Paved guideway topology optimization for pedestrian traffic under Nash equilibrium

Abstract

Without proper flow channelization, congestion and overcrowding in pedestrian traffic may lead to significant inefficiency and safety hazards. Thus, the design of guideway networks that provide a fine balance between traffic congestion and infrastructure construction investment is vital. This paper presents a mathematical formulation and topology optimization framework for paved pedestrian guideway design under physics-based traffic equilibrium in a continuous space. Pedestrians are homogeneous, and their destination and path choices under the Nash equilibrium condition are described by a set of nonlinear partial differential equations. The design framework optimizes the deployment of pavement, which alters the road capacity and directly affects pedestrians’ free flow travel speed. A maximum crowd density constraint is included in the design model to address public safety concerns (e.g., over stampede risks). A series of numerical experiments are conducted to illustrate the effectiveness of the proposed model as well as solution techniques. The proposed framework, which builds on the traffic equilibrium theory, produces optimized guideway designs with controllable maximum pedestrian density, accounts for budget constraints (through an adjustable multiplier that balances pavement construction and travel costs), and allows for control of the spatial configuration of road branches. Comparison with lamellar structures and more conventional guideway designs demonstrates better performance of the outcomes from the proposed modeling and optimization framework.