MT-ITS keynote on active mode modelling
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The document discusses the significance of active modes of transportation, such as cycling and walking, emphasizing their complexity, societal relevance, and the scientific challenges involved in modeling and optimizing these modes. Key findings include the higher capacity of bicycle flows compared to car flows and the negative correlation between bike ownership and BMI. Additionally, it proposes the use of game-theoretical approaches to enhance understanding and control of pedestrian and cycling behaviors in urban environments.
MT-ITS keynote on active mode modelling
- 1. Prof. Dr. Ir. Serge Hoogendoorn, Delft University of Technology Active mode Traffic Science & Engineering 25 years of fascination for pedestrian and bicycle flows…
- 2. Four reasons to focus on the active modes…
- 3. Active modes are wonderfully complex and showcase unexpected dynamics
- 4. Sustainable urban mobility is impossible without active modes
- 5. There are major scientific, technological and engineering challenges to solve, including data collection
- 6. We can learn a lot from the active modes and the modelling and control thereof…
- 7. Let us take a closer look at these four themes…
- 8. Wonderfully complex phenomena in active mode traffic & transport Self-organisation, capacity drops, spontaneous break-downs
- 9. Known phenomena In pedestrian dynamics • Pedestrian flow is characterised by fascinating self-organised phenomena, including: • Bi-directional lanes, diagonal stripes in crossing flows • Freezing by heating and flow breakdowns • Faster is slower effect • Turbulence • What about bicycle flows?
- 10. Controlled experiments Most comprehensive cycling experiments performed so far providing novel microscopic and macropscopic insights Microscopic data (trajectories) for 25 different scenarios, including bottlenecks, crossings, merges, etc.
- 11. Capacity of bottlenecks Study reveals empirical relation between width w of cycle path and capacity Characteristics of self-organised staggered patterns inside bottleneck determine capacity No clear lane regime but complex interaction of longitudinal ‘following’ and lateral distance keeping *) Fact: capacity bicycle flow is ~8 times higher than a car flow! C = 1710 + 4248 ⋅ w
- 12. Bicycle capacity & drop Via our experiments we established the capacity drop for bicycle flows Once queuing occurs (e.g. at intersection), capacity reduces with 23% Finding is extremely relevant for cycling infrastructure and controller design
- 13. Relevantie onderzoek lopen en fietsen Relatie grote maatschappelijke vraagstukken Societal relevance of Active Modes Sustainable modes are essential in achieving true sustainable mobility in liveable cities
- 14. The grand societal challenges Impact on climate change (~20%) Use of scarce resources Liveability, health, safety Impacts on equity and inclusiveness Impacts on scarce space (~25%) Negative impacts of mobility are substantial
- 15. Active modes as a solution to societal issues Towards mobility that is sustainable, efficient and fair • Ecological impact of different modes shows limited impacts of active modes • This holds equally for the spatial impact • Taking a network perspective, the differences on spatial impact are even larger!
