This article examines the demand patterns of Zity, a free-floating electric car-sharing company operating in Milan and identifies temporal and spatial dynamics that influence mobility demand to optimize its reallocation strategy. The findings emphasize the importance of considering specific timeframes for operational activities and highlight the role of residential and working populations as driving factors behind demand. Additionally, the study reveals Zity’s value as a complement to existing transportation options. By understanding these dynamics, stakeholders can optimize resource allocation, enhance accessibility, and promote sustainable shared mobility services in urban areas like Milan.

Introduction

This article is the third part of a free-flow carsharing series and its done in collaboration with Zity, and with New York University CUSP (Center for Urban Science + Progress) students as part of their Capstone Project during the 2022 / 2023 academic year. Zity is a free-floating electric car-sharing company operating in major European cities including Milan.

The first part of this series includes a general overview of the mode typology, and the second part outlines analytical consideration and an applied case study. This article stemmed from the supply and demand imbalance problem Zity was facing. As its operation team manually relocates the vehicles at nighttime based on intuition rather than data, Zity has the potential to optimize its operation by analyzing usage patterns, resulting in data-driven vehicle allocation strategies. This project aims to create an optimized model to maximize the potential accessibility while minimizing the reallocation of vehicles, also providing policy recommendations for the city regarding the integration of private entities such as Zity into urban transportation planning.

Mobility Pattern Analysis

Prior studies have shown the spatial and temporal patterns of car rental events, as well as the external factors that influence the events. Understanding the dynamics of car rental activities and their associated factors is crucial for optimizing transportation systems and improving user experiences. Scholars have explored various aspects of the events such as the geographic distribution of the demand, temporal patterns, and the peak demand time (Schmöller & Bogenberger, 2014; Messa & Deponte, 2021).

Mobility flow analysis is a field of study that examines the patterns, trends, and dynamics of movement between different locations (origin–destination). It encompasses various aspects of human mobility, such as commuting, migration, tourism, trade, and transportation. Understanding the factors that influence mobility flows is essential for effective urban planning, transportation management, and policy development. Two widely used models in this field are the gravity model and the radiation model (Hong et al., 2019).

The gravity model is a global approach to analyzing mobility flow. It operates on the principle that the interaction between two locations is directly influenced by their masses (typically represented by population or economic activity) and inversely affected by the distance between them (Garrels-Garrido et al., 2021). The larger and closer the destinations, the more attractive they are, resulting in higher migration or commuting flows. The gravity model can incorporate distance, demography, and economic data into its equation, allowing for quantitative analysis of mobility patterns. The general form of the gravity model equation is in Equation 1.

Equation 1 Gravity model equation

Here, k is a constant, and α represents the elasticity of distance. The gravity model has been widely applied in various fields, including transportation planning, urban studies, and regional economics, to understand and predict mobility flows between different OD pairs.

Along with the general mobility flow models, spatial regression models can also be used to study the patterns and dynamics of movement. One of the most common approaches is Geographically Weighted Regression (GWR), a spatial regression technique that has gained prominence in the field of spatial analysis. It enables researchers to explore and analyze spatially varying relationships between a dependent variable and a set of independent variables. Unlike traditional regression models, GWR recognizes the presence of spatial heterogeneity by estimating local regression coefficients that vary across geographic locations (Harris et al., 2010). GWR allows for the estimation of local regression coefficients for each geographic location, providing a detailed understanding of how the relationships between the dependent and independent variables change across space. This spatially adaptive modeling approach is particularly valuable in situations where the relationships are not uniform and exhibit significant spatial variation. The GWR equation is described in Equation 2.

Equation 2 Geographically Weighted Regression (GWR) equation

Here, Y_i represents the dependent variable at location i, β₀ (u_i, v_i) is the spatially varying intercept, β_j (u_i, v_i) are the spatially varying regression coefficients for the independent variables X_ij, and ε_i represents the error term (Harris et al., 2010).

Enabling Data and Methodology

To structure the analytical framework, several datasets were collected, such as residential population, working population, Points of Interest (POIs), and public transit accessibility, and normalized on the Uber’s Hexagonal Hierarchical Spatial Index, level 9. The primary data is the rental events acquired from Zity, which includes the record of service usage from June 2022 to April 2023, then relevant datasets were acquired separately from multiple sources, as shown in Table 1.

