ANALYSIS AND FORECAST OF PASSENGER FLOWS IN PUBLIC TRANSPORT – THE CASE OF POLAND

Public transportation provides its services to both urban centers and neighboring areas in the immediate vicinity of the city. The problem of urban transportation is evident, the number of people willing to use public transportation has decreased. Therefore, there is a need to delve into the issue and conduct an analysis of the demand for urban transportation in Poland in 2000-2030, this will allow us to assess in what direction urban transportation is heading, whether there is an increase in the number of people using it, or whether there is a downward trend (Zielińska 2018).
Based on CSO statistics from 2009-2020 for the analysis of demand for public transportation in Poland, a forecast of people using public transportation was conducted using Statistica software for 2021-2030. Due to the situation with the COVID-19 pandemic, the study was conducted in 2 ways – with and without 2020. 
Public transportation will make less and less profit and even losses for the next few years through rising gasoline and energy prices. Virtually in each of the provinces, and likewise throughout Poland, a decline in the number of people willing to use public transportation is evident. conclusions.
On the basis of the surveys carried out, there is a general trend that shows the current state of public transport. In most of the cases studied, a similar conclusion emerges, namely that public transport will experience a marked decline in the coming years. The number of people who want to use public transport will decrease, mainly due to the COVID-19 pandemic and people’s fears for their own safety.


Introduction
Transportation is an activity that aims to cover some area.Taking into account the economic aspect, this enterprise involves the profitable provision of services.The result of transportation activities is the movement of people and material goods, as well as the provision of additional ancillary services that are directly related to the primary services.
Public mass transportation is publicly available regular passenger transportation performed at specific intervals and along a specific line or transportation network.There are five basic subsystems of public transportation found in various cities in Poland, such as buses, trolleybuses, streetcars, subways and light rail.
Public transportation provides its services to both urban centers and neighboring areas in the immediate vicinity of the city.Public transportation in recent years has been trying to develop for the convenience of those who use its services.Despite the continuous and rapid development of transportation, some people have opted for transportation by private means.The problem of urban transportation is evident, the number of people willing to use public transportation has decreased.Therefore, there is a need to delve into the problem and conduct an analysis of the demand for urban transport in Poland in 2000-2030, this will allow to assess in what direction urban transport is heading, whether the number of people using it is increasing or there is a downward trend (Zielińska 2018).
The problem of forecasting is well known in the literature.It has been used, among other things, to forecast the number of traffic accidents.The vector autoregression model has also been used to forecast the number of traffic accidents, the disadvantage of which is the need to have a large number of observations of the variables in order to correctly estimate their parameters (Wójcik 2014), as well as the autoregression models of Monederoa et al. (2021) for analyzing the number of fatalities and al-Madani (2018) curve-fit regression models.These, on the other hand, require only simple linear relationships (MaMcZur 2022), and row autoregression (assuming the series is already stationary) (PiłatoWska 2012) or exponential smoothing (GorZelancZyk et al. 2022).
chudy-laskoWska and Pisula (2015) in their work used the ANOVA method to predict the number of traffic collisions.The disadvantage of this method is that it makes additional assumptions, especially the assumption of sphericity, the violation of which can lead to erroneous conclusions (GreGorcZyk, sWarceWicZ 2012).Neural network models are also used to forecast the number of traffic accidents.The disadvantages of ANNs are the need for experience in the field (chudy-laskoWska, Pisula 2014, Wróbel 2017) and the dependence of the final solution on the initial conditions of the network, as well as the inability to interpret in the traditional way, as ANNs are usually referred to as a black box, where the user provides input data and the model provides output data without knowledge of the analysis (Techniki zgłębiania danych (Data mining) 2022).
A new prediction method is the use of the Hadoop model by kuMar et al. ( 2019).The disadvantage of this method is the inability to work with small data files (Top Advantages and Disadvantages of Hadoop 3 2022).karlaftis and VlahoGianni (2009) used the Garch model for prediction.The disadvantage of this method is its complex form and complicated model (PercZak, fisZeder 2014, fisZeder 2009) On the other hand, McIlroy and his team used the ADF test ( 2009), which has the disadvantage of poor power in the case of autocorrelation of the random component (Mućk 2022).
The authors of publications (shetty et al. 2017, li et al. 2017) also used Data--Mining techniques for forecasting, which usually have the disadvantage of huge sets of general descriptions (MarcinkoWska 2015).One also encounters the combination of models proposed by sebe et al. ( 2008) as a combination of different models.Parametric models are also proposed in the work of blooMfield (1973).On the other hand, the analysis of public transport costs was analyzed in the works (GorZelańcZyk, kocZoroWski 2018a, 2018b).Given the diversity of forecasting methods, the authors used exponential smoothing methods in their work to get an opinion on how demand for urban transportation will develop in the following years in the analyzed provinces, so that measures can be introduced to encourage residents to use public transport instead of individual transport.
The forecasting methods presented can be successfully used to forecast not only road accidents, but also other events, such as forecasting passenger flows in public transport.Taking into account the above literature review, the authors carried out an analysis and forecast of passenger flows in public transportthe case of Poland.

