Multimodal Mobility Modelling: Concept, Methods, and Practical Workflow

1. Motivation: Why Multimodal Mobility Modelling Matters

Urban mobility is no longer well represented by a single dominant mode. A real trip may combine walking, cycling, bus, rail, car, bike-share, scooter-share, ride-hailing, park-and-ride, or a Mobility-as-a-Service platform. Multimodal mobility modelling helps planners understand these combinations and evaluate how policies reshape the whole system.

The motivation is practical. Cities need to reduce congestion, emissions, inequality, and travel time while improving accessibility, reliability, safety, and service quality. A model that treats public transport, cars, walking, and shared mobility separately can miss important interactions such as first-mile access, transfer penalties, parking constraints, crowding, and mode substitution.

Simple definition: Multimodal mobility modelling is the representation and analysis of travel behaviour, transport supply, network interactions, and policy impacts across multiple connected transport modes.

Why this matters

Integrated planning: infrastructure and services are evaluated as one connected mobility ecosystem.
Better accessibility analysis: the model can estimate who can reach jobs, schools, healthcare, and services using realistic mode chains.
Policy evaluation: planners can test fare integration, bus priority, bike corridors, parking pricing, or low-emission zones.
Operational insight: models can reveal transfer bottlenecks, crowding, unreliable connections, and fleet shortages.
Equity and sustainability: impacts can be disaggregated by neighbourhood, income, age, gender, disability, and car ownership.

2. Basic Concept of Multimodal Mobility Modelling

A multimodal model represents both demand and supply. Demand describes who travels, where, when, why, and by which mode or mode-chain. Supply describes the transport system available to them: roads, walking links, cycling links, transit schedules, stops, stations, shared vehicles, fares, parking, and service constraints.

People → Activities → Mode chains → Networks → Decisions

Element	Meaning	Role in multimodal modelling
Traveller	An individual, household, or synthetic agent with needs and constraints.	Represents heterogeneity in income, age, car ownership, preferences, and accessibility needs.
Activity	A reason to travel, such as work, education, shopping, healthcare, or leisure.	Explains why trips occur and how trips are chained into daily schedules.
Mode	A transport option such as walking, bicycle, bus, metro, car, scooter, or ride-hailing.	Forms the alternatives from which travellers choose.
Mode chain	A sequence of modes used in one journey.	Captures first-mile, last-mile, access, egress, and transfer behaviour.
Network layer	A graph representing one mode or service.	Allows multimodal systems to be represented as interconnected multilayer networks.
Scenario	A policy, service, infrastructure, or pricing change.	Used to compare future alternatives against a baseline.

Single-mode versus multimodal view

A single-mode model may estimate car traffic or transit ridership independently. A multimodal model asks how users substitute or combine modes. For example, a new rail line may change walking access patterns, bus transfers, parking demand, bike-share use, and car congestion at the same time.

The key intuition is that multimodal mobility is not only about having many modes. It is about modelling the connections, substitutions, constraints, and behavioural choices among those modes.

3. Mathematical View

Multimodal mobility models can be expressed as a combination of demand, supply, behavioural choice, assignment, and performance indicators. The mathematics does not need to be complicated at first; the important point is to define clearly what is being counted, where it occurs, when it occurs, and through which mode or mode-chain.

3.1 Multimodal travel demand

A compact way to represent multimodal travel demand is to define trips by origin, destination, mode-chain, and time period.

Tᵐ,ᵗᵢⱼ = number of trips from origin i to destination j using mode-chain m during time period t

Symbol	Name	Meaning in mobility modelling
Tᵐ,ᵗᵢⱼ	Multimodal demand	Number of trips from origin i to destination j using mode or mode-chain m during time period t.
i	Origin	Starting zone, stop, station, neighbourhood, grid cell, or coordinate of a trip.
j	Destination	Ending zone, stop, station, neighbourhood, grid cell, or coordinate of a trip.
m	Mode or mode-chain	A single mode such as car or metro, or a sequence such as walk + bus + walk, bike + rail, or car + park-and-ride + metro.
t	Time period	Time interval of analysis, such as morning peak, off-peak, evening peak, one hour, fifteen minutes, or one simulation step.
I, J	Sets of origins and destinations	The spatial units used in the model. Often origins and destinations come from the same zoning system.
M	Set of modes or mode-chains	The available mobility alternatives considered in the model.
τ	Set of time periods	The temporal resolution of the model.

In a simple model, m may be only car, transit, walk, and bike. In a richer model, m may represent complete mode chains such as walk → tram → metro → walk.

