Discrete-Event Simulation: A Leslie System Model for Transportation Demography

Transportation systems are influenced by demographic change, household formation,and patterns of vehicle ownership. These factors affect long-run transportation demand and congestion levels within urban infrastructure. Understanding how demographic dynamics interact with transportation behavior is therefore important for analyzing the long-term evolution of transportation systems. This thesis develops a modeling framework that integrates discrete-event simulation with a Leslie-type matrix model to study transportation–demography interactions.Simulation outputs are aggregated to construct a transition matrix describing changes in transportation states. This matrix acts as a linear (or affine) transformation on the transportation state vector, allowing the system to be analyzed as a discrete linear dynamical system. Using spectral methods from linear algebra, the dominant eigenvalue of the matrix determines the long-run growth rate of transportation demand, while the associated eigenvector describes the stable distribution of households across transportation categories. This framework provides a mathematical basis for studying how demographic evolution influences long-run transportation demand and congestion.