- 16. Network size scaling for different modes Linking city population to network sizes • Sub-linear growth in infrastructures size: big cities are more efficient regarding infrastructure length: networks become relatively shorter (except for metros) • Example: a city with twice as many inhabitants has on average 89% more car infrastructure and only 26% more bike paths! • Relatively limited space taken by active modes of transportation, right? Reggiani, G., et al (2022). A multi-city analysis of bicycle networks (under review)
- 17. The active modes play an essential role in making mobility more sustainable, healthier and more inclusive… As a individual mode As access or egress mode In case of transfers
- 18. Heath impacts? Back to complexity Bike ownership negatively correlated with BMI What about the e-bike? In collaboration with KIM, Mathijs de Haas Lower bicycle ownership implies higher BMI Higher e-bike ownership means higher BMI
- 19. Proposition 1: Cycling increases health True (raise hand) or false (keep hand lowered)
- 20. Causality? Using data from different MPN waves (2013-2018) and advanced statistical modelling*) reveals complexity of relations… • When someone’s BMI gets lower, they cycle more • But when people cycling more, this does not (automatically) lead to a lower BMI… *) Random Intercept Crossed-Lagged Panel Model In collaboration with KIM, Mathijs de Haas
- 21. Proposition 2: E-cycling reduces health True (raise hand) or false (keep hand lowered)
- 22. Causality? Using data from different MPN waves (2013-2018) and advanced statistical modelling*) reveals complexity of relations… • No casual effect found between the use of the e-bike and the BMI (either direction), but: • Increase in e-bike use leads to decrease bicycle use (all trip purposes) • For work trips we see that increase in e- bike use leads to decrease in car and bicycle use *) Random Intercept Crossed-Lagged Panel Model In collaboration with KIM, Mathijs de Haas
- 23. A bicycle is not a two-wheeled car… And a pedestrian is not a cyclist who lost his bike… Due to the urgency to make our societies less car-dependent and more sustainable, we are in dire need of dedicated theory, models and tools to support policy making, design, planning, and control to improve walkability and cyclability My proposition (2014): science has not yet delivered adequate tools (empirical insights, theory, models, guidelines)
- 24. ALLEGRO (2015-2020) With innovative data to a new traffic and transportation theory for pedestrians and bicycles
- 25. Prof. Dr. Frank Koppelman, somewhere in Boston in 2000 “Transportation science is a research field that is assumption rich and data poor”
- 26. Field data collection Video, WiFi / Bluetooth, Social Data Revealed preference route choice, wayfinding Incl. collaboration with MoBike, and The Student H VR and simulators Pedestrian way finding through buildings Short-run and long-run household travel dynamics MPN longitudinal survey active mode “specials”
- 27. Data collected via controlled experiements Data collected with our Intelligent Bicycle Path Stress data collected via FitBits Digitwin TU Campus
- 28. Traffic Operations Route Choice Mode and activity choice Wayfinding and exploring Control, Planning and Design tools and applications
- 29. Traffic Operations Active mode traffic operations theory and modelling
- 30. Our aim is to model the behaviour of an individual cyclist in interaction with the other cyclists…
- 31. Game-theoretical micro modelling Motivation for a game-theoretical approach Inspired by previous work (pedestrian), we looked into differential game theory (cooperative, non-cooperative) as a theoretical framework for active mode operations modelling The pedestrian model generalised established models (e.g., Social Forces model) and reproduced most relevant dynamics Framework is flexible (rules) and and has interpretable parameters
- 32. Microscopic rider modelling • Main assumption “cyclist economicus” based on principle of least effort: For all available options (accel., changing direction, do nothing) a cyclist chooses option yielding smallest predicted effort (distulity) • The predicted effort is the (weighed) sum of different effort components (e.g., risk to collide, cycling too slowly or too fast, straying from intended path, etc.) - like attributes in utility models • Rider predicts situation for various control actions
- 33. How does the ‘mental’ prediction work? • A rider p predicts how applying control u (steering , peddling / braking ) affects the dynamics of her bicycle resulting in a predicted path (location, speed, direction) for [t,t+T) • Trivial model respecting basic dynamics: ω a Approach is generic: more advanced models can be used!
- 34. How does the ‘mental’ prediction work? Path A Path B Path C Destination Shortest path Effort component examples: • Straying from shortest path • Being too close to other cyclist*) • Acceleration / braking • Not adhering to traffic rules… Possible paths result from candidate control actions; there are an infinite number of these paths possible
- 35. Next to own dynamics, the rider predicts the behaviour of the other cyclists (the ‘opponents’ in game theoretical terms) - or pedestrians, e-scooters, cars, etc.
