## 3 Materials and Methods
### Data Analysis  
The analysis consists of spatial and non-spatial analysis. Analysis of the attractiveness of the bike-sharing stations fell under the non-spatial analysis and was focused on statistical evaluation over the years. The attractiveness of bike-sharing stations is based on the processing of the provider's data about bicycle rentals from the beginning of the service in 2019 till the end of the 2023 season. Season 2024 statistics are still in the process, and the operator has not yet provided them for research processing. However, spatial analysis requires just the map's characteristics and basic data about the number and location of the bicycle stations. For this reason, data until the end of the season 2024 was processed. First, the rate of bike-sharing system usage is researched in the form of a general analysis of seasons from 2019 to 2023. The data from the operator Arriva Slovakia a. s., the company of bike sharing in Zilina, is based on the real records about the amount of bicycle rentals, about the average time of one rental, or about the time distribution of bicycle rentals per day or months and grouped in the following Table 2.  
The bike-sharing efficiency can be determined by the indicator describing the average daily number of rides on one bicycle. The optimal value should be between 4 and 8 rides. Lower values indicate the financial unsustainability of the service, while the reason can be caused by the insufficient cycling infrastructure. On the other hand, more than 8 rides, or a very high number of average daily rides, may mean limited availability of bicycles. The dataset contained extreme values in rental duration (up to 200-1200 min), probably caused by incorrect or incomplete termination of the bicycle rental. The dataset included information on how the rental was terminated: either by the user or by the provider. In most cases, rentals with abnormally long durations were terminated by the provider, indicating a malfunction of the locking system or negligence by the user when terminating the rental. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Season** & \begin{tabular}{c} **Number of** \\ **Bicycles** \\ \end{tabular} & \
\begin{tabular}{c} **Number** \\ **of Stations** \\ \end{tabular} &
\begin{tabular}{c} **Free ride Time** \\ **in Minutes** \\ \end{tabular} \\ \hline
2019 & 120 & 20 & 60 \\ \hline
2020 & 120 & 20 & 60 \\ \hline
2021 & 123 & 21 & 30 \\ \hline
2022 & 145 & 30 & 30 \\ \hline
2023 & 145 & 30 & 30 \\ \hline
2024 & 195 & 32 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: BikeKIA bike-sharing service development through the years processed based on provided data from the operator. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**The Year of** & \begin{tabular}{c} **The Population** \\ **the Season** \\ \end{tabular}  & \begin{tabular}{c} **No. of** \\ **of Zilina** \\ \end{tabular}  & \begin{tabular}{c} **No. of** \\ **Bicycles** \\ \end{tabular}  & \begin{tabular}{c} **Duration of** \\ **the Season** \\ **(in Days)** \\ \end{tabular}  & \ \begin{tabular}{c} **Average Daily** \\ **Ride Time** \\ **(in Minutes)** \\ \end{tabular}  & \begin{tabular}{c} **Average** \\ **Daily Rides** \\ **on 1 Bicycle** \\ \end{tabular}  \\ \hline
2019 & 82,867 & 120 & 288,347 & 249 & 14.6 & 9.65 \\ \hline
2020 & 82,494 & 120 & 145,707 & 221 & 17 & 5.49 \\ \hline
2021 & 82,301 & 123 & 148,992 & 250 & 11.6 & 4.85 \\ \hline
2022 & 81,062 & 123–145 & 198,774 & 260 & 10.7 & 5.27 \\ \hline
2023 & 80,342 & 14 According to the operating model of the bike-sharing system, typical rentals last less than 60 min. Rentals longer than 120 min are unlikely and likely reflect user or system error. Afterwards, the reachability of the existing 32 bicycle stations (standing and virtual) will be examined by spatial analysis. First, the availability of isochrones will be estimated. As well as in the case of public passenger transport, there is a possibility of determining the availability isochrone of the bike-sharing service for analysis and later potentially proposals.