  In Section 1, we revisit the partial differential equation (PDE) for the
probability generating function (PGF) of the time-nonhomogeneous BDI
(birth-and-death-with-immigration) process and derive a closed form solution.
To the best of our knowledge, this is a new mathematical result. We state this
result as Proposition 1. We state as Corollary 1 that the negative binomial
distribution of the time-homogeneous BDI process discussed in Part I extends to
the general time-nonhomogeneous case, provided that the ratio of the
immigration rate to the birth rate is a constant. In section 1.2, we take up
the heuristic approach discussed by Bartlett and Bailey (1964), and carry it
out to completion by arriving at the solution obtained above,.
  In Section 2, we present the results of our extensive simulation experiments
of the time-nonhomogeneous BD process that was analyzed in Part III-A and
confirm our analytic results. In Section 3, we undertake similar simulation
experiments for the BDI process that is analyzed in Section 1.
  As we discuss in Section 4, our stochastic model now seems more promising and
powerful than has been heretofore expected. In Appendix B, a closed form
solution for the M(t)/M(t)/infinity queue is obtained, as a special case of
this BDI process model.
