Assessment of Automated Parking Garage Services as a Means to Sustainable Traffic Development in a Mid-Sized City

Abstract

The research in this article deals with verifying the deficit of parking spaces from model examples in the city of Ostrava, Czech Republic. Specifically, it deals with the possibilities of solving these deficits using automated parking systems. The main data collection took place between 2010 and 2019; later, supplemental lockdown data (up until May 2022) were obtained. The main objective of this article was to use data to determine the profitability and functionality of automated parking systems in mid-sized cities such as Ostrava. The RING system was chosen as a suitable model for the automated parking system. The data (using a least-squares approximation) were used via statistical methods to make predictions for future years, including the construction of confidence limits for a given significance level. Based on data from 2011–2019, we found that the RING system would be profitable with a probability of 92.45% in the following years. We compared these predictions with the actual data and made a new prediction.

1. Introduction

An analysis of study data sources from 1927 to 2001 showed that 8 to 74% of urban traffic travel for parking [1]. The number of parked cars affects traffic safety and sustainability [2]. As a result of the automated parking system’s compact, multi-story structure, it can significantly increase the number of parking spaces and, thus, reduce the cost of land per car. Automatic parking systems (a.k.a. automatic parking) came to the market relatively recently, i.e., in 1905, in Paris, France, at Garage Rue de Ponthieu [3]. There can be two views on automatic parking; it is up to the investor which system is the most suitable for a given area or object in terms of space, number of parking spaces, and use in general. The first one relies on modifying the car’s internal systems so that the intelligent car parks in a classic parking space with a “parking assistant” [4]. The second one is entirely different, and it is the one that became the focus of our research. This approach relies on the intelligence of parking spaces or buildings rather than intelligent cars [4]. Automatic parking systems are typically parking garages with computer-controlled automated loading and unloading, using sophisticated technological devices without requesting human intervention. The great advantage of these systems is the reduction in the necessary floor area when compared to a classic garage since it is not necessary to take into account, among other things, areas for the movements of people, lighting, and ventilation during implementation [4]. The lower need for floor space and cubic volume offers the possibility of increasing the capacity of sales and rentable areas, which is one reason why automatic parking systems are increasingly being utilized [5]. Furthermore, the saved space can then be used, e.g., for green areas, improving the air and also cooling the streets [6].

Another reason is the simplicity, convenience, and safety of the parking process, which protects both the owner and the vehicle because a person cannot enter the parking process and the cars’ engines are shut down [5,7]. Moreover, reducing the human factor during the parking process can reduce the emissions caused by fossil fuel cars, as discussed in [8]. As mentioned above, the advantage of an automatic parking system is that it saves space. Rogers et al. [9] state that the lack of building land in cities and the countryside, especially in recent years, has become an expensive and sought-after resource. With the high global demand for mobility, this is an important issue that needs to be addressed, as it means increasing road traffic density and a lack of parking spaces. Many places face shortages of parking spaces due to rapid urbanization and an increase in the number of vehicles, so it is necessary to use building land in a way that improves the quality of life through intelligent and efficient parking systems [10]. Scientific circles have researched the lack of parking spaces, parking garages, and driver behaviors. For example, Hesse et al. [11], investigated what influences the choices of parking spaces and home parking, and what is the most important to drivers, e.g., price, walking distance, etc. Chen [12] studied the time-varying demands for parking. On the other hand, Liu [13] created two logical models of the behaviors of users of typical ground-level parking spaces based on data from a questionnaire survey and the intentions of the users who chose their parking spaces. Some studies have shown that adjusting parking fees can increase the use of parking spaces and parking garages, which has a significant impact on supply and demand [14]. Simicevic et al. [15] analyzed the flexibility of parking fees for off-road parking. The results showed that an increase in parking fees would dynamically reduce the demand for parking and its utilization rate. However, the gap in the conducted research lies in the fact that only a few researchers focused on large automated parking houses, or they were just marginally interested in the factual usability, profitability, and functionality of this kind of automated parking system in a larger city. Parking facilities are critical parts of the infrastructure in terms of traffic systems and area reach [16]. Christiansen states that parking policies significantly affect traffic since most personal rides start and end at parking facilities [17]. According to Wang et al., problems with parking facilities cause not only discomfort to citizens, everyday pedestrians, and local inhabitants, but also a negative impression of the town/city in question [18]. Many studies, on the other hand, suggest a significant spatial correlation to travelers’ behavior [19,20]. Moreover, unexpected factors can derail many models, which are based solely on time factors, as we can see with the current COVID-19 pandemic [21]. Therefore, this became the main aim of our research, specifically using locations in the city of Ostrava, Czech Republic. To achieve the goal, we used standard statistical tools for data analyses, which are described in more detail in the following section. We chose this approach for its clarity and applicability to any parking system with the possibility of obtaining the same amount of data.

