  In this paper we introduce a new diffusion approximation for the steady-state
customer count of the Erlang-C system. Unlike previous diffusion
approximations, which use the steady-state distribution of a diffusion process
with a constant diffusion coefficient, our approximation uses the steady-state
distribution of a diffusion process with a \textit{state-dependent} diffusion
coefficient. We show, both analytically and numerically, that our new
approximation is an order of magnitude better than its counterpart. To obtain
the analytical results, we use Stein's to show that a variant of the
Wasserstein distance between the normalized customer count distribution and our
approximation vanishes at a rate of $1/R$, where $R$ is the offered load to the
system. In contrast, the previous approximation only achieved a rate of $1/R$.
We hope our results motivate others to consider diffusion approximations with
state-dependent diffusion coefficients.
