

Equity in spatial justice can be conceptualized in two dimensions. Horizontal equity means that services and amenities are fairly spread out across different parts of a city so that everyone has the same level of access, regardless of where they live [8,24]. Vertical equity, on the other hand, acknowledges that different groups may have different needs and abilities. To close the gaps that already exist, resources should be distributed in a way that takes these differences into account [8,25]. Together, these concepts underscore that a just city is one in which urban services, ranging from public transport to parking facilities, are distributed in a manner that meets both the general and the specific needs of its residents.

The spatial justice framework, as elaborated by Israel and Frenkel [26], provides a comprehensive approach to understanding and measuring spatial inequality. Their conceptual model emphasizes the necessity of evaluating not only the physical distribution of urban services but also the social and economic ramifications of these distribution patterns. This framework is particularly relevant for analyzing parking distribution, where inefficient allocation may contribute to broader urban inequities by affecting mobility, land use, and quality of life.

2.2. Empirical Studies on Urban Facility Distribution Using Spatial Statistics

A robust body of literature has applied spatial statistical methods to examine the distribution of urban facilities. Techniques such as the ANNI, Kernel Density, and Moran’s I have been widely used to identify patterns of clustering or dispersion in the spatial distribution of services. For instance, Fiez and Ratliff [22] employed kernel density and clustering techniques to analyze curbside parking demand in Seattle. Their study demonstrated that spatial statistics could reveal subtle disparities in the distribution of parking facilities that are not apparent through traditional aggregate measures.

Similarly, Lucas [27] used spatial analysis to evaluate the impacts of parking minimum standards on urban form. By applying measures akin to ANNI and Moran’s I, Lucas showed that rigid parking policies often lead to an oversupply of parking in some urban areas while underserving others. This imbalance, he argued, can exacerbate traffic congestion and lead to inefficient land use, thereby undermining urban equity.

Other studies have expanded on these techniques by incorporating additional analytical tools. Delbosc and Currie [24] demonstrated the use of Lorenz curves, a method traditionally employed in economics, to assess equity in public transport distribution. Despite concentrating on transit, their methodological approach is applicable to parking studies and demonstrates the connection between dispersion measures and equity outcomes.

These empirical studies collectively establish that spatial statistics provide a powerful toolkit for analyzing urban facility distribution. However, while these methods excel at describing patterns of dispersion and clustering, they often do not capture the normative dimensions of equity. Thus, while the technical aspects of dispersion analysis are well developed, there remains a need to link these findings explicitly to issues of social justice and equitable service distribution.

2.3. Parking Equity and Its Broader Impacts

Observance of justice in parking infrastructure is a critical component of urban mobility systems, yet inequality can have far-reaching social, economic, and environmental consequences. Shoup’s [7,21] works have been instrumental in highlighting that underpriced or unequal distribution of parking leads to excessive cruising and traffic congestion. According to Shoup, unequal parking allocation increases travel time and fuel consumption and results in the misallocation of urban space, which disproportionately affects low-income and peripheral neighborhoods.

Litman [21] reinforces this argument by showing that equal parking management strategies such as dynamic pricing and demand-responsive systems can alleviate congestion and promote urban equity. Litman’s analysis indicates that equal parking policies are deeply intertwined with broader economic outcomes, as they influence land use patterns, air quality, and ultimately, the quality of urban life.

Empirical research further supports these claims. Abdeen et al. [3] provides quantitative evidence that inequality in distributed parking can contribute up to 40% of urban traffic congestion. Such inequality not only has environmental impacts, increasing emissions and energy consumption, but also imposes economic costs on residents and businesses. Moreover, unequal parking management as an economic burden is often higher for residents in areas with limited parking availability, as they may incur additional costs in terms of time, fuel, and even opportunity costs related to access to services and employment.

Advanced modeling approaches have enriched our understanding of these dynamics. For example, Fasihi [28] used a semi-supervised hierarchical recurrent graph neural network to predict parking availability at a citywide scale.

Their novel methodology encapsulates the intricate spatial and temporal fluctuations in parking supply and demand, emphasizing how inequitable distribution can result in localized congestion and diminished urban mobility. By combining such advanced models with traditional spatial statistics, researchers are beginning to elucidate the multifaceted impacts of parking inequity on urban systems.

