  The exponential server timing channel is known to be the simplest, and in
some sense canonical, queuing timing channel. The capacity of this
infinite-memory channel is known. Here, we discuss practical finite-length
restrictions on the codewords and attempt to understand the maximal rate that
can be achieved for a target error probability. By using Markov chain analysis,
we prove a lower bound on the maximal channel coding rate achievable at
blocklength $n$ and error probability $\epsilon$. The bound is approximated by
$C- n^{-1/2} \sigma Q^{-1}(\epsilon)$ where $Q$ denotes the Q-function and
$\sigma^2$ is the asymptotic variance of the underlying Markov chain. A closed
form expression for $\sigma^2$ is given.
