Network of queues can become hrrendoulsy difficult to analyze unless one assumes memoryless arrivals etc etc. Network calculus and stochastic network calculus simplifies things a great deal by going after bounds rather than exact answers. You might like it
For "going after bounds rather than exact answers", for analyzing network performance, there is a hugely simplifying approach: Just look at the bottlenecks and largely f'get about the rest; maybe that is related to what you mentioned.
For network queuing, really I was suggesting using that as a paradigm to formulate an analysis; I accept that analytic solutions are unpromising -- more generally, the exact probabilistic calculations out of queuing theory research are complicated even for simple cases. So, for solutions, i.e., actionable information, use Monte Carlo.
Once I knew a guy at IBM's Watson lab who was big on such things. There was a claim that at one time his work was useful in designing some of an IBM mainframe I/O subsystem. He had some software that I used once. His software wanted to collect the usual descriptive statistics, but I wanted the sample paths from the Monte Carlo, got those, and did more analysis of those.
...and now you have :)
> Certainly no such topics were in any of the applied math grad courses I took.
Yeah they are a newer development. Stochastic network calculus more so. Network calculus is older, it even has a wikipedia page https://en.wikipedia.org/wiki/Network_calculus A key idea is convolution but in the max-plus algebra and martingale large deviations.
> For network queuing, really I was suggesting using that as a paradigm to formulate an analysis;
Indeed. SNCs can be a helpful tool there. Yes they are bounds, but a lot of progress has been made to make them tight https://arxiv.org/pdf/1303.4114.pdf they arent quite there yet numerically but tight enough to give an intuition. NC bounds are a lot looser.
At times it has been possible to make some progress on the complexity by regarding each application, virtual machine, server, server cluster, or server farm as a network of queues and apply queuing theory and/or Monte Carlo simulation. In addition some of the old work in optimization under uncertainty likely applies.