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://www.youtube.com/watch?v=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. 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: null 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!