A Review on Macroscopic Pedestrian Flow Modelling
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paper_title: COMBINING SOCIAL FORCES AND CELLULAR AUTOMATA MODELS IN PEDESTRIANS' MOVEMENT SIMULATION

paper_content:

This paper focuses on combining two simulation approaches to model pedestrians’ behavior. The agent oriented architecture is used. Since each pedestrian is modeled individually, it is possible to observe individual behavior and interactions. The overview of cellular automata model and social forces model is provided. The designed social forces model is described in detail and demonstrated. The infrastructure enabling the discrete (cellular automata) and continuous (social forces) movement at once is presented.
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paper_title: Normative Pedestrian Behaviour Theory and Modelling

paper_content:

The normative theory of pedestrian flow behavior presented here is based on the assumption that pedestrians are expected cost minimizers: they schedule their activities, choose the activity areas and the routes connecting these activity areas simultaneously to maximize the expected utility of their efforts. Unlike other transportation network models, pedestrian routes are continuous functions in time and space, and the utility of the route reflects a trade off between the utility of completing an activity and the generalized cost of walking towards the activity areas. The paper also considers the consequences of information feedback, e.g. pedestrians see that their planned route is congested and react by taking another route.
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paper_title: On the fluid mechanics of human crowd motion

paper_content:

The paper presents a theory of the flow of people along a channel which may be of variable width, or have a partial blockage in it. The results are presented in kinetic form to facilitate comparison with observation. It is shown that a crowd fluid may exhibit anomolous gas dynamic behaviour caused by a change in the sign of a well known derivative. This indicates that expansion shocks are possible in crowd fluids.
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paper_title: First-Order Pedestrian Traffic Flow Theory

paper_content:

This paper discusses the validity of first-order traffic flow theory for the description of two-dimensional pedestrian flow operations in the case of an oversaturated bottleneck in front of which a large high-density region has formed. The paper shows how observations of density, speed, and flow that have been collected from laboratory walking experiments can be interpreted from the viewpoint of first-order theory. It is observed that pedestrians present at the same cross section inside of the congested region may encounter different flow conditions. This mainly depends on the lateral position of the pedestrian with respect to the center of the congested region. In the lateral center, high densities and low speeds are observed. However, on the boundary of the congested region, pedestrians may walk in nearly free-flow conditions and literally walk around this congested region. Visualization of these data in the flow-density plane results in a large scatter of points that have similar flows (bottleneck capa...
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paper_title: Non-local first-order modelling of crowd dynamics: a multidimensional framework with applications

paper_content:

Abstract In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd–structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.
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paper_title: A MACROSCOPIC MODEL FOR PEDESTRIAN FLOWS IN PANIC SITUATIONS

paper_content:

In this paper we present the macroscopic model for pedestrian flows proposed by Colombo and Rosini [10] and show its main properties. In particular, this model is able to properly describe the movements of crowds, even after panic has arisen. Furthermore, it is able to reproduce the so called Braess' paradox for pedestrians. From the mathematical point of view, it provides one of the few examples of non classical shocks motivated by real problems, for which a global existence result is available. Finally, its assumptions were experimentally confirmed by an empirical study of a crowd crush on the Jamarat Bridge in Mina, Saudi Arabia, near Mecca, see [17].
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paper_title: COMBINING SOCIAL FORCES AND CELLULAR AUTOMATA MODELS IN PEDESTRIANS' MOVEMENT SIMULATION

paper_content:

This paper focuses on combining two simulation approaches to model pedestrians’ behavior. The agent oriented architecture is used. Since each pedestrian is modeled individually, it is possible to observe individual behavior and interactions. The overview of cellular automata model and social forces model is provided. The designed social forces model is described in detail and demonstrated. The infrastructure enabling the discrete (cellular automata) and continuous (social forces) movement at once is presented.
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Title: A Review on Macroscopic Pedestrian Flow Modelling

Section 1: INTRODUCTION
Description 1: This section introduces the significance of pedestrian simulation and different modeling methods, with a focus on macroscopic models and their uses in crowd management and simulation tools.

Section 2: HYDRODYNAMIC MODELS
Description 2: This section discusses hydrodynamic models using analogies with fluids or gases to describe changes in pedestrian density and speed over time, including their physical foundations and applications.

Section 3: HELBING'S FLUID-DYNAMIC MODEL
Description 3: This section elaborates on Dirk Helbing's fluid-dynamic model for pedestrian movement based on gas-kinetic equations and discusses its underlying principles and applications.

Section 4: HUGHES'S MODEL
Description 4: This section introduces Roger L. Hughes's model that derives pedestrian movement from three hypotheses related to pedestrian speed, destination, and behavior in dense crowds.

Section 5: FIRST-ORDER FLOW MODELS
Description 5: This section covers first-order pedestrian flow theories and their mathematical frameworks for modeling pedestrian movement based on density, speed, and flow.

Section 6: DAAMEN-HOOGENDOORN-BOVY
Description 6: This section explains the fundamental diagrams derived by Daamen, Hoogendoorn, and Bovy from cumulative flow plots and their applications in determining pedestrian flow and density.

Section 7: BRUNO ET. AL.
Description 7: This section details Bruno et al.'s physical framework, emphasizing features of pedestrian behavior including intelligent, non-local, and anisotropic behavior.

Section 8: PHYSICAL MODELLING FRAMEWORK
Description 8: This section introduces a physical modeling framework for pedestrian movement, focusing on mass conservation, velocity fields, and pedestrian interaction.

Section 9: COLOMBO-ROSINI MODEL
Description 9: This section discusses the Colombo-Rosini model, a one-dimensional macroscopic model for simulating real situations like crowd evacuations and reproducing the Braess' paradox.

Section 10: CONCLUSION
Description 10: This section summarizes the computational efficiency of macroscopic models and their suitability for large-scale pedestrian simulations. It also outlines future work on integrating the Colombo-Rosini model into the PedSim simulation tool for hybrid modeling.