- 36. 36 Non-cooperative strategy • Risk-neutral strategy • Cyclist assumes that other cyclists reacts the same way as her- of himself • Nash game Cooperative strategy • Risk-prone strategy • Cyclist assumes that other cyclists cooperate to reach a common objective • Cooperative game Demon opponent strategy • Risk-averse strategy • Cyclist assumes that other cyclists aim to minimise the distance between him and the cyclist • Princes-demon game Gavriilidou, A., Yuan, Y., Farah, H., Hoogendoorn, S.P., 2017. Microscopic cycling behaviour model using differential game theory. In: Proceedings of Traffic and Granular Flow 2017.
- 37. Solving the problem… • We determine the optimal path - via determining the optimal control trajectory - by assuming the rider will minimise the predicted effort (or cost), i.e.: where • Running cost reflects the different components just discussed • Computing the optimal control path? • Minimum Principle of Pontryagin results in necessary conditions • Basis for IRTA (Iterative Real-time Trajectory Optimization Algorithm) which provides efficient numerical solutions (a, ω)* [t,t+T) = argminJ(u[t,t+T)) J(u[t,t+T)) = ∫ t+T t e−ηs Lds L 37 Hoogendoorn, S., Hoogendoorn, R., Wang, M., Daamen, W., 2012. Modeling driver, driver support, and cooperative systems with dynamic optimal control. Transp. Res. Rec. 2316, 20–30.
- 38. Overtaking example • Figure shows results for overtaking interaction for 5s prediction horizon Faster cyclist Current position Predicted path [20,25) Direction
- 39. Crossing bicycle flow interactions • Note that there are no traffic rules implemented (no right of way for either direction) • Forms of self-organisations appear, and flows are efficient (limited capacity loss) • Self-organisation is affected by relative cost of braking compared to steering • Breakdown occurs for higher demand levels, and is affected by heterogeneity (freezing by heating)
- 40. Speed-density relation? 40 v0 ψ = 1 ψ = 0 • Assume cyclist riding in a single file • Equilibrium: no acceleration, equal distances d between cyclists • We can easily determine equilibrium speed for bicycle p (q > p means q is in front) • Speed-density diagram looks reasonable for positive values of anisotropy factor ψ density (Cycle/m) ρ = 1/d
- 41. Outcomes Does the model provide reasonable results? • Model behaviour is plausible, yet needs to be further validated using real data (e.g., for our controlled experiments) • Impact of behavioural strategies is plausible, data needs to reveal which strategy best represents cycling behaviour • Intuitive impact of behavioural parameters • Easy integration of traffic rules
- 42. But is this model not too complex for large scale applications?
- 43. Multi-scale modelling framework Risk- neutral Nash game Risk-prone cooperativ e game Risk- averse demon game ‘Social- forces’ model Continuum modelling Network- wide modelling MFD Simplification of behavioural assumptions Assuming equilibrium and Taylor series expansion Spatial aggregation under equilibrium
- 44. Model simplifications From micro to macroscopic modelling • Straightforward derivation of social-forces Helbing (pedestrians) / Gavriilidou (bicycles) model from Nash-game theoretical model • Subsequently, social-forces model forms the bases of continuum model, consisting of: - Conservation of pedestrian equation (trivial) - Equation for velocity (speed AND direction) can be derived from SF by careful interpretation of the density and Taylor series expansion… ⃗ v
- 45. Derivation of macroscopic model Because you are always dissappointed when there is not math… • Social-forces model as starting point: • Equilibrium relation stemming from model ( ): • Interpret density as the ‘probability’ of a pedestrian being present, which gives a macroscopic equilibrium relation (expected velocity), which equals: ai = 0
- 46. Derivation of macroscopic model Because you are always dissappointed when there is not math… • Taylor series approximation: yields a closed-form expression for equilibrium velocity , which is given by the equilibrium speed and direction: • Speed has two components: density (the denser, the lower the speed) and the density gradient (when density increases, speed is also lower) • Direction is trade-off desired dir. and dir. in which density reduces quickest ⃗ v = ⃗ e ⋅ V V ⃗ e
