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: 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 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: M/M/c queue: M/M/∞ queue: ∞_queue M/G/1 queue: M/G/k queue: G/M/1 queue: G/G/1 queue: Jackson Network: More general queues: ’s_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 ) Other related sources: Markov Chains: ~james/Markov/ Birth-and-death chain: –death_process Bessel functions (for the solution to the differential equations): #Modified_Bessel_functions_:_Iα,_Kα 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: 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: Instagram: Twitter: Patreon: (support if you want to and can afford to!) Merch: Ko-fi: [for one-time support] For my contact email, check my About page on a PC. See you next time!