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The varying phenomena that characterize a pedestrian flow make it one of the most challenging traffic flow processes to manage and control. In the past three decades, we have started to unravel the science behind the crowd. This has led to some important insights that are not only needed to reproduce, predict, and manage pedestrian flow, but will also provide potential avenues to managing other phenomena. In this talk, we will provide a historic perspective on pedestrian flow theory and crowd management. We show some of the key phenomena that have been observed (in controlled experiments, in the field), and how these phenomena can be explained, used or prevented. We will also highlight some of the recent contributions in the field, including the role of AI, novel monitoring technology, and digital twins. We round up the talk showing how the finding can be generalized. We show how the game-theoretical modeling proposed for pedestrian flow models can form a basis for controlling connected autonomous vehicles. Using various examples, we show how self-organization, omnipresent in pedestrian flow, can inspire decentralized control approaches of other flow processes (e.g., autonomous vessels, drones). We show how approaches to reduce flow breakdown for pedestrian flows can be generalized for other flow processes.

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- 1. Harnassing Crowd Intelligence… Prof. Dr. Serge Hoogendoorn Transport & Planning Department Transport & Mobility Institute Delft University of Technology What crowds can teach us…
- 2. Stress testing crowds in CrowdLimits In June 2018, we tried to establish the limits to self-organization in pedestrian flows…
- 3. We did not succeed to induce a breakdown…
- 4. Efficient self-organization is not limited to bi-directional pedestrian flows…
- 5. Examples of self-organisation Formation of diagonal stripes in crossing flows… Viscous fingering when standing and moving pedestrians interact Efficient multi-direction flow interactions
- 6. Massive pedestrian flows during the Hajj remain efficient…
- 7. 25 years of fascination for pedestrian and bicycle flows: Active modes are wonderfully complex and showcase unexpected dynamics
- 8. But there are other reasons to focus on active modes…
- 9. Sustainable urban mobility is impossible without active modes due to their limited spatial and ecological impact, health impact, relevance as first / last mile / transfer mode
- 10. There are major scientific, technological and engineering challenges to solve, including data collection
- 11. We can learn a lot from the active modes and the modeling and control thereof…
- 12. Can we somehow harnass this “Crowd Intelligence”?
- 13. Our first step? Understand and mathematically model these efficient self-organized phenomena…
- 14. Continuum models Cellular Automata models (animation by Prof. Mahmassani) Social Forces models (and variants) by Prof. Helbing
- 15. Instead of borrowing from traditonal traffic flow theory, we looked for a model better rooted in behavioral (game) theory…
- 16. Pedestrian Games Differential games as basis for pedestrian modeling
- 17. Our take on pedestrian modeling… Our behavioral model for pedestrian flow dynamics • Main assumption “pedestrian economicus” based on principle of least effort: From all possible actions (accelerate, decelerate, changing direction, do nothing) a pedestrian chooses the action yielding smallest predicted effort (disutility) • The predicted effort is the (weighed) sum of different effort components (e.g., walking too close / colliding, walking too slowly or too fast, straying from intended path, etc.) - like attributes in utility models
- 18. How does the predicted effort work? Path A Path B Path C Destination Shortest path Effort component examples: • Straying from shortest path • Being too close to other pedestrians • Accelerating / stopping • Not adhering to traffic rules… Possible paths result from candidate control actions; note: there are an infinite number of these paths possible
- 19. Anticipation strategies… Furthering the behavioral foundation • A key element in our modeling approach is that we assume that the ego pedestrian anticipates on the behavior of other pedestrians… • Research in the Seventies and Eighties have shown that: • Pedestrians unconsciously communicate via very subtle movements exchanging their intentions when interacting • Communication sometimes fails, in particular when pedestrians from different cultures interact (“reciprocal dance”) • Our differential game model allows for three different strategies reflecting different levels of (non-) cooperation