2. Situation in the Czech Republic and the RING System

Concerning the development of motorization in the Czech Republic over the past 17 years, 100–200 new parking spaces were built annually. Furthermore, additional spaces arose in new housing estates and central parts of cities. However, according to the statistics of the Transport Office of the Czech Republic, the capacity is still insufficient, and the construction of new parking spaces requires more investment. Town halls’ long-term views on parking regulations is an issue that seems impossible to solve (in regard to meeting everyone’s satisfaction). However, there is clearly a way to increase the number of satisfied motorists. With regard to parking, a better approach is a government-backed strategy to maximize the demand for all parking spaces in an area [22]. In connection with the parking demand, the so-called “SF Park” was introduced in San Francisco. Sensors installed in parking spaces recorded the occupancy of the space and allowed the real-time monitoring of parking demands. Variable parking fees were set based on usage data for each region, and drivers could use a website or mobile app to find real-time information on available parking spaces. The above method can effectively manage parking demand in practice [23,24]. In conclusion, there are many studies on parking demand models for different conditions and scenarios that include different behaviors of parking characteristics. Most of them focus on reducing traffic and optimizing the allocation of parking spaces. Most of these studies have parking prices, walking distances, and travel times in common because these factors affect parking in different locations in different regions [25]. For studies, it is important to strengthen the method of determining the rate trend of use of parking garages. Building management must keep detailed records right from the start of the operation, which would allow parking development institutions to evaluate the suitability of the building and develop different systems in the future. This factor also plays an important role in the selection of the supplier of the given systems, as it is possible to analyze various seasonal effects or the effects of system loads and system failure rates. The Czech Republic is home to several manufacturers of automated parking systems, which also export their systems abroad. Most of these manufacturers are based in Prague. One manufacturer is in Ostrava, where it built two automated parking buildings. This thesis uses the RING automated parking system based in Ostrava as a subject of study. The operator keeps daily and monthly visitor statistics from 2011 to the present. We will analyze the usage using the autocorrelation function (ACF) to determine the Pearson correlation coefficient for sequential time [26,27]. If the number of failures of a given system is recorded, it would be possible to determine when to perform annual system maintenance. Another trend was captured in an article using a regression approximation, which was then used for a simple usage forecast for the years 2020 and 2021. By combining the expected number of cars with the cost of the system, we can determine the minimum fee that the visitor should pay to ensure the profitability of the system in the following years. However, we can compare these data to data during the COVID-19 pandemic and see the effects of lockdowns and other restrictions. The last part of the article examines the dependence of utilization on energy consumption using the Pearson correlation coefficient, which tells us whether there is such a dependence between the two factors. As the demand for automated parking systems increases, planning should take into account possible future expansion or the construction of new ones.

2.1. Situation in the City of Ostrava

This study focused on the issue of parking and automated parking systems in Ostrava. There is a significant lack of parking spots in Ostrava. However, the issue differs in the city center and the suburbs, as well as during the day and the night. Another problematic aspect is that despite this deficit of parking spots, there are still free places in garages and parking spots in certain districts, especially those farther away from the motorists’ homes. This is caused by the fact that people want to have their cars near their homes due to comfort or the feeling of safety (keeping their property in sight). Each apartment building or civic amenity building should have a corresponding number of parking places, based on the parking demand calculation, which also includes the coefficient for the impact of the motorization degree. Of course, the current motorization degree is now very different from what it was 20 years ago, which is why there is such a large deficiency in parking spots.

