Fractional Order Crowd Dynamics

This book illustrates the application of fractional calculus in crowd dynamics via modeling and control groups of pedestrians. Decision-making processes, conservation laws of mass/momentum, and micro-macro models are employed to describe system dynamics while cooperative movements in micro scale, and fractional diffusion in macro scale are studied to control the group of pedestrians. Obtained work is included in the Intelligent Evacuation Systems that is used for modeling and to control crowds of pedestrians. With practical issues considered, this book is of interests to mathematicians, physicists, and engineers.

This book illustrates the application of fractional calculus in crowd dynamics via modeling and control groups of pedestrians. Decision-making processes, conservation laws of mass/momentum, and micro-macro models are employed to describe system dynamics while cooperative movements in micro scale, and fractional diffusion in macro scale are studied to control the group of pedestrians. Obtained work is included in the Intelligent Evacuation Systems that is used for modeling and to control crowds of pedestrians. With practical issues considered, this book is of interests to mathematicians, physicists, and engineers.

Table of Content:Chapter 1 Fractional Model of Microscopic Pedestrians Based on Fractional Decision Making Process1.1 Introduction1.2 Fractional Decision Making Process1.3 Fractional Microscopic Model1.4 Simulation Results1.5 ConclusionChapter 2 Fractional Model of Macroscopic Crowds Based on Fractional Conservation Law2.1 Introduction2.2 Fractional Conservation law of Mass/Momentum2.3 Fractional Macroscopic Model2.4 Simulation Results2.5 ConclusionChapter 3 Fractional Model for Micro-Macro Crowds with Presence of Individual of Disabilities3.1 Introduction3.2 Fractional Potential Field and IwDs3.3 Fractional Mean Field Theory3.4 Fractional Micro-Macro Model3.5 Simulation Results3.6 ConclusionChapter 4 Cooperative Control of Microscopic Pedestrians with Long Range Interactions4.1 Introduction4.2 Relationship between Long Range Interactions and Fractional Calculus4.3 Relationship between Long Range Interactions and Macroscopic Movement4.4 Cooperative Control of Microscopic Pedestrians with Long Range Interactions4.5 Simulation Results4.6 ConclusionChapter 5 Boundary Evacuation Control of Macroscopic Crowds of Pedestrians5.1 Introduction5.2 Fractional Reaction-advection-diffusion Model5.3 Boundary Conditions for Desired Evacuation5.4 Evacuating Controllers for Boundary Robots5.5 Wave-absorbing Re-design of Boundary Evacuating Controllers5.6 Simulation Results5.7 ConclusionChapter 6 Intelligent Evacuation Control of Large Crowds of Pedestrians Using FODIFF-MAS6.1 Introduction6.2 Platform of DIFF-MAS and FODIFF-MAS6.3 Simulation Results of Large Crowds on Micro, Macro and Mesco Scale6.4 Simulation Results of Large Crowds with Long Range Interactions6.5 Intelligent Evacuation Control of Large Crowds6.6 Conclusion