- 20. Solving the differential game… Numerical solution scheme • We determine the optimal acceleration assuming predicted effort minimization: ⃗ 𝑎[","$%) ∗ = arg min 𝐽(𝑢[","$%)) subject to pedestrians’ motion dynamics • Minimum Principle of Pontryagin results in necessary conditions, forms basis for Iterative Real-time Trajectory Optimization Algorithm (IRTA) • IRTA computes equilibrium where ego- pedestrian cannot improve her situation given assumed reaction of others 4.2 Iterative numerical solution In this section, we briefly discuss the iterative numerical solution approach. The algorithm is shown for one prediction period only; the receding horizon generalization is straightforward and left to the reader. Moreover, for the sake of simplicity, we have omitted obstacles, and terminal costs. 1. Initialization of control variables (prediction horizon T, time step h); 2. Initialization of parameters (weights, desired speed; relaxation parameter a, cut-o↵ error eps 3. For each pedestrian, initialization of initial position ~ r(0) and velocities ~ v(0) and target position ~ r1 4. Initialize co-states for the positions ~ ⇤r(t) = ~ 0 and velocities ~ ⇤v(t) = ~ 0 for all t = 0 : t : T 5. While error > eps do (a) Set ~r(t) = ~ ⇤r(t) and ~v(t) = ~ ⇤v(t) (b) For t = 0 : t : T t i. For i = 1 : n A. ~ u(t|i) = ~v(t|i) B. ~ v(t + t|i) = ~ v(t|i) + t · ~ u(t|i) C. ~ x(t + t|i) = ~ x(t|i) + t · ~ v(t|i) (c) For t = T : t : t i. For i = 1 : n A. Compute desired velocity ~ v0 i (t) B. ~r(t t|i) = ~r(t|i) + t · d0 P j6=i e dij /d0 ~ nij C. ~v(t t|i) = ~v(t|i) + t · ⇣ ↵(~ v0 i ~ v(t|i)) + ~r(t|i) ⌘ (d) Relaxation ~ ⇤r(t) = (1 a) · ~ ⇤r(t) + a · r(t) and ~ ⇤v(t) = (1 a) · ~ ⇤v(t) + a · v(t) (e) error = ||~ ⇤ ~|| It is beyond the scope of the paper to analyze the performance of the numer- ical solution in detail. For illustration purposes, Fig. 1 shows the convergence properties of the scheme for a one-on-one drone interaction scenario, with a
- 21. Validation outcomes • Calibration using ML approach + trajectory data • Reproduces all coll. self-organized phenomena • Model yields realistic flow – density relation for a location (FD) and for an entire network (p-MFD)
- 22. Multi-scale modelling framework Risk- neutral Nash game Risk-prone cooperativ e game ‘Social- forces’ model Network- wide modelling MFD Simplification of behavioural assumptions Assuming equilibrium and Taylor series expansion Spatial aggregation under equilibrium Risk-prone pedestrian game Risk- averse demon game Continuum modelling
- 23. Learning opportunities Pedestrian flow theory as inspiration for other domains
- 24. Our proposition: Game-theoretical approach can be used as a basis for decentralized control schemes inheriting efficient self-organization characteristics
- 25. ▪ Use of simple control strategy Modelling cyclist & pedestrians Control of connected & autonomous vessels Lane-free control schemes for CAVs Generic machinery: Differential game theory and dedicated numerical solution algorithm IRTA are broadly applicable Cooperative decentralized schemes for drones
- 26. Decentralized multi- drone conflict resolution • Prospect of drones in (urban) transport and logistics depend on our ability to solve complex drone interaction problems in high density airspace • Multi-drone conflict resolution is a key challenge! • Our proposition: use game-theoretical approach used for pedestrian modeling to formulate and solve multi-drone conflict resolution, assuming that many of the self-organization properties carry over to 3D…
- 27. Game of Drones* Differential games as basis for multi-drone conflict resolution
- 28. Multi-drone conflict resolution Path A Path B Path C Destination Shortest path Cost component examples: • Straying from shortest path • Being too close to the other drones • Acceleration / braking • Not adhering to airspace regulation… Ego-drone can use different strategies that represent different levels of risk taken by the drone given sensor and communication accuracy and reliability Adapted version of IRTA used as solver
- 29. Learning from active modes? Applications to decentralized control
- 30. Decentralized multi- drone conflict resolution • As with pedestrian flows, we see different forms of self- organization • Example shows formation of diagonal patterns in case of two crossing drone flows Top view Side view 1 Side view 2 y y y
- 31. Decentralized multi-drone conflict resolution Self-organized drone roundabouts • Scenario shows patterns drones generate at interaction (center-)point N=10 N=20
- 32. Decentralized multi-drone conflict resolution Self-organized drone roundabouts N=10 N=20