3.2 Total demand, mode share, and OD aggregation

Once demand is indexed by mode and time, useful summary indicators can be derived by summing across dimensions.

Total OD demand: Tᵗᵢⱼ = Σₘ Tᵐ,ᵗᵢⱼ

Total demand by mode: Tₘ = Σᵢ Σⱼ Σₜ Tᵐ,ᵗᵢⱼ

Mode share: Sₘ = Tₘ / Σₘ Tₘ

Symbol	Meaning
Σ	Summation operator. For example, Σₘ means summing over all modes or mode-chains.
Tᵗᵢⱼ	Total number of trips from origin i to destination j during time period t, across all modes.
Tₘ	Total number of trips made by mode or mode-chain m across all origins, destinations, and time periods.
Sₘ	Mode share of mode m. It is the fraction of all trips made using that mode or mode-chain.

3.3 Multimodal network representation

The supply side can be represented as a graph. In a multimodal model, the graph is often multilayer: each transport mode has its own layer, and transfer links connect layers.

G = (V, E, L)

where V = nodes, E = links, and L = mode layers

Walk layer ↔ Bus layer ↔ Rail layer ↔ Bike-share layer

Symbol	Name	Meaning
G	Transport graph	Mathematical representation of the mobility system.
V	Nodes	Intersections, stops, stations, zones, parking areas, bike-share stations, or virtual pickup points.
E	Edges or links	Road segments, walking links, cycling links, transit connections, transfer links, or service links.
L	Layers	Mode-specific network layers, such as walking, cycling, road, bus, metro, rail, or shared mobility.
e	Single link	One connection in the network, such as one road segment or one walking transfer link.
v	Single node	One point in the network, such as one stop, station, intersection, or zone centroid.

3.4 Link attributes and service constraints

Each network link has attributes that affect travel choices and system performance. In multimodal modelling, attributes differ by mode: a road link has congestion and speed; a transit link has schedule, headway, crowding, and capacity; a walking link may have slope, safety, or accessibility constraints.

aₑ = {timeₑ, costₑ, capacityₑ, reliabilityₑ, comfortₑ, accessibilityₑ}

Symbol	Meaning	Example
aₑ	Attribute vector of link e.	All measurable characteristics of a road, path, transit segment, or transfer link.
timeₑ	Travel time on link e.	Five minutes on a bus segment or two minutes on a walking connection.
costₑ	Monetary cost associated with link e.	Fare, toll, parking cost, bike-share unlock fee, or ride-hailing price component.
capacityₑ	Maximum flow or service capacity of link e.	Road capacity, vehicle seats, bike-lane capacity, or maximum station throughput.
reliabilityₑ	Variability or uncertainty of travel time or service availability.	Bus delay variability, traffic congestion variability, or probability that a shared bike is available.
comfortₑ	Perceived comfort or inconvenience.	Crowding, pavement quality, shelter, seating, noise, or weather exposure.
accessibilityₑ	Physical accessibility of the link.	Step-free access, slope, curb ramps, elevators, or barrier-free transfer paths.

3.5 Generalised cost

Travellers rarely choose using travel time alone. A common idea is generalised cost, where different burdens are combined into one comparable measure. The coefficients express how strongly travellers dislike each component.

Cₙ,ₘ = β₁ · IVTₙ,ₘ + β₂ · WTₙ,ₘ + β₃ · WAITₙ,ₘ + β₄ · FAREₙ,ₘ + β₅ · TRₙ,ₘ + β₆ · CRₙ,ₘ + β₇ · RELₙ,ₘ

Symbol	Name	Meaning
Cₙ,ₘ	Generalised cost	Total perceived cost for traveller n when using mode or mode-chain m.
n	Traveller or agent	An individual person, household member, or synthetic agent in the model.
IVTₙ,ₘ	In-vehicle time	Time spent inside a vehicle, such as bus, rail, car, ride-hailing vehicle, or tram.
WTₙ,ₘ	Walking time	Time spent walking to, from, or between modes.
WAITₙ,ₘ	Waiting time	Time spent waiting for a bus, train, ride-hailing vehicle, shared vehicle, or connection.
FAREₙ,ₘ	Monetary cost	Fare, toll, parking charge, subscription price, shared-mobility fee, or ride-hailing price.
TRₙ,ₘ	Transfer penalty	Extra perceived burden from changing vehicles, modes, platforms, or services.
CRₙ,ₘ	Crowding or comfort penalty	Disutility caused by crowding, lack of seats, unsafe conditions, weather exposure, or discomfort.
RELₙ,ₘ	Reliability penalty	Penalty for uncertain travel time, missed connections, service disruption, or vehicle unavailability.
β₁ ... β₇	Behavioural coefficients	Weights showing how strongly each component affects perceived cost. These are usually estimated from data.