These studies collectively underscore that parking equity is not an isolated issue. Rather, it plays a profound role in the overall functioning of urban systems, impacting traffic patterns, environmental sustainability, economic productivity, and social well-being. As such, addressing parking equity is essential for achieving broader urban sustainability and social justice goals. Therefore, the need and demand for urban parking is not merely a transportation issue but also a reflection of spatial justice and urban inequality.

2.4. Studies in the Iranian Context

While international literature provides a rich context for understanding the impacts of parking distribution on urban equity, several studies have begun to address these issues within the Iranian context. Research in Iran has traditionally focused on urban service distribution using spatial statistics, though less attention has been given specifically to parking equity. Furthermore, studies in Iran have not provided a framework for assessing spatial justice in urban parking distribution by combining statistical methods, and this paper fills that gap.

Mahmoudi et al. [29] examined the spatial accessibility of public parks in District #11 of Tehran using methods such as ANNI, Kernel Density, and Moran’s I. Although their primary focus was on parks, their approach demonstrates how spatial statistics can be integrated with a spatial justice framework to assess equity in urban amenity distribution. This study offers a methodological framework suitable for analyzing parking facilities.

Similarly, Pourkhaksar [30] analyzed urban park accessibility in Tehran, revealing significant disparities in the distribution of green spaces across the city. The study employed GIS-based methods and spatial statistical techniques to highlight inequities that mirror those observed in parking distribution. Although not focused solely on parking, this research underscores the need for equitable distribution of urban facilities, a need that is equally applicable to parking infrastructure.

Additionally, Eskandari et al. [31] developed a mathematical programming model to determine the optimal location for off-street parking facilities in Isfahan. Their work, while methodologically rigorous, stops short of incorporating a spatial justice lens. Amanpoor et al. [32] also looked at the spatial distribution of urban services (like parking) in Mashhad from a spatial justice perspective. These studies collectively indicate that there is growing recognition in Iran of the importance of integrating equity considerations in urban service distribution analyses.

2.5. Bridging Dispersion Analysis with Equity Considerations

Despite the advances in both spatial statistics and equity-focused urban planning research, there remains a noticeable gap in the literature: hardly any studies explicitly bridge traditional dispersion analysis with spatial justice considerations in the context of parking distribution. International studies robustly apply techniques such as ANNI, kernel density, and Moran’s I to reveal patterns in facility dispersion [29,30], but they typically focus on quantifying spatial patterns rather than evaluating their equity.

The works of Shoup [7,33] and Litman [21] implicitly suggest that misallocated parking causes congestion and perpetuates social inequities by favoring certain urban areas over others. However, there is limited research that explicitly links the quantitative outputs of spatial dispersion analyses to normative criteria for equity.

This gap is especially clear in Iran, where research on the distribution of urban facilities has mostly looked at parks [29,34] and not at parking.

By integrating the spatial justice framework with traditional dispersion analysis methods, this study aims to fill that gap. It combines quantitative spatial statistics with an evaluation of parking demand and supply data to assess whether the distribution of off-street parking lots in Shiraz is equitable. This approach not only provides a detailed understanding of parking dispersion but also contextualizes these patterns within broader social, economic, and environmental impacts.

In doing so, this study contributes to a growing international debate on urban equity. The integration of spatial statistics with equity assessments, exemplified by studies such as Delbosc and Currie [24] and Israel and Frenkel [26], demonstrates that technical analyses of facility distribution can and should be linked to social justice outcomes. Developing policies that guarantee equitable access to critical amenities, such as parking, for all urban residents is crucial.

By synthesizing the international and local literature, it becomes evident that bridging dispersion analysis with equity considerations is not only methodologically feasible but also critical for informing urban planning policy. In a time when cities are growing quickly, making sure that parking infrastructure is spread out fairly can help ease traffic, improve the environment, and improve people’s social and economic well-being. This study, therefore, seeks to contribute to the global debate by providing an innovative model that integrates spatial statistics with the spatial justice framework, offering a novel approach to evaluating parking distribution in Shiraz. However, the key difference between the present article and others in this field is its transformation of traditional statistical models into a framework for assessing spatial justice in urban parking distribution. While past related studies have employed individual statistical methods, none have synthesized them into a unified conceptual and statistical model for evaluating parking distribution equity at the city scale.