The current parking solution concept for the city of Ostrava states that in the upcoming years, specifically in the district of Ostrava-South, it will be necessary to build about 6000 parking spots, 5000 spots in Ostrava–Poruba, and 4500 spots in the greater city center, both on the surface and in parking houses. Since 2015, 72 new parking spots have been built in Zábreh, 119 in Hrabuvka, 52 in Dubina, and 27 in Vyškovice. Adding up the number of new places since 2015, it is clear that the actual number is a fraction of the demand for parking. A similar situation can be found in other significant residential districts, such as the center of Ostrava or Poruba [28]. The city only uses the customary, time-tested measures for solving the parking situation, such as parking zones, and does not try to implement smart parking management solutions, only mentioning these as prospective measures in strategic plans. There is a range of ongoing projects for parking houses and collection parking places but their implementation is slow.

As an example of the lack of parking spaces in the city, we can mention one specific housing estate, which is located in the city of Ostrava. With the growing trend of two or more cars per family, there is a problem with a lack of parking spaces. Cars park in places that are not reserved for parking and do not comply with the applicable regulations. The situation is so chaotic that cars park in green areas and sidewalks. We calculate how many parking spaces are missing on Cholevova street and on Františka Lýska street, which is located in Ostrava-South, in the Hrabůvka district [29].

The calculation of the number of parking spaces N is based on the formula

$$N=O_o·k_a+P_o·k_a·k_p,$$

(1)

where

• N is the total number of parking spaces needed for the area addressed;
• $O_o$ is the basic number of stopping spaces according to Art. 14.1.6. ČSN 73 6110;
• $P_o$ is the basic number of parking spaces according to Art. 14.1.6. ČSN 73 6110;
• $k_a$ is the influence factor of the degree of motorization, for Ostrava it is 1:2.5, the factor is 0.84;
• $k_p$ is the reduction factor (does not apply to apartment buildings).

The basic number of parking spaces is set at 1 space per 20 inhabitants. In other words, we used $P_o=\frac{\mathrm{no}.\mathrm{of} \mathrm{inhabitants}}{20}$. There are approximately 564 inhabitants in Cholevova Street, so $P_o=28$. The number of inhabitants was determined by the number of flats. In total, there were 7 solved entrances from 23 residential units, which means that there were 161 apartments, with an occupancy of 3.5 people, which is 564 people. Using Equation (1), we obtained 159 parking spaces. The current number of parking spaces on Cholevova street is 97, which means that 62 spaces are missing.

Similarly, for Fratiška Lýska street, the basic number of parking spaces is set at 1 space per 20 inhabitants. There are approximately 798 inhabitants on F. Lýska street, so $P_o=40$. Using Equation (1), we obtained 225 spaces, whereas the current number of parking spaces on F.Lýska street is 128, which means that 97 spaces are missing.

2.2. Ring Automated Parking System

There are two automated parking buildings in Ostrava. One is located at the crossroad of Bílovecká street and Dr. Braun Square, near the train station of Ostrava–Svinov, and is intended for the general public. The second system is located on the premises of the Technical University of Ostrava. This building is accessible only to employees and students. Both of these buildings have been built and are operated by KOMA Industry s.r.o, which is one of the manufacturers of these systems, both in the Czech Republic and abroad. The company has supplied automated parking systems in Brno, Slany, Bratislava (Slovakia), and Warsaw (Poland).

The RING APS was one of the first projects in the Czech Republic and the APS that we discuss in this article. The location of this particular APS is outside of the city center and right next to an important railway station, where regional, long-distance, and international traffic occur (GPS coordinates: 49°49′21.33″ N, 18°12′29.892″ E). Thus, commuters may drive to this traffic node and then use a vast variety of eco-friendly public transport here (regional end long-distance trains, trams, LNG buses, etc.). This APS is used mostly by travelers, thus COVID-19 travel restrictions surely affected the use of this particular APS vastly. Although it is reasonable to point out that individual transportation is a better way toward sustainable traffic and ecological situation, the number of cars in the city is growing and the importance of dealing with parking must be addressed as a necessary step before reaching the point of universal public transportation. Furthermore, hybrid and electronic cars are slowly replacing fossil fuel cars and also need to be dealt with.