The coefficients can vary across population groups. For example, low-income travellers may be more sensitive to fare, while people with limited mobility may be more sensitive to walking time, transfers, and step-free access.

3.6 Utility and mode-choice probability

Many behavioural models use the idea of utility. A traveller is assumed to prefer the alternative with higher utility. Since real behaviour is uncertain, the model estimates probabilities rather than deterministic choices.

Uₙ,ₘ = Vₙ,ₘ + εₙ,ₘ

Vₙ,ₘ = αₘ − Cₙ,ₘ + γ · Xₙ + δ · Zₘ

Pₙ,ₘ = exp(Vₙ,ₘ) / Σₖ exp(Vₙ,ₖ)

Symbol	Name	Meaning
Uₙ,ₘ	Total utility	Overall utility that traveller n receives from alternative m.
Vₙ,ₘ	Observed utility	Part of utility explained by measured variables, such as time, cost, income, car ownership, and service attributes.
εₙ,ₘ	Random error	Unobserved factors affecting choice, such as mood, habit, personal preference, weather perception, or incomplete information.
αₘ	Alternative-specific constant	Baseline preference for mode m not explained by measured variables.
Xₙ	Traveller characteristics	Attributes of person n, such as income, age, gender, disability, household size, or car ownership.
Zₘ	Mode or service attributes	Attributes of alternative m, such as frequency, payment integration, comfort, reliability, or station quality.
γ, δ	Estimated parameters	Weights showing how traveller characteristics and service attributes affect utility.
Pₙ,ₘ	Choice probability	Probability that traveller n chooses mode or mode-chain m.
k	Alternative index	Used in the denominator to sum over all available alternatives.

3.7 Assignment and network loading

After demand and choices are estimated, trips must be assigned to routes and services. Assignment determines how many travellers use each road link, transit line, transfer, bike facility, or shared-mobility service.

xₑ,ᵗ = Σᵢ Σⱼ Σₘ Σᵣ Tᵐ,ᵗᵢⱼ · pᵐ,ᵗᵢⱼᵣ · 𝟙(e ∈ r)

Symbol	Name	Meaning
xₑ,ᵗ	Link flow	Number of travellers or vehicles using link e during time period t.
r	Route	A path through the network, possibly including several modes and transfers.
pᵐ,ᵗᵢⱼᵣ	Route choice probability	Probability that a trip from i to j using mode-chain m during t chooses route r.
𝟙(e ∈ r)	Indicator function	Equals 1 if link e is part of route r, and 0 otherwise.
xₑ,ᵗ / capacityₑ	Volume-to-capacity ratio	Used to detect congestion, crowding, bottlenecks, and overloaded services.

3.8 Accessibility indicator

Accessibility is one of the most important decision indicators. It measures how many opportunities can be reached from a place within a given cost, time, or utility threshold.

Aᵐᵢ = Σⱼ Oⱼ · f(Cᵐᵢⱼ)

Example threshold form: Aᵐᵢ = Σⱼ Oⱼ · 𝟙(Cᵐᵢⱼ ≤ θ)

Symbol	Name	Meaning
Aᵐᵢ	Accessibility of origin i by mode m	Number or weighted value of opportunities reachable from origin i using mode or mode-chain m.
Oⱼ	Opportunities at destination j	Jobs, schools, hospitals, shops, services, people, or other destinations of interest.
Cᵐᵢⱼ	Generalised cost from i to j	Travel time, perceived cost, or utility-based impedance between origin i and destination j by mode m.
f(Cᵐᵢⱼ)	Impedance or decay function	Function that gives less weight to opportunities that are harder to reach.
θ	Threshold	Maximum acceptable travel time or generalised cost, such as 30 minutes by transit.

Key interpretation: The mathematical core of multimodal mobility modelling is not one equation. It is a connected structure: demand tells us how many trips exist, the network tells us which alternatives exist, generalised cost and utility explain choices, assignment loads trips onto the system, and accessibility translates model results into decision evidence.

4. Data Sources for Multimodal Mobility Models

Modern multimodal mobility modelling depends on data fusion. Traditional surveys remain essential because they explain purpose and demographics, while passive and operational data provide larger-scale movement and service observations.