3. Methodology

This study employs a quantitative approach to examine the spatial distribution of off-street parking lots in Shiraz and to assess the equity implications of their distribution within a spatial justice framework. The reasons for selecting these statistical methods can be listed as follows: (1) the high accuracy of these methods in examining the spatial distribution of locations, (2) their simplicity and high implementability in various situations, (3) their high compatibility with other methods, enabling the selected methods to be integrated, and (4) the prevalence and frequent use of these methods in prominent papers within this field. The methodology integrates spatial statistical analyses with supplementary correlation tests to provide a comprehensive understanding of parking supply and demand. This section outlines the spatial statistical methods utilized and explores their integration into the conceptual framework of equity in parking distribution. This paper suggests a combined spatial analysis model that is based on the Average Nearest Neighbor Index (ANNI), Kernel Density Estimation (KDE), Moran’s I, and correlation analysis to comprehensively determine the equity of urban parking distribution. The novelty of this framework in terms of the methods is that ANNI is not just used as a descriptive measure of the spatial patterns but as a diagnostic tool to categorize parking distributions as clustered, random, or dispersed before the density and spatial autocorrelation analyses.

These analyses are followed by the complementary application of the KDE and Moran’s I analysis to assess both the extent of inequity in access to parking and the spatial autocorrelation of these patterns. The multi-level integration allows the determination of the spatial concentration and spatial autocorrelation at the same time, which provides a more complete and accurate evaluation of the parking equity compared to simple single-method models. Furthermore, correlation analysis was used to assess the relationship between demand management and the supply of parking.

On the whole, the suggested workflow is capable of enhancing the current spatial analysis paradigms by connecting spatial pattern recognition that is based on ANNI with statistical inferences on clustering, equity, and contextual urban variables that affect the distribution of parking. Although the same types of analysis have been common with the determination of access to policy services like parks [29,30], the systematic and combined use to determine spatial disparity in urban parking allocation, which is often viewed as a type of private good but with major implications by the government, is the essential innovation of the study.

To assess the spatial distribution and equity of parking facilities, the study applies a suite of spatial statistical techniques using ArcGIS 10.5, IBM SPSS Statistics 22, and GeoDa 1.20.0. These techniques include the ANNI, Kernel Density Analysis, and Spatial Autocorrelation Analysis. Each of these methods was selected and subsequently integrated not for mere description, but to simultaneously assess both justice and spatial distribution. Each method is described below.

3.1. Average Nearest Neighbor Index

We chose this method because it compares actual distances with a random pattern, and at the same time the ANNI is a well-established spatial statistic used to determine the dispersion pattern of point features in a study area [27,35]. This method offers an objective assessment of spatial injustice, revealing the extent of distributional equity across the urban fabric [36]. Furthermore, ANNI compares the observed average distance between each parking facility and its nearest neighbor with the expected average distance under a random spatial distribution. Figure 2 visually illustrates the concept of nearest neighbor distances and their relation to spatial clustering.

The following equation calculates the ANNI:

$$ANN= {\displaystyle \frac{D_O}{D_E}}$$

(1)

where $D_O$ is the average distance observed between each phenomenon and its nearest neighbor, and is it measured based on the equation below?

$$D_O={\displaystyle \frac{{\sum }_{i=1}^n d_i}{n}}$$

(2)

In this equation, $d_i$ represents the distance between a phenomenon (i) and its nearest neighboring phenomenon, n indicates the total number of analyzed phenomena, and $D_E$ is the expected average distance of each phenomenon that is measured based on the equation below:

$$D_E= {\displaystyle \frac{0.5}{\sqrt{\frac{n}{A}}}}$$

(3)

where A indicates the area of a minimum enclosing rectangle around all features, and n includes the total number of features.

