In this chapter, we look at how Monte Carlo simulations and the Markov
chain theory can be used to analyze urban transportation problems. Vectors describing the starting and final states of a public transportation network are introduced as
fundamental notions. The transition probability matrix and the stochastic matrix are
investigated as potential tools for modeling the dynamic evolution of urban mobility
using discrete-time Markov Chains. The features of Markov Chains, as revealed by
their eigenvalues and eigenvectors, are examined. The Markov Chain Monte Carlo
technique for statistical sampling and analysis of urban mobility issues is also discussed. The methodologies’ potential utility in urban transportation planning and
decision-making is emphasized. Understanding and addressing the difficulties of
urban mobility are greatly aided by the theoretical and conceptual groundwork laid
out in this chapter.
Keywords: Discrete-time Markov chain, eigenvalues, eigenvectors, Markov chain Monte Carlo, regular matrix, states, stochastic matrix, transition probabilitiesr, . transition probability matrix, urban mobility issues, vector in the initial state, vector in a steady state.
