 The embedded Markov chain has transition matrix

where

and "F"("u") is the service time distribution and λ the Poisson arrival rate of jobs to the queue.Markov chains with generator matrices or block matrices of this form are called M/G/1 type Markov chains, a term coined by M. F. Neuts.The stationary distribution of an M/G/1 type Markov model can be computed using the matrix analytic method.