 
Summary: A diffusion regime with nondegenerate slowdown: Appendix
Rami Atar
June 15, 2011
Abstract
In this appendix to "A diffusion regime with nondegenerate 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 [1], [2],... refers to the bibliographic list at the end of this
appendix.
A.1 Convergence of queuelength
In this subsection we prove Theorem 2.1. Let us introduce some notation. Let
Tn(t) =
kKn
Tkn(t), ¯Tn(t) = n1
Tn(t), (A.1)
An(t) = n1/2
(An(t)  nt),