The other reason for choosing RING is that it is a sophisticated system of rings that turn and store cars in spiral sequences, taking into consideration the load distributions of buildings. This system has operated since 2006; however, concerning the long parking times and high energy consumption, it is no longer being built. The currently designed systems are much smarter and more sophisticated. The building is used to park passenger cars automatically and has a capacity of 105 spots. The average time for parking is 219 s and 218 s for leaving. Part of the facility is being rented for commercial purposes, namely hairdressers and financial counseling.

3. Materials and Methods

In this section, we discuss the mathematical methods used for the analysis of the utilization rate in the RING APS.

3.1. Data Collection and Preparation

For the RING parking house, the input data consist of the number of visitors from 2011 to May 2022. The data are divided by individual months and years, containing the exact number of cars per month. The data also include the peak occupancy during each month. Other statistical data (in terms of the possible relation between energy consumption and utilization rate) involved the reading of electricity meters for 2018 and 2019.

3.2. Methods

We used standard methods and tools to analyze the time sequences. We only mention them briefly but readers who are interested in the matter may refer to Shumwaya et al. [30,31].

Since our data were gathered continuously in the time period and the number of samples (in our case months) exceeds 100, we will consider this dataset as a time series. Our goal is to analyze the trend of the utilization rate as well as potential seasonal impacts.

First, let us consider the possible internal correlation in our data, meaning the correlation among samples in our time series. One way to approach this question is by using the autocorrelation function ($ACF$). This function evaluates Pearson’s correlation coefficient for time series and a delayed (lagged) version of itself. The lag is the variable of $ACF$. It follows trivially that $ACF\left(0\right)=1$ because the correlation of identical datasets is maximum. In general, the $ACF\left(k\right)$ value represents the correlations between moments in time series, i.e., in our case months, for samples shifted from each other. If the $ACF\left(k\right)$ value differs from 0 significantly, then this documents a correlation between sample t and sample $t+k$. This may also take into consideration possible influences between these two samples; it does not need to be a direct influence necessarily. A significant $ACF$ may partially indicate a certain level of seasonal impacts, as well as periods with certain trends. More formally, the $ACF$ is defined as

$$ACF\left(k\right)=\frac{1}{s^2(n-k)}\sum _{t=1}^n\left(X_t-\overline{X}\right)\left(X_{t+k}-\overline{X}\right),$$

(2)

where

• n is the number of samples;
• $X_i$ is the i-th sample of the timeline;
• s is the sample standard deviation;
• $\overline{X}$ is the average of all values of the time series;
• k is the shift (lag).

To capture the direct influences between factual pairs of lagged series, partial $ACF$ ($PACF$) is employed. This evaluates the correlation coefficient of the remaining samples, without considering the impacts of the samples in between. In other words, the $PACF$ for delay k corresponds to the coefficient $a_{t-k}$ in the linear adaptation model

$$X_t=a_{t-1}{X}_{t-1}+\dots +a_{t-k}{X}_{t-k}+\epsilon .$$

(3)

However, seasonal effects may be distorted by the trends of the time series and the tendencies for the growth/drop. We used the sliding average method to isolate this effect. The sliding average method takes a given time window and replaces the values of the samples with the arithmetic mean of the values in that time window. This is the basic form of sliding averages, but other replacement methods can be used, such as an exponentially weighted average (as we used in our case). Since we used 6- and 12-month sliding windows, we put more weight on more recent data, which is exactly the purpose of the exponential weighing (for details, see, e.g., [32]). The resulting values should be “smoothed out” and capture potential trends without random spikes and, hence, be more suitable for analysis than the unprocessed data.

Another way to capture the trend of the data and to predict the behavior, which is key for us in this work, is to approximate data using regression. In other words, we approximate data via a curve

$$y=\sum _{m=1}^k{c}_m{f}_m\left(x\right)$$

(4)

where

• $f_m\left(x\right)$ are the chosen basis functions,
• $c_m$ are the corresponding coordinates of the approximation in the chosen basis.

