The stationary distribution of waiting time for a D/M/1 queue is well known if the first-come first-serve (FCFS) discipline is adopted.
If, however, the last-come first-serve (LCFS) discipline is adopted, then no theoretical results appear in the literature (as far as I can see).
This would be a surprising gap in the literature, especially since a relevant computer simulation is so easy to write.
Am I missing something in my literature search? Thoughts or suggestions would be most appreciated.
It turns out that Wishart (1960) answered my question, although I didn't know this fact until a fairly short time ago.
I've gathered relevant information about the D/M/1 queue in
https://arxiv.org/abs/2210.08545
for others to see. Section 2 contains formulas concerning the LCFS policy, also called LIFO (last-in-first-out). Figure 1 exhibits a plot of the probability density function for the waiting time. Two other preprints of mine discuss the M/D/1 queue.