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.

In this section, you will learn: 

• Why is an economic evaluation of rail services conducted? 

• How was the commercial potential of rail services verified? 

The main purpose of the economic evaluation is to categorize rail routes into those requiring subsidies from the transport authority and those that can operate fully commercially without financial support. These results are a critical output of the project and will be shared with potential train operators during the market consultation phase. Additionally, the evaluation will help determine the level of compensation for services expected to be launched under a Public Service Contract (PSC). Data for the economic evaluation of rail services are sourced from the Passenger Transport Model. 

1. Basic Indicators 

a) Number of Passengers

In transport, passengers as a unit of measure represent the number of people traveling on a specific train route (from origin to destination) within a given time period (e.g., daily or annually) without making transfers. 

b) Transport performance or Revenue Passenger Kilometers (RPK) 

Revenue Passenger Kilometers (RPK) is a key metric in passenger transport, calculated as the total distance traveled by all revenue-generating passengers. This measurement can be reported for a single train or across the entire network. 

c) Operational performance or Train–Kilometers

Operational work is a key metric in rail services, often measured in train-kilometers or vehicle-kilometers, indicating the total extent of operational activities. 

2. Supply-Related Indicators 

a) Number of Seats

The number of seats is a measure of supply capacity, representing the total seating available for sale on a single train, across an entire route, or throughout the rail network. 

b) Available Seat Kilometers (ASK) 

Available Seat Kilometres (ASK) is the product of the number of seats in a train and the distance travelled by that train. It is a basic efficiency metric in both rail and air transport and is often presented in relation to the total supply, whether it be a specific route or the entire network. 

c) Seat Factor (SF) and Load Factor (LF)

Seat occupancy can be measured in two ways. The first is the Seat Factor (SF), which is the ratio of the number of passengers travelling on a specific section to the total number of seats available. However, this measure is not very representative since a seat may be used more than once on a single journey. To obtain a more objective measure of the relationship between demand and supply, the Load Factor (LF) is used. The Load Factor is the ratio of Revenue Passenger Kilometres (RPK) to Available Seat Kilometres (ASK). 

d) Average Number of Passengers per Train 

This is the average number of passengers on a train. It is calculated by dividing the total Revenue Passenger Kilometres (RPK) by the total kilometres travelled by the train (RPK/train kilometres). This metric can be presented for a single train or across the entire network. 

3. Cost-Related Indicators 

a) Train Operating Cost

The cost of operating a train is the product of the cost per train kilometre and the number of train kilometres operated within a specified period. This cost has been calculated for each planned train route. 

b) Cost per Available Seat Kilometer (CASK) and Revenue per Available Seat Kilometer (RASK) 

The Cost per Available Seat Kilometre (CASK) is a key economic cost indicator. It is calculated by dividing the cost of operating a train by the number of available seat kilometres for that train, train route, or all services offered by a train operator. In subsequent stages of the Horizontal Timetable project, this indicator will be compared with the Revenue per Available Seat Kilometre (RASK) to assess the profitability of an entire route or a specific train on a route. 

c) Yield

Average amount of revenue generated per paying passenger who travelled one kilometre. Calculated as passenger revenue/RPK. 

d) Minimum Ticket Price (Break-Even Price) 

The minimum ticket price is calculated by dividing the train operating cost by the number of passengers carried. This gives a hypothetical average ticket price that each passenger would need to pay to cover the costs. Although a lower price is preferable, this measure is not always entirely objective. From a passenger’s perspective, shorter routes may inherently require cheaper tickets due to the reduced distance and travel time. However, from an operational standpoint, shorter routes can still incur significant costs. Pricing strategies must consider various factors beyond route length, such as operational costs, demand, and competitive pricing. Therefore, while lower prices for shorter routes are generally expected and preferable for passengers, they do not always reflect the full economic picture for train operators. 

e) Cost per Kilometer

One way to address the issue above is to introduce a cost per kilometre indicator, which is the ratio of the break-even price to the length of the train route. Similar to the previous indicator, a lower value is preferable. However, this indicator may be significantly understated for very long-distance routes. 

f) Cost Efficiency 

Cost efficiency is the ratio of the minimum ticket price to the average number of passengers per train. This indicator provides an estimate of profitability—the lower the value, the higher the likelihood of covering costs. 

In this section you will learn:

• What is the role of the Integrated Traffic Model in the Horizontal Timetable Project?

• What is the Integrated Traffic Model and what is its structure?

• How are forecasts performed in the Integrated Traffic Model?

• What are the rules for accessing the Integrated Traffic Model?