In other words, we use the linear regression model in the sense of linearity with respect to the coefficients $c_m$, which are calculated using the least squares method, minimizing the sum of the squares of approximation errors; hence, this approximation of data by functions $f_m\left(x\right)$ is the best in the sense of the quadratic norm. As soon as we have an approximation for the trend, we can use it to make simple predictions. The limits for the $100(1-\alpha )$% confidence interval for the predicted values are calculated using the following formulae:

$$\begin{array}{ccc}\hfill \overline{y_i}& =& \sum _{m=1}^k{c}_m{f}_m\left(x\right)+s_i{t}_{n-k,1-\frac{\alpha }{2}},\hfill \end{array}$$

(5)

$$\begin{array}{ccc}\hfill \underline{y_i}& =& \sum _{m=1}^k{c}_m{f}_m\left(x\right)-s_i{t}_{n-k,1-\frac{\alpha }{2}}\hfill \end{array}$$

(6)

where

• n is the number of samples;
• $s_i$ is the standard deviation of the predicted value; ${\sum }_{m=1}^k{c}_m{f}_m\left(x_i\right)$,
• $t_{n-k,1-\frac{\alpha }{2}}$ is the $(1-\frac{\alpha }{2})$-quantile of the Student’s t-distribution with $n-k$ degrees of freedom.

The formula above also gives a heuristic formula for the significance level $\alpha$, given the desired sum of values $\underline{y_i}$ for $i=1,\dots ,N$:

$$\alpha =2-2F_{n-k}\left({\displaystyle \frac{{\sum }_{i=1}^N\left({\sum }_{m=1}^k{c}_m{f}_m\left(x_i\right)-\underline{y_i}\right)}{{\sum }_{i=1}^N{s}_i}}\right)$$

(7)

where $F_{n-k}$ is the cumulative distribution function of the Student’s t-distribution with $n-k$ degrees of freedom. Our confidence levels depicted in Section 5 are derived via this formula.

4. Analysis

Figure 1 represents the $ACF$ of our data. The band along the horizontal axes, surrounded by dashed lines represents the insignificance area, i.e., values in this band are not considered significant and do not nod toward autocorrelation. As we can see, the most significant fluctuation of the $ACF$ occurs around lag = 6, and then one around lag = 12, half a year, and one year, respectively. This indicates a certain level of seasonal behavior.

Figure 2 shows that a significant positive $PACF$ is present within a delay of 5 and 11. This confirms a certain level of seasonal impact, as indicated by the $ACF$. If we compare these observations with our data, we can state that, in the summer, the number of visitors is smaller than in the spring and at the end of the year, where it seems that the data reach higher values (for 5–6 and 11–12, the monthly shifts have positive $ACF$ and $PACF$) [30]. It would be interesting to compare these expectations with the fault rates in the RING system, assuming that faults and defects will be tracked. This review also proposes that the system should undergo yearly maintenance, probably during the summer holiday months, and other repairs and maintenance could be concentrated in months such as May, November, and December.

Figure 3 depicts the data and their decompositions into trend, seasonal, and random (leftover) components.

• The trend is captured by moving averages and represents the overall growth/decrease in data.
• The seasonal component is the strictly periodic component of the data.
• The random component consists of the rest of the data and does not contribute to the trend and seasonal (periodic) part of the time series.

We can clearly see that the seasonal component further confirms our hypothesis of seasonal behavior, based on $ACF$ and $PACF$, since it is non-zero.

Based on the aforementioned seasonal expectations and components from Figure 3, we used sliding averages for time windows of 6 and 12 months, as depicted in Figure 4 below. It seems that the 12-month window smooths out the curve and correctly captures the trend, while the 6-month window still contains some seasonal fluctuations. We can also do the same for the data that included the COVID-19 period; the results can be seen in Figure 5.

One reason why we analyzed both the pre-pandemic data and the whole dataset was to show the possible developments if COVID-19 did not happen, and to analyze the impacts of the pandemic on the operations.

5. Results

The lockdown “shuffled” with the utilization of RING APS significantly. We are going to compare the prediction based on the years 2011–2019 with the actual data to obtain the magnitude of COVID-19 effects on the number of cars parked.

