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 (changes)

• 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: 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.
• The second $M$ refers to the service process, which is also a 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

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