Data source	What it contributes	Main limitation
Household travel surveys	Trip purpose, demographics, attitudes, income, car ownership, mode choice, and value of time.	Small samples, high cost, infrequent updates, and recall bias.
Census and land use	Population synthesis, employment, schools, services, land-use intensity, and equity analysis.	Often static, spatially coarse, and updated slowly.
GTFS and transit schedules	Routes, stops, frequencies, planned timetables, transfers, and public transport accessibility.	Scheduled service may differ from real vehicle operations.
Smart card / AFC data	Boardings, regular users, transfer inference, public transport demand, and OD estimation.	Often missing alighting, purpose, demographics, and non-transit access modes.
AVL / GPS traces	Observed vehicle location, speeds, travel-time reliability, delays, and route performance.	Requires map matching, cleaning, and integration with schedules.
Mobile phone and app traces	Large-scale OD patterns, trajectories, mode detection, and temporal rhythms.	Privacy risk, sampling bias, spatial uncertainty, and limited trip purpose information.
Shared mobility feeds	Bike-share, scooter-share, ride-hailing, car-share, station availability, and fleet usage.	Operator-specific access, inconsistent standards, and incomplete user attributes.

Data fusion principle

No single source is sufficient. Surveys explain why people travel, passive traces show where and when they move, operational data show how the system performs, and network data describe what alternatives are available.

5. Practical Data-to-Decision Pipeline

A strong multimodal model should begin with a decision problem, then build the data, behavioural, and simulation components needed to answer that problem.

Question → Data → Demand → Supply → Simulation → Decision

Step	Purpose	Practical outputs
1. Frame the decision	Define the policy, investment, or operational question.	KPI list, baseline, scenarios, stakeholders, spatial and temporal scope.
2. Build the supply model	Represent roads, transit, walking, cycling, transfers, parking, and shared fleets.	Multilayer network, schedules, fares, capacities, service areas.
3. Infer demand	Estimate trips, OD flows, activity patterns, mode chains, and time-of-day demand.	OD matrices, synthetic population, trip tables, activity schedules.
4. Estimate behaviour	Model how users choose modes, routes, departure times, and services.	Choice parameters, utility functions, transfer penalties, willingness-to-pay.
5. Calibrate and validate	Check that the model matches independent observations.	Mode share checks, link counts, boardings, alightings, travel times, trip lengths.
6. Simulate scenarios	Test infrastructure, service, pricing, fleet, or platform alternatives.	Scenario comparison, sensitivity analysis, uncertainty ranges.
7. Translate to decisions	Convert technical outputs into planning evidence.	Maps, trade-off tables, equity diagnostics, investment recommendations.

Practical rule: Do not let data availability define the decision. Start with the decision question, then decide which data and modelling depth are necessary.

6. Main Modelling Families

The literature contains several modelling traditions. Each family is useful for different decisions, scales, and data environments.

Four-step and OD-based models

Traditional planning models estimate trip generation, trip distribution, mode choice, and network assignment. They are transparent and widely used, but less flexible for trip chaining and dynamic behaviour.

Strategic planning OD matrices Assignment

Discrete-choice models

Behavioural models estimate how travellers choose between alternatives using time, cost, comfort, transfers, reliability, and personal characteristics.

Logit Mixed logit Latent class

Activity-based models

Travel is derived from daily activity schedules. These models better represent trip chains, household constraints, timing, and purpose.

Activities Tours Daily plans

Agent-based simulation

Synthetic individuals interact with dynamic networks. This supports detailed scenario testing, congestion feedback, and heterogeneous behaviour.

MATSim Agents Dynamic networks

Multilayer network models

Modes are represented as layers in a connected graph. This supports connectivity, resilience, accessibility, transfer, and robustness analysis.

Layers Graph theory Accessibility

Machine learning and graph learning

ML models predict demand, speeds, ridership, mode, and anomalies. Graph neural networks are especially useful for spatial-temporal transport data.

GNN Forecasting Prediction

How to choose a method

Decision need	Suitable modelling approach	Reason
Long-term infrastructure planning	Four-step, activity-based, or agent-based model	Captures future demand, land-use scenarios, and large-scale network effects.
Transit OD estimation	Smart-card OD inference and transit assignment	Uses AFC, AVL, schedules, and transfer rules to infer flows.
Mode-shift analysis	Discrete-choice or agent-based model	Represents behavioural sensitivity to cost, time, reliability, and service quality.
Operational forecasting	Machine learning, time-series, or graph neural networks	Useful for short-term ridership, traffic, or shared-fleet prediction.
Network resilience and accessibility	Multilayer network analysis	Represents interdependence between mode layers and transfer points.

7. MaaS and Modern Extensions

Mobility-as-a-Service extends multimodal modelling by adding digital platforms, integrated payment, subscription bundles, real-time information, and coordination among multiple operators.

