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Have you looked at stochastic network calculus ?

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




I never heard of "Network calculus and stochastic network calculus". Certainly no such topics were in any of the applied math grad courses I took.

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.


> I never heard of "Network calculus and stochastic network calculus".

...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.




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