Several steps of data cleaning and data hygiene were performed, ensuring completeness and consistency among the rental dataset, and by targeting outliers in trip duration and distance, namely the bottom 5% of trips duration (less than 2.8 minutes ), the top 5% of trips duration (over 146 minutes), and the top 0.5% of trip distances (over 122 km) were discarded from the dataset. This process resulted in a dataset that was reduced to 92.7% of its original size. This dataset, cleansed of extreme outliers, presents a more accurate depiction of typical vehicle usage patterns, and provides a robust foundation for our subsequent exploration of vehicle allocation modeling.

Mobility Pattern Analysis

Initial data exploration led to the application of seasonal decomposition analysis to find the period length of the service usage for further analysis in the time series modeling and additional exploration in the mobility pattern analysis step. Moreover, the hourly trend of total rental events was analyzed to understand the peak and bottom operational hours – both information are vital to plot the relocation strategy. The daily timeframe was categorized into five buckets: early morning (1 am – 5 am), morning (6am – 11 am), noon-afternoon (12 pm – 4pm), afternoon-evening (5pm – 7pm) and night (8pm -12 am). Which were used to perform hotspot and coldspot analysis to preliminary identify movement patterns, as shown in Figure 1.

Morever, understanding the temporal patterns of Zity usage is crucial for optimizing resource allocation and improving service quality. The general trip data analysis aims to provide an understanding of trip durations and user preferences. Notably, 80% of Zity trips are completed within 30 minutes, emphasizing the service’s popularity for short-distance travel. Conversely, only 5% of trips extend beyond an hour, suggesting that Zity is predominantly chosen for quick journeys.

To gain further insights into peak usage hours and variations in speed, trip data was aggregated and analyzed hourly. The results revealed distinct temporal patterns in Zity usage. The morning peak was observed at 8:00 AM, while the evening peak spanned from 6:00 PM to 8:00 PM. Interestingly, the lowest usage of Zity occurred during the early morning hours (e.g., 3:00 AM), coinciding with the highest speeds during this period.

Temporal and Spatial Models

The methodology employed for the time series model in this study followed a systematic approach to capture and analyze the temporal patterns and trends within the dataset. This involved considering various models, such as autoregressive integrated moving average (ARIMA), or more advanced models like Seasonal ARIMA (SARIMA), using a linear regression model as the baseline to time series models. The validated time series model was then used for forecasting future values or trends. Forecast intervals and prediction intervals were estimated to quantify the uncertainty associated with the predictions. The results were interpreted and presented with appropriate visualizations and statistical summaries to facilitate understanding and decision-making.

To investigate the relationships between rental event numbers and various predictors, a Geographically Weighted Regression (GWR) model was developed. The independent variable in the analysis was the rental start end event number in the H3 grid, representing the demand for rental services in different locations. As for the predictors, several variables were considered, related to population and transit public accessibility, namely the residential population, working population, and the number of Points of Interest (POI).

In the initial phase of the analysis, the GWR model iteratively was ran iteratively, incorporating all available predictors, with a stepwise process to assess the explanatory power of each predictor and identify the most influential factors. Based on this evaluation residential population, working population, and the number of POIs were chosen as the predictors for our GWR analysis.

Results

As outlined above, the time modelling started from the linear regression, which results indicate that the linear model only captures the general ascending trend and fails to account for the complexity inherent in the dataset, appearing insufficient for accurately predicting car rental events characterized by intricate temporal dynamics. In contrast to the linear regression model, the time series models were specifically designed to capture the temporal patterns present in the car rental data. These models demonstrate a remarkable ability to capture the weekly trend, resulting in significantly improved prediction performance compared to the baseline model.

Further analysis was conducted to compare the performance of the autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models. The results, shown in Figure 3, indicate that the SARIMA model exhibits enhanced sensitivity in capturing the weekly peaks within the car rental events. This finding underscores the advantage of incorporating seasonality into the model, enabling more accurate predictions of peak periods.

On the other hand, the spatial modelling was approach initially with a Ordinary Least Squares (OLS) on the start location of rental events in ArcGIS and used it as a baseline. From the OLS report, the p-value shows that the selected three features are significant, which are the number of POI in each hexbin, the number of working population and residential population. The R² of OLS method is 0.55.

Significant Koenker (BP) values indicate spatial heterogeneity in the features, pointing to the need for a  Geographically Weighted Regression. With the method of GWR in ArcGIS, we can find that the R² of GWR model is 0.77, which is better performing than the result of the OLS method, as shown in Table 2.

