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Currently Playing: 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: https://youtu.be/xiX1QoX8i6M 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. 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_queue M/M/c queue: https://en.wikipedia.org/wiki/M/M/c_queue M/M/∞ queue: https://en.wikipedia.org/wiki/M/M/%E2%88%9E_queue M/G/1 queue: https://en.wikipedia.org/wiki/M/G/1_queue M/G/k queue: https://en.wikipedia.org/wiki/M/G/k_queue G/M/1 queue: https://en.wikipedia.org/wiki/G/M/1_queue G/G/1 queue: https://en.wikipedia.org/wiki/G/G/1_queue Jackson Network: https://en.wikipedia.org/wiki/Jackson_network More general queues: https://en.wikipedia.org/wiki/Kendall%27s_notation 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/Markov/ Birth-and-death chain: https://en.wikipedia.org/wiki/Birth%E2%80%93death_process Bessel functions (for the solution to the differential equations): https://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions_:_I%CE%B1,_K%CE%B1 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: https://www.facebook.com/mathemaniacyt Instagram: https://www.instagram.com/_mathemaniac_/ Twitter: https://twitter.com/mathemaniacyt Patreon: https://www.patreon.com/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!