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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. For the files created for this video, please visit https://www.mathemaniac.co.uk/download and enter the password: queuingmodelM/M/1 and follow the instructions on the website. If you can't enter the website, watch the latest video! It always changes when a new video is up. 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_... Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I use PowerPoint, GeoGebra, and (sometimes) Mathematica to produce the videos. Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   Patreon:   / mathemaniac   (support if you want to and can afford to!) Merch: https://mathemaniac.myspreadshop.co.uk Ko-fi: https://ko-fi.com/mathemaniac [for one-time support] For my contact email, check my About page on a PC. See you next time!