Finally, the z-score of ANNI is calculated using this equation:

$$z= {\displaystyle \frac{D_O- D_E}{SE}}$$

(4)

$$SE={\displaystyle \frac{0.26136}{\sqrt{\frac{n^2}{A}}}}$$

(5)

3.2. Kernel Density Analysis

Kernel Density Analysis is a non-parametric way to estimate the probability density function of a random variable. In spatial analysis, it is used to generate a continuous surface that represents the density of point features, in this case, off-street parking lots, across the study area [26].

The kernel density function is defined as

$$\tilde{\lambda }\left(s\right)={\sum }_{i=i}^n {\displaystyle \frac{1}{{\tau }^2}}k\left({\displaystyle \frac{s-s_i}{\tau }}\right)$$

(6)

where k() is the kernel function (commonly a Gaussian function), τ is the bandwidth (threshold radius), s is the location where density is being estimated, and s_i is the location of the ith parking facility. The bandwidth τ is selected based on the spatial scale of interest and the typical range of parking influences (e.g., the average distance drivers are willing to walk). Sensitivity analysis is conducted by varying τ to determine its effect on the density surface.

3.3. Spatial Autocorrelation Analysis

Spatial autocorrelation analysis assesses the degree to which similar values (e.g., parking capacity or demand) are clustered in space. This study employs both global and local measures.

Global Spatial Autocorrelation (Moran’s I): Moran’s I is a widely used statistic that quantifies the overall spatial autocorrelation of a variable across the study area. It is defined as:

$$I= {\displaystyle \frac{n{\sum }_{i=1}^n {\sum }_{j=1}^n w_{ij}\left(x_i- x\right)\left(x_j- x\right)}{{\sum }_{i=1}^n {\sum }_{j=1}^n w_{ij}{\sum }_{i=1}^n {\left(x_i- x\right)}^2}}$$

(7)

where

• n is the number of spatial units (zones),
• x_i is the value of the variable (e.g., parking capacity) in zone i,
• x is the mean value of the variable,
• w_ij is the spatial weight between zones i and j.

Values of Moran’s I range from −1 (perfect dispersion) to +1 (perfect clustering), with values near 0 indicating randomness.

Local Spatial Autocorrelation (LISA): LISA provides a measure of the degree of clustering at the local level. LISA can identify clusters (high-high or low-low) and spatial outliers (high-low or low-high) by analyzing each zone in relation to its neighbors [27,37]. LISA outputs are often presented as cluster maps, where different colors represent the type and significance of local spatial associations.

3.4. Supplementary Analyses

In addition to the spatial statistical methods described above, a correlation analysis was performed to evaluate the relationship between parking supply (measured as the capacity of off-street parking lots) and parking demand (projected for the peak hour). This analysis was conducted using IBM SPSS Statistics 22, and the Pearson correlation coefficient (r) was computed. A significance level of p < 0.05 was used to determine statistical significance. This analysis offers clarification about whether zones with higher parking capacity align with higher parking demand, and it informs the equity assessment within the spatial justice framework.

3.5. Integration with the Spatial Justice Framework

The spatial statistical methods described above are integrated within a spatial justice framework to assess the equity of parking distribution. Traditional dispersion analyses quantify the physical distribution of parking facilities. However, to assess spatial justice, these quantitative measures are interpreted in the context of accessibility and demographic distribution. For instance, zones with high parking density may not necessarily exhibit equitable access if the facilities are concentrated in areas with low demand or predominantly serve high-income populations.

By overlaying spatial statistical outputs with socio-economic data (e.g., population density, income levels), the study evaluates whether the observed distribution of parking aligns with the principles of horizontal and vertical equity. Horizontal equity is assessed by comparing parking availability across zones, while vertical equity is evaluated by considering differential needs among diverse population groups [8,25].

To ensure the robustness of our findings, sensitivity analyses were conducted for key parameters in the spatial statistical methods. For Kernel Density Analysis, the bandwidth τ was varied systematically, and the resulting density surfaces were compared to evaluate the stability of the identified clusters. Similarly, for the ANNI calculation, different definitions of the study area (e.g., using a minimum enclosing rectangle versus a convex hull) were tested to assess the sensitivity of the expected distance $D_E$.

