In this section, you will learn: 

• Why are mathematical models used in transport planning? 

• What is the Passenger Transport Model (Pasażerski Model Transportowy – PMT) and how is it utilized? 

• Who can use the Passenger Transport Model? 

A widely accepted standard in transport planning in many countries is demand modelling using advanced mathematical models. For this purpose, sophisticated IT tools are employed to process various data and determine how many people and goods will use the existing and planned infrastructure in the future. Historically, for investments in existing infrastructure, particularly in simpler cases, so-called indicator methods for traffic forecasting were used. These methods relied on analysing existing traffic and processing it using various conversion factors (e.g., indicator changes related to GDP dynamics). However, indicator methods are not feasible in case of more complex infrastructural systems. They are also inadequate for constructing transport infrastructure in new alignments (outside existing corridors), as there is no current traffic (it is zero). Therefore, the modern standard for railway traffic forecasting in Poland involves using macroscopic simulation models developed in specialized software. 

A traffic model is a mathematical representation of the movement of people and goods in a designated area (e.g., country, region, agglomeration) within a given time unit (e.g., day, peak hour). It is an IT-engineering tool that incorporates findings from sociological research and uses mathematical formulas to reflect processes within the transport system. The basic form of a traffic model presents a picture of traffic intensities across the infrastructure network in individual and public transport. It depicts movements using various modes of transport, such as passenger cars, freight trucks, buses, trains, aircraft, and inland and maritime vessels. Unlike detailed microsimulation, this model provides a comprehensive view of how the transport system functions, diagnoses existing and future problems, and assesses the effectiveness of planned investment options in transport. This enables reliable, efficient, and informed planning and designing of the transport system. 

For the Horizontal Timetable project, the Passenger Transport Model (PMT) was used for analysis and forecasting. The PMT is a four-stage multimodal model, encompassing different modes of transport, allowing for the consideration of their complementarity and competitiveness. It can analyse passenger flows in public transport compared to forecasted volumes of individual road traffic. The PMT was developed in the PTV VISUM environment, used by many leading carriers and infrastructure managers in countries like Germany, Austria, Switzerland, the Netherlands, the Czech Republic, Spain, Italy, and the Baltic countries. CPK experts have been working on the PMT internally since 2019. The model’s foundation was the PKP PLK Traffic Model project, initiated from 2014 to 2019. 

The PMT has been divided into traffic zones, which represent areas from and to which people travel. These zones correspond to municipalities, with some large cities further divided into more zones to enhance the accuracy of source-to-destination trips. The spatial scope of the PMT covers Poland and its border areas, consisting of a total of 2,800 traffic regions. Including border areas in the model is necessary to accurately represent cross-border travel. 

In the supply layer, the PMT utilizes various input data, such as the characteristics of road and rail networks, bus and rail timetables, and air transport data. Critical to the analysis are the so-called explanatory variables, which include all socio-economic data and indicators, as well as characteristics related to the spatial development of the analyzed areas. These variables impact the traffic-generating potential of the areas and, consequently, the results of the traffic analyses and forecasts generated by the model. 

These include, among others: 

• Demographic data, including the number of residents, their spatial distribution along with migration phenomena, age structure, etc. 

• GDP growth forecasts 

• Car ownership indicators 

• Number of jobs 

• Office spaces 

• Accommodation spaces 

One of the key elements of the PMT is the demand model, developed based on research findings on transportation behaviour (how people use transport). The data was obtained from seventeen local studies and national survey results by the Polish Main Statistical Office, representing a sample of transportation behaviour for approximately 183,000 individuals (about 80,000 households). Incorporating this data has enabled the creation of an effective, flexible, and easily updatable model. 

The PMT includes data for several time horizons, covering the years 2019, 2025, 2028, 2030, 2035, 2040, 2050, and 2060. 

The model for the year 2019 (the last relevant period before the COVID-19 pandemic and the war in Ukraine) is referred to as the existing state model. Its results have been validated against available historical data on road, rail, and air transport. High measures of fit between the model’s calculated values and actual data indicate that the model accurately reflects reality. 

Thus, the results of the PMT calculations for future time horizons can be considered a reliable source of traffic forecasts for transport analyses, enabling the assessment of the effectiveness of planned investments. 

Regarding the railway network model in the PMT, detailed parameters of the existing railway infrastructure (both lines and interchange nodes) and assumptions for forecast horizons, such as permissible speed, number of tracks, and electrification, have been reflected. The locations of existing and planned passenger service points, along with the planned implementation years for each investment, have been precisely mapped. The PMT also incorporates a dedicated algorithm that, based on detailed dynamic parameters of the rolling stock assigned to train routes and the assumed speed, estimates train travel times across the railway network for different time horizons. 

The PMT also includes air transport infrastructure, such as the planned airport between Warsaw and Łódź, new railway lines, and roads scheduled for implementation in the coming years. Forecasted road traffic has been distributed across the planned network for the year 2050, according to the Government’s National Roads Construction Program and assumptions for road network development for further time horizons. 

By forecasting the number of passengers not only on railway lines and stations but also across individual transport lines, the PMT is a fundamental tool in the development of the Horizontal Timetable. It enables the determination of train route structures, as well as the frequency and number of trains required to meet the forecasted demand for transport services. 

Rules for the Dissemination of the CPK Passenger Transport Model  

 CPK provides free access to: 

• A technical report detailing the model’s content and construction method 

• The Passenger Transport Model along with procedures, inputs and outputs 

The model can be used by interested institutions such as local government units, professional entities (consulting and design firms), train operators, or transport authorities for planning purposes. Integrating the railway conditions specified in the PMT into planning activities will facilitate a more cohesive and effective development of the transport system, ensuring that all stakeholders work with reliable and comparable assumptions. 

 Access to the Passenger Transport Model requires only a licensing agreement with CPK.  

 Detailed information about accessing the PMT is available on the CPK website: https://www.cpk.pl/en/pmt.