Methods and measures
The object of the research work is to conduct an analysis of the demand for public transportation of Polish society in 2000-2030.The results of the research will show the direction in which public transportation is heading.With the help of statistical research, the development or regression of public transportation will be determined.
The study was conducted in 2021 based on data collected by the Central Statistical Office in Poland.Due to the situation with the COVID-19 pandemic, the survey was conducted in 2 ways -with and without 2020 (i.e., excluding the pandemic year).Statistica program was used to conduct the survey.
The Statistica program offers access to a wide range of forecasting methods.One of the methods that was used in the study is the exponential smoothing method.The research method is considered the most accurate of all existing methods.The exponential smoothing method involves using the forecast for period t, which is equal to the forecast of that variable for period t-1, adjusted by the product of the smoothing parameter α, 0 ≤α≤ and the value of its absolute error:

Piotr Gorzelańczyk, Adrian Pawłowski
The parameter α is chosen using the smallest error criterion of expired forecasts (rabiej 2012).The exponential smoothing method is a method for forecasting time series with one-dimensional data.Forecasts made using exponential smoothing methods include a weighted average of preceding observations.The weights are distributed proportionally to the extinction of historical observations.Thus, the more recent the observation, the higher the weight (Introduction to exponential smoothing 2022).

Results
Surveys conducted by the Central Statistical Office (CSO) were used to analyze the research.The surveys conducted by the CSO were carried out from 2009 to 2020.In earlier years, surveys were not conducted by various types of institutions, as well as public transportation facilities were not required to keep relevant statistics showing the scale of people using public transportation in 2000-2008.The results of the survey presented in Tables 1 and 2 are collected for the entire Polish population and for individual provinces in Poland.The data are presented in millions of passengers using public transportation in Poland.The data presented in the tables, come from CSO statistics from 2009-2020 by province.The tables also include information on forecasting the number of people using public transportation in 2021-2030 (with the pandemic) and 2020-2030 (without the pandemic).The next step after collecting the relevant data is to create a graph of it, which will show whether the historical values are cyclical, seasonal, linear trend, constant or random.This procedure will allow the selection of an appropriate research method.Figure 1 shows a graph with collected data on demand for urban transportation in Poland.The graph shown for Poland indicates the random nature.cont.Table 1 Piotr Gorzelańczyk, Adrian Pawłowski Thus compiled, the author entered the data into Statistica software, which made it possible to develop a forecast for 2021-2030.The study was conducted in 2 ways.With 2020 and without 2020.The author conducted the analysis in this way, because 2020 is the year of the COVID-19 pandemic, in this way it is possible to predict how transportation demand would have developed without the pandemic year, and to see what effects the pandemic had on urban transportation.
The methodology of the study for each province will be presented in 1 of the examples.The same study will be conducted for the collected data of the entire country.The rest of the results will be presented in a summary table that will show the results for the other surveyed centers.
