Queueing Theory

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 times and 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. It's usually unpredictable.
  • Service Process: the process in which the server accomplishes the work.
  • Queueing discipline: how queue handles the waiting work, the rules under which an organization processes incoming items. For example, First Come, First Served, Last In First Out, First In Still Here, etc.

• 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

• The Principles of Product Development Flow

Backlinks

• M/G/1 Queue
• Queues in Product Development