Integrated Traffic Model in the Horizontal Timetable Project

The fundamental conceptual and analytical work on timetables is conducted in the CPK Passenger Transport Model (PMT). The Integrated Traffic Model in the Horizontal Timetable project is used to evaluate (verify) railway timetables and ensure consistency with strategic planning regarding transport infrastructure. Timetables iteratively developed in Passenger Transport Model are imported into the Integrated Traffic Model to verify service assumptions and assess the consistency of results between models.

How the Integrated Traffic Model is Constructed 

The Integrated Traffic Model is a strategic planning support tool and a crucial element in fulfilling the European Commission’s basic condition for the 2021-2027 Programming Period, under which Poland plans to secure funds for further transport infrastructure development.

It is a model built, maintained, and developed by the Centre for EU Transport Projects (CUPT) that provides comprehensive support to Polish EU fund beneficiaries in the preparation and implementation of transport investment projects. CUPT plays a vital role in ensuring that Poland’s transport infrastructure aligns with European Union standards and requirements. By leveraging this model, Poland can strategically plan and execute projects that enhance connectivity and efficiency.

The Integrated Traffic Model is a multimodal passenger model that reflects the Annual Average Daily Traffic between all municipalities in Poland, divided into individual and public transport, which includes railway and bus lines. During the computation process, the mutual interaction of competing modes of transport is considered. This is a key factor from the perspective of traffic forecasting, as it allows for parallel consideration of road and railway investments. By accurately modelling these interactions, the Integrated Traffic Model aids in making informed decisions that optimise the balance between different transport modes, ultimately enhancing the efficiency and effectiveness of Poland’s transport network.

In the mutual interaction of different modes of transport, key aspects that influence travelers include:

• Travel distance

• Travel time

• Monetary costs incurred

The model serves as a tool particularly for:

• Supporting decisions on strategic programmes and their optimisation

• Reflecting the passenger perspective and responses to the current state of transport networks

• Analysing passenger traffic results on the forecast network

• Testing scenarios for network development and socio-demographic changes

The Integrated Traffic Model Structure 

 The Integrated Traffic Model consists of a supply layer and a demand layer.

The supply layer includes the road network and railway network along with the public transport network, i.e., public transport stops, railway and bus lines, and the sequence of stops and travel times between them. In the Integrated Traffic Model, the public transport network is based on the frequency of service rather than exact departure times from stops, using the average interval between services. This approach simplifies implementing changes and planning new connections in the future.

The road network reflects roads in Poland – from motorways and expressways to national, regional, county, and municipal roads. Road sections are described by class, manager, cross-sections, and, most importantly, speed under free-flow conditions. Similarly, the railway network reflects the railway lines in Poland. Sections are parameterised by maximum transit speeds. Planned railway sections are also encoded according to strategic plans, described by name, year of completion, and the maximum speed achievable on that section. The railway network in the Integrated Traffic Model is imported directly from the CPK Passenger Transport Model.

Public transport lines encoded on road and railway sections include local buses, long-distance buses, long-distance railways, and regional railways.

 The model specifies 2,875 traffic analysis zones such as:

• Municipalities, with selected cities additionally divided

• Point zones:

• • Airports

• • Seaports

• • Intermodal terminals

• • Border crossings

Traffic analysis zones are described by explanatory variables such as:

• Population (pre-working, working, post-working)

• Number of jobs (trade and services, other sectors)

• Number of school and university places

• Number of accommodation facilities

• Number of households

• Vehicle ownership rate

The population figures, both for the base year and forecast years, include migrants, who constitute a significant proportion of the population in Poland and consequently impact the transport network.

The demand model reflects travel demand within Poland on an average day of the year. Using appropriate assumptions for mathematical formulas, it can represent the number of trips and point-to-point relations divided by available means of transport. A key element of the demand model is mobility indicators, which determine the average daily number of trips per person.

The demand model is built on a four-stage approach, dividing the decision-making process about travel into four stages:

• Trip Generation – The need to undertake a trip

• Trip Distribution – Choice of destination and trip purpose

• Mode Choice – Choice of mode of transport

• Route Assignment – Choice of travel route

Forecasts in the Integrated Traffic Model 

In forecasting models, transport behaviours are transferred and calibrated based on the base model. This approach allows for demonstrating responses to supply changes and socio-demographic changes, such as an ageing population.

These forecasts enable the analysis and planning of new investment options and the strategic development of the country’s transport infrastructure.

The Integrated Traffic Model forecasting models are primarily developed for the years 2030, 2040, and 2050 and are designed to answer “What if?” questions. It is also possible to generate a forecast scenario for any given year and transport network development assumptions. Below is an example of such a question in the context of railway transport.

The results of the Integrated Traffic Model are illustrated in the figure below, showing traffic intensity for the years 2023 and 2050, divided by vehicle categories.