Furthermore, while the current study focuses on conventional Euclidean distances, future research may incorporate network-based analyses to better capture the real-world travel distances between parking facilities and demand centers. Advanced methods such as graph-based network analysis or machine learning approaches (e.g., those described by Fasihi [28] could offer additional information about the dynamic interplay between parking supply, demand, and urban equity. Figure 3 summarizes the analytical steps, ensuring a systematic evaluation of spatial equity in parking distribution. This conceptual framework enables us to examine the outcomes based on the principles of spatial justice and sustainable transportation planning, and it can be used to integrate spatial justice in the context of parking distribution with sustainable urban transportation planning.

4. Results

This section presents the outcomes of our “Conceptual Framework of Equity in Parking Distribution” in the Shiraz Traffic Control Zone. We begin with step one: study area and data collection. Steps two and three involve examining statistical methods such as Group 1 and Group 2, along with the resulting spatial equity. Step four analyzes the regression coefficient between parking supply and demand, while step five presents a synthesis of the data for the final assessment of equality in parking distribution.

4.1. Step One: Study Area and Data Collection

The study area comprises the Shiraz Traffic Control Zone (Figure 4), which extends beyond the central business district (CBD) to include 56 individual traffic zones in Shiraz, the capital of Fars Province in southern Iran. According to the Iranian Statistical Centre census, Shiraz has a population of approximately 1.75 million residents and covers an area of 17,889 hectares within its city limits [35]. The Traffic Control Zone, delineated by local transportation authorities, represents a strategic area characterized by high vehicular activity and significant congestion issues due to the increasing number of private vehicles.

We obtained data for this study from several sources. The primary data on off-street parking locations, capacities, and projected peak-hour demand were sourced from the modernization plan of comprehensive studies on transportation and intra-city traffic in Shiraz [35]. These data were supplemented with population data and land use information from the Iranian Statistical Centre and relevant municipal departments. The parking database distinguishes between on-street and off-street parking; however, this study focuses exclusively on off-street parking facilities, as these are more amenable to detailed spatial analysis and are directly influenced by urban planning policies.

Given that on-street and off-street parking facilities collectively meet only a portion of total parking demand, it is assumed that additional strategies such as Travel Demand Management (TDM) will address the remaining demand. For the purposes of this study, 80% of the total parking demand during peak hours is considered in the analysis, in line with previous research in the Iranian context [31,35]. Since this integrated data combines demographic data and spatial data related to parking and land use, it enables the present study to examine aspects of spatial justice and equitable access to parking for Shiraz communities. Finally, it should be noted that this area was selected due to the high concentration of parking demand coupled with spatial access issues to parking, especially in the city’s central districts.

4.2. Step Two and Three: Spatial Statistical Methods (ANNI, Kernel Density, Spatial Autocorrelation)

Our initial analysis employed the ANNI to determine the overall dispersion pattern of off-street parking lots in the Traffic Control Zone. The ANNI was calculated as the ratio of the observed mean distance (Do) between each parking facility and its nearest neighbor to the expected mean distance (DE) under a random distribution. The computed ANNI was 1.03, with a z-score of 0.12 (p > 0.05), indicating that the parking lots exhibit a random spatial distribution (Figure 5). This random pattern suggests a lack of systematic clustering or dispersion across the studied area, which may imply that the allocation of parking facilities is implicitly planned without regard to local demand patterns. In parallel, Kernel Density Analysis was performed to generate a continuous surface of parking lot density. The resulting density map (Figure 6) reveals that certain areas, particularly along the borders of municipality districts 1, 2, and 8, exhibit higher densities of parking facilities. Areas surrounding landmarks such as Namazi Square, Paramount Crossroad, Darvaze-Kazeroon, and the vicinity of the Northern Bazaar Vakil show pronounced density peaks. These findings indicate that, while the overall distribution is random, there are localized areas with a concentration of parking facilities. However, the kernel density map also highlights areas with sparse parking supply, especially in parts of the western zone where demand appears high (Figure 7).

Spatial autocorrelation analysis was conducted to assess whether similar values of parking capacity and parking demand tend to cluster together in space. Using GeoDa software, we computed Moran’s I for both parking capacity and parking demand across the 56 zones.