The various forecasting techniques used for the study are as follows: -M1 -moving average method 2-points; -M2 -moving average method 3-points; -M3 -moving average method 4-points; -M4 -exponential smoothing no trend seasonal component: none The essence of this method is that the time series of the forecast variable is smoothed using a weighted moving average, and the weights are determined according to the exponential function.The weights were optimally selected by the program, Statistica, in which the study was conducted.The forecast in this case is based on a weighted average of the current and historical values of the series.The result of the forecast using this method, depends on the choice of the model and its parameters.
The following errors of expired forecasts determined from equations were used to calculate measures of analytical forecasting perfection: -ME -mean error -MAE -mean everage error -MPE -mean percentage error -MAPE -mean absolute percentage error -MSE -mean square error (5) where: n -the length of the forecast horizon, Y -observed value of urban transportation demand, Y p -forecasted value of urban transportation demand.
On the basis of the exponential smoothing and forecasting error methods adopted, the forecasting method for which the value of the mean absolute percentage error was the smallest was selected and the results are shown in the figures below.
Then the same analysis was performed for the same example, but excluding the 2020 pandemic year.The methodology for the other models and subsequent provinces is the same as shown in the Figures above.The results of the analysis will be presented in Table 3 and Figures 2, 3, 4. Based on the analysis, it can be concluded that the results of the study are greatly influenced by the COVID-19 pandemic and thus the way of travel and developments in the next few years.On the other hand, the forecast with the pandemic year cut out in most cases is very optimistic.It even depicts a gentle increase in willing people using public transportation.This means an increase in demand for public transportation if pandemic years are not taken into account.cont.Table 3 Piotr Gorzelańczyk, Adrian Pawłowski   3, a decrease in demand for public transportation is visible due to the COVID-19 pandemic.Taking into account the absence of the pandemic, a slight decrease is visible for Lubelskie Province.In contrast, a slight increase in demand is evident for Lubuskie and Lodz provinces.Table 5 and Figures 8, 9, 10 contain the forecast for the provinces of Lesser Poland, Mazovia and Opole.The results of the analysis indicate a decrease in the demand for public transport in the following years when 2020 is taken into account.However, the situation is reversed in the years when 2020 is not taken into account.In this case, the situation varies, however, a decrease is forecast for Małopolska province.In the case of the Mazowieckie and Opolskie provinces, a decrease is evident in the years with the pandemic year, while an increase in willingness to use public transportation can be observed without this year.With the help of Table 6 and Figures 11,12,13, the forecast for Podkarpackie, Podlaskie and Pomorskie provinces can be seen.It can be seen that for Podkarpackie and Pomorskie Voivodeship, an increase in public transport demand is visible excluding 2020 and with 2020.However, for Podlaskie Voivodeship, a decrease is visible for both analyses.cont.Table 6 Piotr Gorzelańczyk, Adrian Pawłowski Table 7 and Figures 14, 15, 16 show the forecast results for Silesian, Świętokrzyskie and Warmian-Masurian provinces.The development of public transportation is predicted for the Warmian-Masurian Voivodeship, if the result of the forecast without 2020 is taken into account.Also minimal growth can be seen for the results of the forecast in the Świętokrzyskie province without 2020.The remaining results show a regression regardless of whether the results with or without 2020 are taken into account.cont.Table 7 Piotr Gorzelańczyk, Adrian Pawłowski In the Wielkopolska and West Pomeranian Voivodeships, with the help of Table 8 and Figures 17, 18, it is apparent that there is a decrease in the need to use public transportation if the pandemic year 2020 is considered and there is also a decrease if 2020 is not considered, with the regression being smaller.cont.Table 8 Piotr Gorzelańczyk, Adrian Pawłowski