In our case, we chose the following eight basis functions for the approximation:

$$\begin{array}{c}\begin{array}{ccc}{f}_1\left(x\right)=1,\hfill & f_2\left(x\right)=x,\hfill & \\ f_3\left(x\right)=sin\left(\frac{\pi x}{3}\right),\hfill & f_4\left(x\right)=cos\left(\frac{\pi x}{3}\right),\hfill & \hfill f_5\left(x\right)=\frac{1}{1+{\mathrm{e}}^{\frac{54-x}{12}}},\\ f_6\left(x\right)=sin\left(\frac{\pi x}{6}\right),\hfill & f_7\left(x\right)=cos\left(\frac{\pi x}{6}\right),\hfill & \hfill f_8\left(x\right)=\frac{1}{1+{\mathrm{e}}^{\frac{108-x}{12}}}.\end{array}\end{array}$$

The reason behind these functions is as follows: the first two functions are basis functions for capturing the linear trend. Trigonometric basis functions have the periods 6 and 12, based on $ACF$ and $PACF$ calculated before, trying to capture seasonal influences. The remaining two functions are scaled and shift the logistic functions for capturing increasing ($f_8$) or decreasing ($f_5$) growth trends. The resulting approximation can be seen in Figure 6:

The red area corresponds to the 84.9% confidence interval for the prediction for the upcoming two years (2020, 2021). In other words, there was a probability of at least 84.9% that the new data would occur inside the red area.

The trends show that during the first three years of the monitored period, the utilization systematically grew. After that, it stabilized to more-or-less constant values, while at the end of the monitored period, we once again see a trend toward growth. As the demand for parking systems increases, it would seem that planners should consider possible future expansions of existing systems in Ostrava or the construction of new ones.

Through the accounting and visitor data (obtainable from the authors on demand, but not published directly due to company policies), we estimated that for the year 2020, the facility needed 8923 cars parked through the course of the year, taking into account the average payment of 90 CZK per car/day. Using Formula (7), we concluded that there was at least a 92.45% probability of profit since we used our lower estimate so that it summed to 8923, which resulted in $\alpha =15.08\%$. Since the lower estimate means that there was only a $1-\alpha /2$ probability of the actual data being lower, this led us to the conclusion that there was a 92.45% probability of profit.

However, COVID-19 hit many branches and local restrictions resulted in very limited travel, namely long-distance ones (because of lockdowns of whole regions), which employ the APSs most widely. Recall that the RING system is located right next to an important train and bus station. The actual number of cars for the year 2020 was not the desired 8923, but a mere 5147 cars. Notice that the APS was closed for the entirety of two months (March and April) due to maintenance and pandemic issues. Thus, we can conclude that the COVID-19 pandemic influenced the utilization rate of the APS vastly, losing around CZK 340,000 of profit (again, based on accounting and visitor data). A similar loss also occurred for the year 2021, which was not ’more giving’ than the previous one, to only start the APS to refresh its former utilization rate from spring 2022.

The new prediction with current data is not very optimistic, but since the pandemic was (and partially still is) an unexpected and heavily influencing factor, we decided to modify the new prediction in the sense of a weighted scalar product within the projection, giving much smaller weight to the most pandemic-influenced data. We chose the weight formula heuristically as follows:

$$\begin{array}{ccc}\hfill w_i& =& \left\{\begin{array}{cc}0.01,\hfill & 110<i<135,\\ 1,\hfill & \mathrm{otherwise}.\end{array}\right.\hfill \end{array}$$

(8)

This means that the data during the pandemic (March 2020–February 2022) are considered somewhat negligible for the previously stated reasons. However, this does not mean that the projection does not take them into account since they still form a formidable “gap” within data, which takes a certain level of the effect itself. Note that the weights are bounded and positive, which means the bilinear form

$$\begin{array}{ccc}\hfill \left(x,y\right)& =& \sum _{m=1}^N{w}_m{x}_m{y}_m\hfill \end{array}$$

(9)

is still symmetric positive-definite, so it still represents an inner product, thus projection using this mapping still satisfies the best possible approximation in the sense of the quadratic norm. Moreover, we slightly altered the logistic functions for prediction as the size of the dataset changed from 108 to 137; thus, to have similarly positioned logistic functions, we need to shift them:

$$\begin{array}{ccc}\hfill f_5\left(x\right)& =& \frac{1}{1+{\mathrm{e}}^{\frac{66-x}{12}}},\hfill \end{array}$$

(10)

$$\begin{array}{ccc}\hfill f_8\left(x\right)& =& \frac{1}{1+{\mathrm{e}}^{\frac{132-x}{12}}}.\hfill \end{array}$$

(11)

This does not impact the properties of the projection since our set of basis functions is still linearly independent.