- 47. Macroscopic modelling results Plausible outcomes, difficult numerics • Model inherits properties from SF model (e.g., lane formation, diagonal stripes, breakdown at high demands) Bottleneck experiment SPH model Bi-direction flow experiment
- 48. 1. Monitoring Microscopic data is collected via video-based sensors, and combined with smartcard data Smart station and MPC 2. Estimation Based on data, current state is estimated and used as initial state for prediction 3. Prediction & optimisation Optimal control signal is computed, yield a 10% decrease in crowding cost
- 49. Active Mode traffic dynamics of networks Towards the pedestrian MFD • We can then derive the average flow- rate for the entire area: • Here, denotes the spatial variation of the density: • Equation shows how the MFD is a function of the spatial averaged density and the spatial variation q σ2 Area *) Illustration only: we consider walking pedestrians Ω Ωi ρi
- 50. Active Mode traffic dynamics of networks Towards the pedestrian MFD • Let us simplify our model even further by assuming no influence of the density gradient on the speed (i.e., ): • Note: this is exactly the Greenshields FD with • Let us now consider an area that is made up from small areas • We assume that for all small areas, the Greenshields FD applies (i.e., flow is a function of the density in the area ) β0 = 0 α0 = v0 /ρjam Ω Ωi ρi Ωi V = v0 − α0ρ Q = ρ ⋅ V = ρ(v0 − α0ρ)
- 51. Multi-scale modelling framework Risk- neutral Nash game Risk-prone cooperativ e game Risk- averse demon game ‘Social- forces’ model Continuum modelling Network- wide modelling MFD Simplification of behavioural assumptions Assuming equilibrium and Taylor series expansion Spatial aggregation under equilibrium
- 52. Some notes on the MFD… Uses and misuses… • MFD (pedestrians / cyclists) relates average flow-rate in (large) area to space-averaged density and spatial density variation : • Great tool to describe flow conditions and causes for flow degradation on a network level • The (factors that determine) the shape helps in determining management schemes (e.g., perimeter control, density balancing) • Not so useful for prediction purposes, unless can be predicted as well which is often not the case (e.g., depends on applied control) - this also limits control applications • Other approaches for coarse applications may be more appropriate… q ρ σ2 q = Q(ρ) − γ ⋅ σ2 σ2 σ2
- 53. Use of AI for prediction and risk assessment Digital Twin for Risk Decision Support • Using ‘basic’ AI technology for short- term prediction (for operational support) and 6 day ahead (for planning) forecasting • Infusing our domain knowledge yields approaches that better generalise (Graph-based Neural Networks)
- 54. Learning opportunities Active mode theory as inspiration for other domains
- 55. Active modes show efficient interactions and self-organisation + we have advanced modelling schemes = applications to other domains?
- 56. Application examples by our group ▪ Use of simple control strategy Modelling cyclist & pedestrians Control schemes for connected & autonomous vessels Lane-free control schemes for CAVs Generic machinery: Differential game theory and dedicated numerical solution algorithm IRTA are broadly applicable Cooperative schemes for drones
- 57. Learning from active modes? Applications to distributed cooperative control • Capitalise on efficient self- organisation properties of pedestrians for distributed control of autonomous (flying) vehicles • Example shows distributed control of drones, revealing self- organisation in 3D using IRTA • Provides efficient solution to hard problem (multi-drone conflict resolution) for different risk-attitude strategies
- 58. • Note 1: Multi-scale approach for pedestrians / bikes will also carry over to drones / 3D, with similar benefits and downsides Learning from active modes? Applications to distributed cooperative control • Note 2: failing self-organisation for high demands will eventually result in need to intervene • We are currently developing a hierarchal control approach to tackle impact of failing self- organisation
- 59. Summary of talk • Discuss the importance of the active mode via four themes: - Fascinating complexity - Societal relevance - Scientific challenges - As an inspiration for other applications • Generic game theory framework • Multi-scale framework • Distributed cooperative control schemes for multi-drone conflict resolution