Discussion
Summarizing the results of the forecasting studies by province and for Poland with and without 2020 (the year of the pandemic), there is a general trend that shows the current state of urban transportation.In most of the cases studied, a similar conclusion is revealed, which is that public transportation will experience a marked regression in the coming years.There will be a decrease in the number of people who are willing to use public transportation.
Considering the pandemic year and comparing all provinces with each other, the survey results leave no illusions.Outside of the Podkarpackie province, a dramatic decline can be seen, by 2030 the number of people using public transportation will drop by more than half compared to 2020.However, if you cut out the pandemic year of 2020 from the forecast, you can see that the situation is changing.There is a noticeable increase in the number of people willing to use public transportation.This is true for individual provinces, but is also reflected in the results for Poland as a whole.However, despite the fact that the year 2020 is not taken into account, the Kuyavian-Pomeranian, Lublin, Podlasie, Silesian, Greater Poland and West Pomeranian provinces score a regression.Nevertheless, this is not as significant a difference as the decline in demand for public transportation in the 2020 forecast.
The reason for such a development when considering the 2020 forecast is the very small share of less developed provinces, namely Warmian-Masurian and Podlasie, as well as the area-small provinces of Lubuskie and Świętokrzyskie.The exception in this case is the Podkarpackie province, which, despite being called moderately developed, achieves high development scores compared to other provinces.
The decline in the number of demand for urban transportation is also the result of underdeveloped transportation to smaller towns.Especially those living in villages, are forced to have an individual means of transportation.In most families that live in rural areas, each person has his or her own means of transportation.Official errands, work or the desire to expand one's knowledge are the main factors by which people living in rural areas have to travel to larger cities.
Considering the results of the analysis, it can be concluded that the demand trend indicates a decline in the number of people willing to use public transportation in the coming years.A major influence on this situation is the COVID-19 pandemic, which has had a clear impact.
Referring to the research conducted by Piotr Gorzelańczyk Change in the mobility of Polish residents during the COVID-19 pandemic, it can be seen that the way Polish urban and rural residents move has changed.From the research conducted by Gorzelańczyk, it can be noted that during the pandemic, people using public transportation in cities were forced to change their mode of transportation to cars, bicycles and walking.In smaller towns and villages, the situation during the pandemic did not change, because there access to public transportation is negligible, meaning that cars are mainly used for transportation.Gorzelańczyk's study and the research presented above show how much of an impact the COVID-19 pandemic had on the way people moved.One can also see a change in the purpose of movement, before the pandemic the main purposes of movement were work, shopping and then social life.During the pandemic, social life was replaced by school.On the other hand, doctor's appointments, rest or visits to parents were completely abandoned (GorZelancZyk 2022).With the development of civilization, people's desire for individual means of transportation increased.Pandemic COVID-19 changed Polish society's perception of travel.This was due to the existing restrictions that the government put in place, such as a limit on the number of people who can travel by public transportation.In addition, measures were taken to lower fuel prices, making most people more willing to use individual transportation.This has had a clear effect, as can be seen in the available historical data.
If, on the other hand, the COVID-19 pandemic had not occurred historically, research shows that the Polish public, would increasingly use public transportation, but not in every province.However, the impact of the COVID-19 pandemic on the current demand for public transportation in Poland is significant.The result is a major regression that is unlikely to ever be restored to its pre-pandemic state.COVID-19 had an impact on reducing the number of people using road transport by an average of 10-15% depending on the province studied.
The survey, which was conducted, also helped show the transportation preferences of Polish society.Polish society is much more inclined to move by individual means of transportation, such as cars, than by public means, such as the city bus, streetcar or subway, according to the survey presented above.The Polish public uses public transportation in a small group.The survey was influenced by the epidemiological situation related to the infectious disease COVID-19.The population sought to protect itself from infection, so it opted for individual means of transportation.Before the outbreak of the pandemic, people were more likely to swap the personal car for public transportation.
In the current situation, it is virtually impossible to rebuild the position of public transportation.A large number of people who switched from public to individual transportation during this period will not return to use public transportation services again.

Fig. 3 .
Fig. 3. Demand for urban transportation in the Lower Silesian province from 2020 to 2030 Source: based on Transport pasażerów (2021).

Fig. 18 .
Fig. 18.Demand for urban transportation in the West Pomeranian region from 2020 to 2030 Source: based on Transport pasażerów (2021).
Analysis and Forecast of Passenger Flows in Public Transport -the Case of Poland 167 -M10 -exponential smoothing exponential seasonal component: none; -M11 -exponential smoothing exponential seasonal component: additive;

Table 3
Forecast for Poland, Lower Silesia and Kujawsko-Pomorskie with and without 2020

Table 4 and
Figures 5, 6, 7show the forecast results for Lubelskie, Lubuskie and Łódzkie provinces.As in Table

Table 6
Forecast for Podkarpackie, Podlaskie and Pomorskie Voivodeships with 2020 and without 2020