The problem sounds like it can be solved with queueing theory. The (common) inductive proof method is covered by the wikipedia article: https://en.wikipedia.o

The problem sounds like it can be solved with queueing theory. The (common) inductive proof method is covered by the wikipedia article: https://en.wikipedia.org/wiki/Queueing_theory#Example_analysis_of_an_M/M/1_queue https://en.wikipedia.org/wiki/Queueing_theory#Example_analys... However since the arrival of messages can be modeled as a probabilistic or continuous rate, differential equations can also be used. I'm not sure if this is how Feynman did it, but this paper shows how to model queueing using differential equations: http://pi.math.cornell.edu/~rand/randpdf/ENOC2017_queueing.pdf http://pi.math.cornell.edu/~rand/randpdf/ENOC2017_queueing.p...