Upper bound on the rate of convergence and truncation bound for non-homogeneous birth and death processes on Z

摘要

We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on Z with the time–varying and possibly state-dependent intensities. First in the literature upper bounds on the rate of convergence are provided. Upper bounds for the truncation errors are also given. The condition under which a limiting (time-dependent) distribution exists is formulated but relies on the quantities that need to be guessed in each use-case. The developed theory is illustrated by two numerical examples within the queueing theory context.