Pedro Arantes
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# Queueing Theory

It can provide essential insights to product developers because there're similar problems of unpredictable work arrival time and unpredictable task durations.
#agner-krarup-erlang
Zettelkasten, July 24, 2021
## Notes - Queueing theory originated in 1909 with a paper written by a mathematician named Agner Krarup Erlang. - He accurately estimated the probability that a call would be blocked at different capacity utilization levels. - It can provide essential insights to product developers because there're similar problems of unpredictable work arrival time and unpredictable task durations. - Queueing systems: - **Queue**: the waiting work. - **Server**: the resource performing the work, whose time to complete the work may be unpredictable. - **Arrival Process**: the pattern with which work arrives, which is usually unpredictable. - [**Service Process**](/zettel/queue-service-process): the process in which the server accomplishes the work. - **Queueing discipline**: how queue handles the waiting work. - Kendall notation: $M/M/1/\infty$ queue. - The first $M$ refers to the **arrival process**, in this case, is the [Markov process](/zettel/markov-process). - The second $M$ refers to the **service process**, which is also a [Markov process](/zettel/markov-process). - The number $1$ refers to the number of parallel **servers** in the system. - The final term $\infty$ describes the upper limit on queue size. ## References - [The Principles of Product Development Flow](/books/the-principles-of-product-development-flow) ## Backlinks - [M/G/1 Queue](/zettel/m-g-1-queue) - [Queue Capacity Utilization](/zettel/queue-capacity-utilization)
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Queue Service Process