ON THE ESTIMATION OF PROBABILITIES FOR BIRTH AND DEATH PROCESSES

Let X(t) be a non-homogeneous birth and death process. In this paper w e develop a general method of estimating bounds for the state probabil ities for X(t), based on inequalities for the solutions of the forward Kolmogorov equations. Specific examples covered include simple estima tes of Pr(X(t) <j\X(0)=k) for the M(t)/M(t)/N/0 and M(t)/M(t)/N queue- length processes.