The resulting approximation and prediction are depicted in Figure 7. Estimating the rising prices for the utilization of APSs and expecting 12,000 cars by the end of the year 2023 resulted in a rather poor $\alpha =0.67$, which, coincidentally, results in approximately (recall $1-\alpha /2$) a 67% chance of profit in the nearest future. As we can see, the pandemic affected the possibilities of APSs significantly. However, it is still not a desperate estimate and the trends from both predictions and moving averages suggest that, shortly, the utilization rate could return to pre-pandemic levels. Note that according to additional data from the practitioner, the utilization rate peaked at around 40% even before the pandemic. This shows that the system has not reached its full potential yet.

Finally, we compute the Pearson correlation coefficient (the calculation is analogous to $ACF$ for time series) between energy consumption and utilization, based on pre-pandemic data (2018, 2019). Again, the data are obtainable from authors on demand. The Pearson correlation coefficient expresses the amount of linear dependence. In our case, the Pearson correlation coefficient was −0.139. This means that the dependency is, paradoxically, nearly inverse, but the coefficient is so close to zero that it is difficult to make concrete claims based on it. The data are either not linearly dependent at all, or the amount of linear dependence is very low. Furthermore, since the data do not contain any outliers, this indicates no dependence between energy consumption and the number of cars parked. This is probably mainly caused by the technical architecture of the RING system and by other services within the building. This suggests that the more the garage is utilized, the less energy expense per parked car is needed.

6. Discussion

From the current finding of parking in housing estates or the central part of the city of Ostrava, as we saw in the examples in Section 2.1, we can state that parking and parking spaces are missing. APSs can address this deficit. Parking garages that use APSs have several fundamental differences compared to conventional parking garages. APSs are characterized by computer-controlled automatic vehicle storage processes using sophisticated technological equipment. The driver does not have access to the garage area, the handover and collection of the vehicle take place in a special module. APSs progressively solve the insufficient supply of parking spaces in locations where, due to the lack of space, it is not possible to apply conventional parking systems. The main advantage of the system involves the best possible use of available space and spaces in garages with APSs are not internal communications, they are mainly pallet systems consisting of storage modules/boxes and stacking systems.

Pros:

• Minimum space requirements;
• Convenient parking;
• The system does not burden the environment;
• Parking speed, automated and self-service operations without entering the building and a long search for free space;
• Weather protection (cars);
• Without access from unauthorized persons (prevention of damage and theft);
• Low operating costs (lighting, personnel costs);
• No need for facilities for the driver (sanitary rooms, barrier-free access, elevators, stairs, air conditioning).

Cons:

• More demanding technologies;
• Higher initial costs;
• Dependence on alternative sources in the event of a power failure;
• Inexperience of designers and low technical competence of companies in the Czech Republic in design and implementation;
• Distrust and habits of motorists and builders.

In the past, several studies were carried out focusing on modeling and predicting demand for parking on an aggregated as well as non-aggregated level. Each statistic for the utilization of the landscape then affects the generation of parking for the specific building area, in one way or another [25].

This work presents the basic findings on the topic of parking in the city of Ostrava. The key parts of the city do not have sufficient amounts of parking spaces. An automatic parking system is certainly a technology of the future and, hence, it should come as no surprise that parking systems also come with certain disadvantages. On the one hand, a client wishing to collect his/her car might need to wait longer than in the case of standard parking houses, i.e., if 40 people come simultaneously, the last customer will need to wait more than an hour for his/her car. This factor can, however, be suppressed by a suitable technical adjustment and optimization of the release time, and finding a solution to this problem is one of the aims of virtually every manufacturer of parking systems. One way to address this could be by combining APS houses with automatic parking assistants, which can relieve the human factor even further and make the docking process more efficient [33]. However, parking systems have multiple advantages, including capacity increases of dozens of percentage points compared to classical parking houses (there is no need to include handling areas; the client loads the vehicle in the system and can leave) as well as energy savings—photovoltaic panels and recuperation options allow houses equipped with such parking systems to operate in so-called island modes and, hence, not only supply energy to themselves but also send excess energy back to the network. This could be an even bigger factor using state-of-the-art photovoltaic technology (see, e.g., [34]).

