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: the process in which the server accomplishes the work.
    • Queueing discipline: how queue handles the waiting work.
  • Kendall notation: M/M/1/M/M/1/\infty queue.

    • The first MM refers to the arrival process, in this case, is the Markov process.
    • The second MM refers to the service process, which is also a Markov process.
    • The number 11 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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