- 33. Decentralized multi-drone conflict resolution Self-organized drone roundabouts N=20 • Different factors influence self- organized patterns, including demand level • Important factor: desired speed variability • Large variation breaks formation of roundabouts • Other self-organized patterns are also influenced by heterogeneity
- 34. Limits to self-organization • Impact of heterogeneity well known for pedestrian flows: “freezing by heating” describes the fact heterogeneity messes up self organization • As a result, heterogeneous flows break down at a lower demand than homogenous flows • Shows possible impact of (local) homogenization to increase capacity of a bottleneck 1.2 1.4 1.6 1.8 2.0 1.0 0 1 Demand (P/s) Breakdown prob. medium low high
- 35. Limits to self-organization Higher pressure leads to reduced capacity and longer evacuation times • Faster-is-slower effect describes the reduction of bottleneck capacity due to increase haste due to arc formation • Insight leads to different types of local interventions to improve situation (e.g., placing obstacle in front of door to reduce pressure, or the ‘polonaise’)
- 36. Queues at local bottlenecks spill back, possibly causing grid-lock effects, in turn leading to turbulence and asphyxiation… When self-organization fails: Local problems may eventually lead to deterioration at network level
- 37. Using insights for design and management Improved design to limit crossing flows prev. spill-back Inflow reduction by using gating Spreading of Pilgrims using different flows Remove bottlenecks in design Testing interventions by simulation Using our understanding for Management & Design: Example Grand Mosque
- 38. Towards effective crowd management Classify intervention strategies at 3 levels… INDIVIDUAL Efficient decentralised strategies Influencing individual behaviour BOTTLENECK Increase bottleneck capacity Reduce break-down probability by homogenisation NETWORK Reduce inflow into network Increase network outflow Spread traffic over network and separate flows Increasing traffic demand
- 39. Similar approach could work for drones! Three level approach to managing drone traffic operations INDIVIDUAL Efficient decentralised strategies LOCAL Priority regulations Speed homogenisation Control of interacting flows NETWORK Schedule inflow into network Reroute drone flows Increasing traffic demand
- 40. But if we understand the processes so well… Why does it still go wrong?
- 41. Lack of accurate and reliable real- time datasources Lack of effective decision support tools for real-time decision making and planning
- 42. Data collection Sensing technology • Adequate data collection technologies have become available only recently • Still, single datasources seldom provide complete picture (spatial coverage, granularity, bias) • Acurate / complete information requires methods to process, fuse, and enrich multi-source data 3D camera, BT scanner, and climate sensor Mood & stress detection (DCM, GreshamSmith) Use of location-based services (Resono) Social-data crawler
- 43. Use of AI for prediction and risk assessment Digital Twin for Real-Time Decision Support and event planning • Advanced multi-source data collection and effective decision support come together in CSM • XAI technology for data fusion, short-term and long-term prediction of crowdedness • Future work focusses on risk assessment (EMERALDS)
- 44. Risk assessment is about much more than crowding…
- 45. Asphyxiation due to overcrowding Riots during the pandemic Stabbing incidents after a hot and crowded day at the beach Risk of being pushed of platform (courtesy of J van den Heuvel, NS Stations)
- 46. Our current work focuses on using advanced monitoring, data fusion, XAI, and decision support tools for advanced predictive risk assessment
- 48. Making impact! Keeping education open during the pandemic… • Sensing locations and distances with wearables and beacons • Dashboard shows areas of concern: where do the critical interactions occur? • Design interventions (floorplans, circulation strategies, occupancy limits) • Establish critical interactions between “bubbles” (groups/classes), so that only students at risk had to be isolated in case of infection
- 49. Main take aways From Crowd Intelligence to Artifical Crowd Intelligence • Show how efficient self-organized phenomena in active mode traffic can be modeled using decentralized schemes, generalizing well-known models • Show how approaches can be generalized to other problems, including multi- drone conflict resolution • Show (limits to) self-organization and how interventions can help improve • Discuss future steps in decision support using Artificial Crowd Intelligence Overall, I aimed to show you the importance of sharing knowledge across domains and not reinventing the wheel!