Queuing theory and Poisson process
Queuing theory is indispensable, but here is an introduction to the simplest queuing model - an M/M/1 queue. Also included is the discussion on Poisson process, which is the underlying assumption for the M/M/1 queue.
Second channel video on variance of Poisson distribution: • Poisson distribution (extra)
To me, this is mainly a "prequel" which serves as a prerequisite for the next video, even though the next video is not as long.
This channel is meant to showcase interesting but underrated maths (and physics) topics and approaches, either with completely novel topics, or a well-known topic with a novel approach. If the novel approach resonates better with you, great! But the videos have never meant to be pedagogical - in fact, please please PLEASE do NOT use YouTube videos to learn a subject.
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queuingmodelM/M/1
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Sources:
Different queues:
M/M/1 queue: https://en.wikipedia.org/wiki/M/M/1_q...
M/M/c queue: https://en.wikipedia.org/wiki/M/M/c_q...
M/M/∞ queue: https://en.wikipedia.org/wiki/M/M/%E2...
M/G/1 queue: https://en.wikipedia.org/wiki/M/G/1_q...
M/G/k queue: https://en.wikipedia.org/wiki/M/G/k_q...
G/M/1 queue: https://en.wikipedia.org/wiki/G/M/1_q...
G/G/1 queue: https://en.wikipedia.org/wiki/G/G/1_q...
Jackson Network: https://en.wikipedia.org/wiki/Jackson...
More general queues: https://en.wikipedia.org/wiki/Kendall...
The (transient) solution: Computer Networks and Systems. New York, NY: Springer New York. p. 72 (uses moment-generating function and Laplace transforms); for more details, see Gross, D. and Harris, C.M., Fundamentals of Queueing Theory, Wiley, New York, 1974, 1985. (Section 3.11.2)
Other related sources:
Markov Chains: https://www.statslab.cam.ac.uk/~james...
Birth-and-death chain: https://en.wikipedia.org/wiki/Birth%E...
Bessel functions (for the solution to the differential equations): https://en.wikipedia.org/wiki/Bessel_...
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