I’ve implemented queuing simulators in the past, but two questions I’ve always been bugged by (which I feel like are easily answered if I ever took proper math

I’ve implemented queuing simulators in the past, but two questions I’ve always been bugged by (which I feel like are easily answered if I ever took proper math courses…): 1. I don’t understand how you “know” you’re in the steady state, beyond looking at the graph — I’ve always just made it go like 10k steps to force it, but this seems needlessly wasteful. I imagine you could track the derivative but if it oscillates? 2. I don’t know how to verify if the distributions are poisson/exponential in reality, except by plotting More relevant note, I’ve always been surprised by how little exists online on the subject, and how little code it actually requires; I forget the terms but multiple event classes, multiple agent, infinite buffer sim took maybe 100 LoC C# from stdlib. Maybe 60 LoC in python — probably 25% was just tracking the stats I wanted like wait time. Biggest performance trick is that poison inter-arrival rate is exponential, and so you can generate all arrival times up front; then instead of simulating every second, you can just skip forward in time to when the events actually occur… so your sim scales on number of events occurring, rather than length of time simulated. Pretty sure you can even do arbitrarily length simulations in constant memory but never tried