Parking houses in Ostrava are certainly useful components of a well-working transportation network. People who need to travel for some time often desire to park their cars in a parking house since this protects them against the risk of break-ins and damage; furthermore, in the winter they do not need to worry about defrosting the windows or locks [35,36]. The localization of the parking system plays an important role here, notably because it is located in the vicinity of a train station.

However, the parking house in Svinov has a huge disadvantage, notably its energy demands compared to its efficiency: if you want to collect one car, you might need to move thirteen of them (specifically in the third section). This is counterbalanced by its very low defect rate. Despite its disadvantages, the system is still operational and its utilization is not declining (not counting the pandemic, as the utilization rate has more or less returned to pre-pandemic levels), which has also been documented in various utilization graphs, etc. However, other approaches for data processing and prediction are certainly other ways to deal with this topic in the future, i.e., by correcting/confirming these results. We chose linear regression for its convenient prediction formula and the possibility of heuristically choosing basis functions. On the other hand, neural networks could bring different insights into the data.

In the city of Ostrava, it is necessary to revive the current parking situation so that the dissatisfaction of motorists does not increase. Automatic parking garages could be beneficial solutions to public satisfaction and could at least partially solve this problem. The city should choose the best supplier and look at the management of statistics, failure analysis, and the traffic of these systems.

7. Conclusions

Given the predicted growth of the auto industry, it is clear the existing capacities of static transport will not be able to satisfy the expected demands and it will be necessary to adopt differentiated approaches to individual groups of users and design new solutions [28]. Furthermore, the larger implementation of autonomous vehicles and parking assistants could benefit automatic garages, since the parking process could be relieved from the human factor completely. On the other hand, as we mentioned, many people are still too skeptical about the usage of autonomous vehicles. For instance, one study [37] found that nearly 60% of its respondents felt that way, mostly for safety reasons. However, the technology of autonomous vehicles is evolving rapidly, for example, reference [38] showed that most people cannot tell the difference between an AI-driven car and a human-driven car from the passenger experience. The future will show how fast autonomous vehicles will become common phenomena, at least from technological and legislative points of view.

The high-quality statistical database of the RING system in Ostrava–Svinov allowed us to examine the trends of the system’s utilization and potential seasonal influences. This was the first automated parking system in Ostrava, built in 2006, and it was necessary to let motorists become acquainted with the new system. Afterward, it was necessary to collect contracts between the operators of the automated system and railway transport operators since the system is located in the vicinity of a train station. The graphs depict a growing utilization trend.

This review proposes that the system undergo yearly maintenance, probably during the summer holidays, and other repairs or maintenance could be concentrated in months such as May, November, and December. Repairs mainly include actions, such as the replacement of broken light bulbs, cog belts, tracks, various other components, new paint, revisions, etc.

A simple prediction suggests that the system’s utilization will probably not drop in the short run and should achieve profitable levels, despite COVID-19, although given the present data, the probability for profit decreased from 92.45% to 67% due to the pandemic. This means that even when accounting for future repairs, revisions, energy, and rental costs, the system should still generate a profit. That being said, it is difficult to predict the exact impacts of the COVID-19 pandemic, which have negatively impacted the utilization of the system. In particular, public transport has experienced a loss of long-standing commuters, who have decided to switch to safer modes of transport (e.g., cars). There is a need for sustainable systems from the perspective of both robustness toward technical issues (malfunctions) and societal ones, such as the COVID-19 pandemic. Further study of the new data with other possible methods of prediction, e.g., other types of regression or neural networks, and finding the possible optimal solutions for “ambivalent” sustainability are our goals for future work.