Summary: A diffusion regime with non-degenerate slowdown: Appendix
June 15, 2011
In this appendix to "A diffusion regime with non-degenerate slowdown", Op. Res. (2012), we
provide the proofs of the main results. Theorem 2.1 is proved in Subsection A.1 and Theorem
2.2 in Subsection A.2.
For the notation used in this appendix, see the end of Section 1 of the main body of the paper.
Equation and theorem numbers, such as (1), (2),..., Theorem 2.1, etc. refer to the main body of
the paper. Literature citation such as , ,... refers to the bibliographic list at the end of this
A.1 Convergence of queue-length
In this subsection we prove Theorem 2.1. Let us introduce some notation. Let
Tkn(t), »Tn(t) = n-1
An(t) = n-1/2
(An(t) - nt),