Gravity‐Type Interactive Markov Models—Part I: A Programming Formulation of Steady States
研究重力型交互马尔可夫迁移模型中稳态的唯一性和稳定性，第一部分将稳态问题转化为规划形式，证明当吸引力因人口拥挤而减弱时稳态唯一。
An important class of interactive Markov migration models is characterized by gravity‐type transition kernels, in which migration flows in each time period are postulated to vary inversely with some symmetric measure of migration costs and directly with some population‐dependent measure of attractiveness. This two‐part study analyzes the uniqueness and stability properties of steady states for such processes. In this first part, it is shown that a flow version of the steady‐state problem can be given a programming formulation which permits global analysis of steady‐state behavior. Within this programming framework, it is shown that when attractiveness is diminished by increased population congestion, the steady states for such processes are unique. The second part of the study will employ these results to analyze the stability properties of such steady states.