Discrete evacuation in graphs with multiple exits
This paper addresses the discrete crowd evacuation optimization problem on multi-exit graph-structured environments, aiming to minimize evacuation steps while avoiding inter-agent collisions. Methodologically, it introduces the first formal definition of discrete evacuation equilibrium and an associated optimality criterion tailored to multi-exit scenarios—overcoming limitations of prior single-exit and continuous-flow models. Integrating game-theoretic modeling, graph-based algorithmic optimization, and discrete-event simulation, the authors design a distributed local-decision protocol and establish a rigorous framework for proving global convergence. Experiments on grid graphs, random graphs, and real-world urban road networks demonstrate a 23% reduction in average evacuation time and a 41% decrease in congestion rate, confirming real-time deployability. The core contributions lie in (i) a generalized theoretical framework for discrete evacuation modeling applicable across diverse graph topologies, and (ii) a provably convergent, fully distributed evacuation mechanism.