Consider the following process: $X$ is a nonnegative real function of a continuous time variable $t$,
so long as $X\geq 0$, it decreases deterministically at rate $\mu$ (i.e., $X(t+dt) = X(t) - \mu\, dt$ if $X(t)\geq 0$), except that
randomly according to a homogeneous Poisson process with density $\lambda$, it increases by $1$ (i.e., $X(t+dt) = X(t)+1$ with probability $\lambda\, dt$, or maybe write $X(t)+1-\mu\,dt$ of course this doesn't change anything).
I hope this formal description is clear enough. (Alternatively, for $N$ large, consider a discrete time Markov chain which replaces $X$ by $\max(0, X-\mu/N)$ and then replaces $X$ by $X+1$ with probability $\lambda/N$, and make $N\to+\infty$.)
This is a continuous-time variant of what I think is called the M/D/1 queue process.
Assuming $\mu>\lambda$, which I do, this has a stationary distribution (sanity check: the latter has an atom at $0$ and is continuous w.r.t. Lebesgue measure for $x>0$, i.e., has a density function, which is itself, I believe, discontinuous at $1$ and only there).
Question: What is a closed form for this stationary distribution or where might I find it? (Similar to the closed form given for the stationary distribution of the discrete-time M/D/1 queue process in the Wikipedia article linked above.)