Calculation Of Quasi-Stationary Distributions For Two Special Birth And Death Processes

In 1995,Ferrari proposed the method of compute the quasi-stationary distributions.The basic idea is as follows:For a Markov process X(t),its transition matrix is Q=(qij,i,j≥0).Now,by transforming Q matrix,we can get a new Q matrix Qμ=(qij μ,i,j≥1),qij μ=qij+qi0μj,μ is a probability measure.If the stationary distribution mj of markov process corresponding to the new matrix Qμ is equal to μj,then μ is quasi-stationary distribution of the markov process X(t).By this method,we fomulate a family of quasi-stationary distribution of M/M/1 queue models and the probability generating function of quasi-stationary distribution of linear birth and death processes.