You have discrete event simulation in Kendall’s notation a M/G/3 model. Since you have a memory-less arrival process, 3 servers and the service time is not exponentially distributed. In R you “need” a priority queue for the events, rpois and runif for the events and service times. You sample an event and put it into the queue.
I don’t see what it has to do with Stan? There is a way with Stochastic Differential Equations. Thus if
you transform the problem, it might be put into Stan ODE solver.

Seriously, dude?

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More seriously, who’s teaching a class with Stan that we don’t know about?

on that theme, if there are any teaching materials anyone could recommend? I’m trying to get my team up to speed on Stan but it’s slow going since I have to prep slides and examples myself.

What level are you looking for?

I guess that’s a good question. Competent modelers but unfamiliar with Bayesian approaches. In other words, they can optimize a model with SciPy or MATLAB, and now want to compute posterior distributions.

If you get past the preliminaries I really like the case studies. Specifically I think some of Bob’s case studies do a really good job of working with derived quantities and that demonstrates the advantages of Bayesian inference really well.

There are some books and youtube videos (linked on the main website). The Stan team also give paid short courses that can be tailored for a particular audience if that’s an option for you. Contact Bob or Mike or Andrew for information about that.