For parking capacity, Moran’s I was found to be 0.022 (Figure 8), indicating a weak but positive spatial autocorrelation. This suggests that zones with similar parking capacities are slightly more likely to be adjacent than would be expected by chance. The LISA (Local Indicators of Spatial Autocorrelation) analysis indicated that there were two separate groups. One cluster (a Low-Low cluster) was identified in zone 19, where both the zone and its neighbors have below-average parking capacity. Additionally, a small group of zones (classified as low-high) was detected, where zones with below-average parking capacity are adjacent to zones with above-average capacity (Figure 9). The significance tests for these clusters were robust at the 95% confidence level.

The weak positive spatial autocorrelation for parking capacity may reflect historical development patterns, zoning laws, or a lack of coordinated planning in allocating parking spaces.

Similarly, for parking demand, Moran’s I was calculated to be 0.017 (Figure 10), which again indicates a weak positive spatial autocorrelation. The LISA analysis for parking demand revealed two distinct patterns: five zones were classified as low-low, where low demand clusters together, predominantly located in the eastern part of the Traffic Control Zone, and one zone (zone 4) was identified as a low-high outlier, exhibiting low demand while surrounded by zones of high demand (Figure 11). These findings are significant at the 95% level and indicate that local discrepancies exist in the spatial pattern of parking demand.

Furthermore, a bivariate spatial autocorrelation analysis was conducted to examine the relationship between parking capacity and parking demand across zones. The bivariate Moran’s I was 0.08 (Figure 12), indicating a weak but positive spatial correlation between the two variables. The analysis identified two types of clusters: Low-Low clusters, where both parking capacity and demand are below average, and Low-High clusters, where a zone with low parking demand is adjacent to zones with high parking capacity (Figure 13). These results indicate that the allocation of parking facilities often fails to adequately consider the parking demand of adjacent zones.

4.3. Step Four: Pearson Correlation Coefficient

To further understand the relationship between parking supply and demand, we conducted a Pearson correlation analysis between the parking capacity (supply) of off-street parking lots and the projected parking demand during peak hours. The analysis, which was conducted using SPSS, produced a Pearson correlation coefficient of r = 0.266 (p = 0.048, N = 56 zones; see

Table 2. Pearson correlation coefficients between parking capacity and parking demand.

Correlations
		Parking Capacity	Parking Demand
Parking Capacity	Pearson	1	0.266 *
	Correlation	56	0.048
	Sig (2-tailed)		56
	No
Parking Demand	Pearson	0.266 *	1
	Correlation	0.048
	Sig. (2-tailed)	56
	No		56

* Correlation is significant at the 0.05 level (2-tailed).

). This correlation is statistically significant at the 0.05 level, but its strength is low. This means that there is a positive relationship between parking supply and demand, but the two are not very closely related. The weak correlation between parking supply and demand reveals a significant spatial inequality. This misalignment signifies an unjust distribution where high-demand zones lack adequate supply, directly contravening spatial justice principles by unequally burdening certain communities with access deficits and congestion.

In addition to the correlation coefficient, a scatterplot (Figure 14) illustrates the relationship between parking capacity and demand. The figure shows that zones with higher parking capacities tend to exhibit higher demand, but a considerable number of zones deviate from this trend. For example, several zones in the western part of the Traffic Control Zone experience high parking demand despite having relatively low parking capacity. This discrepancy indicates that the allocation of parking facilities may not adequately serve areas with the highest need, thereby contributing to spatial inequity.

4.4. Step Five: Equity Synthesis

The combination of spatial analyses reveals critical equity implications. The ANNI result indicates a random distribution of parking lots, but kernel density maps show significant local disparities in availability. Zones in the western part of the traffic control zone, for instance, exhibit high parking demand alongside insufficient capacity. This spatial mismatch demonstrates that parking facilities are not optimally allocated to meet local demand, despite the overall random pattern.

