In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure.
[1] The method was developed "largely by Marcel F. Neuts and his students starting around 1975.
"[2] The method requires a transition rate matrix with tridiagonal block structure as follows where each of B00, B01, B10, A0, A1 and A2 are matrices.
To compute the stationary distribution π writing π Q = 0 the balance equations are considered for sub-vectors πi Observe that the relationship holds where R is the Neut's rate matrix,[3] which can be computed numerically.
[7] Such models are harder because no relationship like πi = π1 Ri – 1 used above holds.