In this chapter, we introduce through formal definitions but also with
schematics and fully solved examples the main parts of the random walk Continuous Time Markov Chain Process. This chapter is particularly oriented to the modeling
of waiting lines which are cases of wide applicability in all scientific disciplines.
The chapter begins by describing the Exponential and Poisson distribution which
are articulated in the Continuous-Time Markov Chain Process as the elements of
the matrix of conditional probabilities, and then follow the same methodology of
the discrete case characterizing that matrix in aperiodic or irreducible to finally
solve it as a System of Linear Equations by the usual methods or through its diagonalization by means of its eigenvalues and eigenvectors.
Keywords: Aperiodic Matrix, Continuous-Time Markov Chain Process, DiscreteTime Markov Chain Process, Distribution Functions, Ergodicity, Exponential Distribution, Initial State Vector, Irreducible Matrix, Markov Chain Process Markov Matrix, Poisson Distribution, Stationary Distribution, Steady-State vector, Transition Matrix Diagonalisation.