From a spatial justice perspective, these inequities have negative repercussions. They exacerbate traffic congestion, as drivers in underserved zones endure longer search times, increasing travel time, fuel consumption, and emissions [3,7]. They also lead to economic inefficiencies by misallocating valuable urban land, impacting local businesses and productivity [13]. Furthermore, residents in areas with inadequate parking may experience reduced access to services and increased financial burdens, deepening urban inequalities [28,33]. The weak positive correlations from both the bivariate analysis (r = 0.266) and bivariate Moran’s I (0.08) confirm that local allocation does not consistently match needs. High-demand zones, particularly in peripheral or lower-income areas, are often underserved. This aligns with international literature showing that an uneven spatial distribution of parking can perpetuate congestion and social inequity, even when aggregate supply appears sufficient [33].

To correct these spatial inequities, Shiraz’s urban planning must adopt integrated mechanisms. This includes engaging local communities in participatory planning, establishing institutional units for spatial equity monitoring, and implementing policy mechanisms like redistributive planning that prioritizes high-demand zones and dynamic pricing. Combining land use and transport planning is indispensable for creating equitable urban mobility. Ultimately, while the aggregate distribution appears random, detailed analyses confirm that localized supply-demand mismatches pose a significant risk of exacerbating congestion and socio-economic inequity. When we analyze spatial justice through vertical and horizontal equity, a local mismatch between supply and demand also contributes to service inequality.

5. Discussion

5.1. Interpreting Distribution Patterns: Randomness vs. Equity

The findings reveal that while the ANNI indicates a largely random distribution of parking facilities, a more granular analysis using kernel density and spatial autocorrelation reveals significant local disparities. This random pattern might suggest an absence of systematic planning; however, it does not equate to an equitable distribution. Ideal equity requires that parking facilities be strategically located to meet the specific demand of each zone, especially in areas where traffic congestion and socio-economic disadvantages are most acute [21]. International literature argues that such misallocation of parking resources leads to inefficiencies that extend well beyond mere spatial randomness [7,21]. While a random pattern may appear to indicate spatial disorganization on the surface, within the framework of spatial justice, it reveals a deeper meaning of inequality in the distribution of urban services.

5.2. The Supply-Demand Mismatch and Its Drivers

The correlation analysis yielded a weak yet statistically significant positive correlation (r = 0.266, p = 0.048). This situation indicates a neglect of local demand in parking policy and highlights the role of economic constraints in Shiraz, as well as the shortage of suitable land, in perpetuating spatial inequality. These findings echo observations that even when overall parking numbers appear adequate, a misalignment between supply and localized demand can persist [36]. The weak correlation suggests that factors such as high real estate prices, the uneven spatial distribution of trip attraction centers, and land-use constraints may be more influential in determining parking allocation than demand alone, a subtle mismatch also reported in other data-driven analyses [22].

5.3. Local Clustering and Spatial (In)justice

Kernel Density Analysis identified high-density parking clusters near key landmarks while exposing areas with high demand but sparse supply. Spatial autocorrelation analyses provided further insight: the weak but positive Moran’s I values indicate a slight tendency for clustering, but the LISA cluster maps reveal crucial local variations, including Low-Low clusters and Low-High clusters where a zone’s low parking capacity is juxtaposed with high-capacity neighbors. These patterns are essential for comprehending spatial equity, as such clustering frequently signifies a disjunction between policy planning and local requirements [24,26]. This spatial inconsistency undermines the principle of horizontal equity, which demands uniform availability of urban services.

Furthermore, the bivariate spatial autocorrelation analysis (Moran’s I of 0.08) underscores that the distribution of parking facilities is not strongly correlated with local demand. This indicates that allocation may be driven more by extrinsic factors like land availability than by actual demand patterns. When parking is inadequate in high-demand zones, drivers are forced to circle, contributing to increased congestion and environmental degradation [22]. Therefore, Low-Low and Low-High clusters not only reveal spatial patterns but also reflect a gap in horizontal equity and the inefficiency of parking allocation policies.

5.4. Socio-Economic and Policy Implications

The inequitable distribution has significant socio-economic implications. High parking demand in underserved zones leads to increased travel times and higher transportation expenses, which may discourage economic activity and reduce access to essential services. This scenario is particularly detrimental to low-income residents who rely more heavily on private vehicles, thereby imposing disproportionate burdens on vulnerable populations and exacerbating urban social inequity [28,33].