Moreover, Figure 4 shows the comparison between the ground truth and prediction of GWR for the start location and end location of rental events, with the distribution patterns of start data and end data closely resembling the predicted outcomes. It is evident that there is a higher concentration of car rentals originating from the core areas, indicating a higher occurrence of rental events ending in these regions. Particularly, the areas in the northern part of the central city exhibit a significant number of trips and are accurately predicted by the model. For future reallocation strategies, prioritizing these areas would be beneficial.

During the investigation of the coefficients for total rental events and various variables, it emerged that both POI count and working population have a negative influence in the central areas of the city. This can be attributed to the abundance of rental events in these regions, where the extent of growth in these variables does not align proportionately with the number of rental events. It is possible to observe the opposite phenomenon on the outskirt, where the relatively lower overall quantity of rental events in the surrounding areas tends to amplify the significance of the predictors’ impact. In terms of reallocation strategies, these findings may not have practical implications as the overall number of rental events in these areas remains relatively low.

Conclusion

This article summarize a research project aimed at analyzing the demand patterns for free-flowing shared car service Zity in Milan and at exploring the driving factors behind these patterns. The findings of our analysis align with previous studies and contribute valuable insights to understanding the dynamics of mobility demand in the city. Firstly, our analysis revealed strong temporal patterns in the mobility demand. These temporal variations highlight the importance of considering specific timeframes when planning operational activities such as charging and manual relocation. Secondly, the Geographically Weighted Regression (GWR) model shed light on the spatial aspects of the mobility demand, with the results indicating that residential and working populations may be significant driving factors behind the demands.

In conclusion, this study provides insights into the temporal and spatial dynamics of urban mobility demand in Milan. By considering both the temporal patterns and the spatial distribution of demand, stakeholders can make informed decisions regarding operational activities, optimize resource allocation, and enhance the accessibility and environmental sustainability of shared mobility services. Future research should focus on long-term trends and user behavior changes to further refine and improve mobility service planning and implementation in urban areas.

Policy Recommendations

Based on this study, the following policies are recommended, to ensure that shared mobility services are more inclusive and accessible to low-income populations. All these suggestions require a collaborative effort between public and private entities to create solutions that remove these barriers and provide equitable access to shared mobility services for all members of the community.

• Establish a data sharing protocol with private entities: data from shared mobility services holds significant value for understanding urban mobility and capturing complex patterns associated with emerging shared mobility services, but needs to be handled with users’ privacies in mind since the data can reveal sensitive information about individuals. The city must actively engage in maintaining the partnership with shared mobility private entities and take the lead in establishing clear guidelines for secure and responsible sharing of mobility data, addressing data privacy, security, compliance with relevant regulations, and ensure anonymization and aggregation of personal information.

• Integrate shared mobility services within the framework of multi-modal routing planning: public transit systems typically operate in areas where there is sufficient demand. However, through collaboration with the private entities like Zity, cities have the opportunity to integrate shared mobility services into their transportation networks as part of a multi-modal routing approach.

• Remove barriers  for low-income population: the cost of using a private service like Zity is much higher than the public transit fare. For the low-income population to use the service freely, three key challenges can arise (Kodransky & Lewenstein, 2014).

• Physical Barrier: ensure the number of the vehicles in the low-income neighborhood.

• Logistic Barrier: make sure that private entities provide a way for using a service without a document, exploring options such as alternative forms of identification or implementing streamlined city-wide registration processes.

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The results of this research has been published on Zenodo: Jo, H., Laras, A., Song, J., Deng, Z., Messa, F., Ceccarelli, G., Gorrini, A., Choubassi, R., Figueira, T. S., Remondini, M. (2024). Vehicle Allocation Modeling: Optimizing the Logistics Behind a Free-Flow Carsharing in Milan, Italy. Transform Transport Working Papers Collection, 2. https://doi.org/10.5281/zenodo.14232091

Acknowledgments

We thank Hanbyul Jo, Azaria Laras, Junru Song, Zhuohao Deng, and Dr. Mona Sloane (New York University, USA) for their contribution to this research. We thank Zity for their fruitful collaboration and for sharing data. The analyzed data were treated according to the GDPR-General Data Protection Regulation (EU, 2016/679). This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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