Rules for Accessing the Integrated Traffic Model 

The Integrated Traffic Model was developed with public funds, including EU co-financing. Both the base model for 2023 and the forecasting models for 2030, 2040, and 2050, along with the technical report, are available free of charge to interested parties under a licensing agreement. More information about the Integrated Traffic Model can be found on the website: www.cupt.gov.pl/centrum-unijnych-projektow-transportowych/zintegrowany-model-ruchu/.

In this section, you will learn: 

• What is the Railway Microsimulation Model? 
• What types of analyses can be performed using the Railway Microsimulation Model? 

Railway Microsimulation Model (KMM – Kolejowy Model Mikrosymulacyjny)

The Railway Microsimulation Model is an advanced digital tool that provides a detailed representation of railway traffic. Its role is to support decision-making processes related to railway operations. The model is used for analysing railway traffic while accounting for factors affecting train movement, distinguishing it from other analytical tools used within the Horizontal Timetable Project. 

The Model has been developed by Centralny Port Komunikacyjny sp. z o.o. (CPK) and PKP Polskie Linie Kolejowe S.A. (PLK S.A.). Within the Horizontal Timetable framework, the model refines timetable assumptions initially generated using the Passenger Transport Model. It enables detailed verification of timetables, including checking for conflicts in traffic, assessing infrastructure usage and capacity, and analysing resilience to operational disruptions. The result is a timetable that, thanks to comprehensive validation using simulation methods, is free from flaws that could hinder or prevent its practical implementation. 

When developing a timetable, special attention must be paid to railway nodes, which often act as “bottlenecks” due to increased train traffic and the convergence of routes from various directions. In the current phase of work (Q2 2024), the model simulates the largest railway nodes in Poland. This allows for coordinated timetable development, considering constraints in the node areas that may be undetectable in the macroscopic Passenger Transport Model. In the next phase, the model will cover key network sections planned for long-distance passenger and freight trains. Ultimately, the Railway Microscopic Model will encompass the entire Polish railway network, becoming its digital twin. As new versions of the Horizontal Timetable are developed, the Railway Microscopic Model will be continuously updated to reflect infrastructure parameters and model newly planned sections. 

Model Structure 

The Railway Microsimulation Model consists of two main, closely related layers: 

• Infrastructure Layer 

• Timetable and Analytical Layer 

The Infrastructure Layer is a detailed digital representation of railway infrastructure for traffic simulation areas. It includes railway tracks with parameters like maximum speeds, geometric layout, and electrification type. It also models station track layouts and signal control posts, detailing every track, switch, platform, and signal. Crucially, it defines logical dependencies between infrastructure elements, setting rules for railway traffic control, such as signalling device operation times. 

The Timetable and Analytical Layer applies the train timetable to the railway network represented in the Infrastructure Layer. Real-world characteristics of railway rolling stock are also necessary for constructing the timetable. Using these elements and train movement equations, travel times for individual trains are calculated, including necessary technological reserves. Notably, multiple independent timetable versions can be created from a single infrastructure layer scenario. 

The Railway Microsimulation Model as an Analytical Tool 

The Railway Microsimulation Model enables several types of analyses to verify a proposed timetable. 

1. Designing of Timetables
   

The primary analysis involves attempting to create a timetable on the simulated railway network. This analysis verifies whether the infrastructure can accommodate the planned railway traffic, aiming to generate a conflict-free time-distance graph between train routes. 

2. Examination of Capacity Utilisation
    

This analysis examines capacity utilisation by densifying train schedules. It involves filling empty spaces in the time-distance graph with additional trains while maintaining necessary reserves and traffic logic. The goal is to determine how many additional trains the infrastructure can handle while ensuring smooth traffic and required resilience to timetable disruptions. 

3. Examination of Capacity Utilisation of Individual Infrastructure Elements 

This analysis identifies the degree of utilisation of individual infrastructure elements, highlighting those most burdened by train traffic within the analysed timetable. This information is crucial for operational decisions, such as routing trains around nodes and assigning platform edges at stations. It also helps identify critical elements that may cause secondary delays if disruptions occur. Pinpointing these critical points supports the development of comprehensive infrastructure solutions to address these issues. 

4. Simulation of Delays 

A unique feature of the Railway Microsimulation Model (KMM) is its ability to simulate timetable scenarios under “emergency situations.” It uses random delay distributions and nondeterministic simulations by varying delay input parameters to track the propagation or dampening of delays over time, assessing whether initially planned train routes are maintained. Minor delays simulate small incidents, like door issues, while larger delays test the timetable under significant disruptions, such as track closures. This allows for real-world scenario simulation, helping to minimise negative impacts before actual implementation.