Where MaaS fits

Transit Bike-share Scooter Ride-hailing → MaaS Platform → User choice

In MaaS modelling, the object is not only the transport network. The model may also represent digital search, booking, payment, bundles, subscription plans, real-time availability, operator incentives, and platform governance.

Extension	What changes in the model?	Practical issue
Fare integration	Users compare bundles, subscriptions, discounts, and transfer pricing.	Requires modelling willingness-to-pay and revenue impacts.
Real-time availability	Shared vehicles and services may or may not be available at the decision moment.	Requires dynamic supply and fleet-position modelling.
Platform choice	Users choose not only a mode but also a planning and payment interface.	Requires adoption models and digital-inclusion analysis.
Operator economics	The model includes costs, revenues, subsidies, and settlement among providers.	Often under-modelled compared with user demand.
Privacy governance	User identity, payment, location, and trip history may be combined.	Requires privacy-by-design, aggregation, consent, and secure data sharing.

How to position MaaS in a literature review: MaaS is a modern extension of multimodal modelling where behavioural choice, digital platforms, integrated services, and institutional governance are modelled together.

8. Applications of Multimodal Mobility Modelling

Multimodal models are used in strategic planning, tactical service design, real-time operations, and policy evaluation. Their value is strongest when a decision affects several modes at once.

Application area	Why multimodal modelling is useful	Example use
Public transport planning	Captures access, egress, transfers, crowding, and competition with other modes.	Testing a bus network redesign or new rail extension.
Active mobility	Shows how walking and cycling connect to transit and local destinations.	Evaluating a cycling corridor or pedestrian-access improvement.
Shared mobility	Represents fleet availability, first-mile and last-mile service, and mode substitution.	Determining bike-share station locations or scooter service areas.
Climate policy	Estimates shifts in vehicle kilometres, emissions, energy use, and active travel.	Testing low-emission zones, parking pricing, or car-use restrictions.
Equity and accessibility	Measures who benefits and who loses across income, age, disability, and neighbourhoods.	Mapping access to jobs or healthcare by transit, walking, and cycling.
Mobility hubs	Models how users transfer between transit, cycling, shared mobility, and walking.	Choosing hub locations and evaluating transfer quality.
Real-time operations	Supports short-term forecasting, disruption management, and dynamic service control.	Predicting crowding, rerouting services, or rebalancing shared fleets.

9. Challenges and Research Gaps

Although multimodal mobility modelling is powerful, it is difficult to implement well. The main challenges involve data bias, behavioural realism, model validation, privacy, and decision communication.

Data representativeness

Mobile, smart-card, and app data may underrepresent children, older adults, low-income groups, cash users, tourists, and people without smartphones.

Missing purpose and demographics

Passive traces show movement but often not trip purpose, income, disability status, household constraints, or subjective preferences.

Mode-chain complexity

Access, egress, waiting, transfers, missed connections, bike parking, crowding, fares, and vehicle availability strongly affect real choices.

Calibration and validation

A model can match total trips while failing on route flows, boardings, travel times, transfers, or neighbourhood-level impacts.

Transferability

Models calibrated in one city may not transfer to another because land use, weather, culture, fares, parking, and safety perceptions differ.

Supply-side realism

Many models are rich on demand but weak on operator costs, fleet constraints, profitability, reliability, and platform governance.

Privacy and governance

Fine-grained mobility traces can reveal home, work, habits, social patterns, and sensitive routines.

Explainability

Black-box forecasting can be accurate but hard to justify in public planning unless paired with interpretable diagnostics.

Important open questions

How can passive mobility data be corrected for demographic and spatial bias?
How should models represent first-mile and last-mile behaviour without excessive complexity?
How can behavioural choice models and machine-learning models be combined transparently?
How should MaaS models represent both user adoption and operator/platform economics?
Can multimodal models preserve privacy while still supporting high-resolution planning?
How can uncertainty and equity impacts be communicated clearly to decision-makers?

10. Conclusion

Multimodal mobility modelling is best understood as a framework for representing how people move through a connected system of modes, services, infrastructure, and digital platforms. The classical planning view focuses on OD demand and assignment, while modern approaches add activity-based behaviour, agent-based simulation, multilayer networks, passive data, graph learning, and MaaS.

The strongest explanation structure is therefore: motivation → basic concept → mathematical view → data sources → data-to-decision workflow → modelling families → MaaS extensions → applications → challenges.

The future of the field is not only about better prediction. It is about models that are behaviourally credible, privacy-preserving, equity-aware, operationally realistic, and useful for real planning decisions.

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