Policy implications emerge clearly. The random aggregate distribution masks local disparities, requiring targeted interventions, such as prioritizing zones with high demand but low supply for additional infrastructure. Dynamic pricing strategies could help balance supply and demand [21], and integrated land-use planning must take into account both horizontal and vertical equity. This could be done by changing the minimum number of parking spaces needed and using mixed-use developments [38]. Policies based on income, land price, and the level of car dependency in different areas exacerbate these inequalities.

5.5. Methodological Contribution and Future Research

The integrated analytical framework suggested in this work showed obvious benefits over the common single-method techniques like standalone Kernel Density Estimation (KDE) and the Moran I analysis. In single-variable methods, each index represents only a portion of the spatial reality. For example, KDE considers only the density of points and ignores the spatial relationships between zones, while Moran’s I determines whether spatial autocorrelation exists but does not indicate its strength.

Conversely, the combined ANNI-KDE-Moran I framework used in this study could simultaneously indicate spatial concentration patterns and spatial correlations and provided a more detailed picture of spatial inequities in parking distribution.

The findings of this comparison show that the suggested framework works with more accuracy and interpretation in determining the areas of spatial inequality, especially those with mixed land use and high travel density. This result indicates that multi-level integration of indicators does not only increase the accuracy of the analysis but also the comprehension of the distribution of parking supply and demand in space. Hence, the hybrid approach suggested can be used as a successful model to evaluate spatial justice in other forms of urban infrastructure, too.

The integration of spatial statistical analyses with a spatial justice framework represents a novel methodological contribution. This approach demonstrates that conventional spatial statistics can be effectively combined with equity-based evaluations to inform more just urban planning policies [24,28]. Future research should build on this basis by incorporating network-based measures, real-time parking occupancy data, and advanced modeling approaches like graph neural networks to offer greater clarity about the dynamic interplay between parking supply, demand, and urban mobility [32]. The integration of statistical methods and spatial justice can serve as an analytical framework for other developing cities as well. Furthermore, future studies could investigate temporal equity (changes over time) or incorporate parking behavior data.

5.6. Implications for Transport Equity

The findings reveal a critical misalignment between parking supply and demand, directly informing transport equity policy. The weak correlation and local disparities indicate that the current distribution imposes disproportionate burdens, like increased congestion and costs, on underserved communities. This necessitates equity-oriented interventions, such as targeted infrastructure in high-demand, low-supply zones and dynamic pricing, to ensure fair access and prevent vulnerable populations from bearing the negative impacts of inefficient parking planning [39,40,41,42]. Improving equity in parking distribution can be part of broader sustainable transportation policies and is directly linked to the objectives of SDG 11 (Sustainable Cities and Communities).

6. Conclusions

This study introduced and applied an integrated analytical framework that synthesizes spatial statistics with a spatial justice approach to assess parking distribution in Shiraz. Our core innovation lies in this methodological fusion, which moves beyond mere pattern description to explicitly evaluate equity.

The analysis revealed that the ostensibly random spatial pattern of parking conceals profound local inequalities. We identified specific clusters where high demand critically outstrips supply, demonstrating that current allocation policies are inefficient and unresponsive to localized needs. These disparities exacerbate traffic congestion, environmental pollution, and social inequity for residents in underserved districts. The primary practical application of this framework is its utility as a diagnostic and planning tool for urban policymakers. Planners in other developing cities can directly employ this model to:

• Identify Priority Areas: Pinpoint exact neighborhoods suffering from parking shortages.
• Formulated Targeted Policies: Guide investments in new facilities and the implementation of demand-management strategies like dynamic pricing.
• Advance Broader Goals: Align parking management with sustainable development objectives (SDG 11) by promoting transport equity and reducing vehicle emissions.
• To build upon this work, future research should:
• Integrate temporal data to understand how parking demand and equity fluctuate throughout the day.
• Incorporate parking behavior data to model user decision-making more accurately.
• Expand the model to a metropolitan scale to analyze cross-city mobility patterns.

Ultimately, this study demonstrates that equitable parking distribution is not merely a transportation issue but a fundamental component of sustainable urban development. The proposed framework offers an actionable path toward creating more just and efficient cities.