3 ms·

It's not explicitly mentioned in the article, but the arrival rate and queue sizes are related via Little's Law [0] — the average number of people in a system i

by jcalx 2y ago

It's not explicitly mentioned in the article, but the arrival rate and queue sizes are related via Little's Law [0] — the average number of people in a system is equal to the arrival rate multiplied by the mean wait time, regardless of the arrival distribution, service distribution, or service order (e.g. FIFO, LIFO, random). I was fortunate enough to take some great queueing theory classes in college, and fondly remember flailing about in Simio [1] trying to get a bank teller simulation to work. Really useful stuff to learn, although it did make me incredibly susceptible to Factorio and similar games. [0] https://en.wikipedia.org/wiki/Little%27s_law https://en.wikipedia.org/wiki/Little%27s_law [1] https://www.youtube.com/watch?v=xCzAhKtucck https://www.youtube.com/watch?v=xCzAhKtucck

dleeftink 2y ago
You may have seen it already, but the queueing saga by Defunctland remains fascinating [0]. [0]: https://youtu.be/9yjZpBq1XBE https://youtu.be/9yjZpBq1XBE
kqr 2y ago
Queueing theory is one of my favourite secret superweapons. You can use it to back-of-the-napkin solutions out of feasibility much quicker than it'd take to simulate. I warmly recommend Harchol-Balter: https://www.amazon.com/Performance-Modeling-Design-Computer-Systems/dp/1107027500 https://www.amazon.com/Performance-Modeling-Design-Computer-... It is an eminintly practical book which is written in terms of computers, goes beyond the basic M/M/1 but without being overbearing. (The other secret superpower is statistical process control.)
code_biologist 2y ago
Agreed! The Principles of Product Development Flow by Donald G. Reinertsen[1] is one of my favorite product management books because it's very conceptual, but man the concepts hit home fast. This summary has a lot of great details [2] and the third chapter is entirely dedicated to the properties of queues. After, Little's law, he introduces the First Queue Size Control Principle (Q13): Controlling queue size rather than capacity utilization offers a more effective way to manage cycle time and process efficiency. — No mister business stakeholder, adding items to the dev team's to-do list and making sure they are working 110% isn't going to get stuff delivered faster. Diffusion Principle (Q15): Random processes can lead to queues spinning out of control; these high-queue states can last long and cause significant economic damage. — No mister business stakeholder, we can't fix this one little thing right now, it's bigger than you think and is going to make it harder to deliver the big important project. [1] https://www.amazon.com/Principles-Product-Development-Flow-Generation/dp/1935401009 https://www.amazon.com/Principles-Product-Development-Flow-G... [2] https://www.joecotellese.com/posts/principles-of-product-development-flow-book-summary/ https://www.joecotellese.com/posts/principles-of-product-dev...
- JoeC3 1y ago
  It is a great PM book. Thanks for linking to my write up!
vismit2000 2y ago
Little's law comes up in the beautiful book 'Programming Pearls' by Jon Bentley in 'Back of the Envelope' calculations: - `Little’s Law`: The average number of objects in a queue is the product of the entry rate and the average holding time - Response-time formula for a multi-user system: - Assume n users of average think time z are connected to an arbitrary system with response time r. - Each user cycles between thinking and waiting-for-response, so the total number of jobs in the meta-system (consisting of users and the computer system) is fixed at n. - If you cut the path from the system's output to the users, you see a meta-system with average load n, average response time z + r, and throughput x (measured in jobs per time unit). - Little’s Law says n = x × (z + r), and solving for r gives r = n/x – z.

by jcalx 2y ago

dleeftink 2y ago

You may have seen it already, but the queueing saga by Defunctland remains fascinating [0]. [0]: https://youtu.be/9yjZpBq1XBE https://youtu.be/9yjZpBq1XBE

kqr 2y ago

Queueing theory is one of my favourite secret superweapons. You can use it to back-of-the-napkin solutions out of feasibility much quicker than it'd take to simulate. I warmly recommend Harchol-Balter: https://www.amazon.com/Performance-Modeling-Design-Computer-Systems/dp/1107027500 https://www.amazon.com/Performance-Modeling-Design-Computer-... It is an eminintly practical book which is written in terms of computers, goes beyond the basic M/M/1 but without being overbearing. (The other secret superpower is statistical process control.)

code_biologist 2y ago

Agreed! The Principles of Product Development Flow by Donald G. Reinertsen[1] is one of my favorite product management books because it's very conceptual, but man the concepts hit home fast. This summary has a lot of great details [2] and the third chapter is entirely dedicated to the properties of queues. After, Little's law, he introduces the First Queue Size Control Principle (Q13): Controlling queue size rather than capacity utilization offers a more effective way to manage cycle time and process efficiency. — No mister business stakeholder, adding items to the dev team's to-do list and making sure they are working 110% isn't going to get stuff delivered faster. Diffusion Principle (Q15): Random processes can lead to queues spinning out of control; these high-queue states can last long and cause significant economic damage. — No mister business stakeholder, we can't fix this one little thing right now, it's bigger than you think and is going to make it harder to deliver the big important project. [1] https://www.amazon.com/Principles-Product-Development-Flow-Generation/dp/1935401009 https://www.amazon.com/Principles-Product-Development-Flow-G... [2] https://www.joecotellese.com/posts/principles-of-product-development-flow-book-summary/ https://www.joecotellese.com/posts/principles-of-product-dev...

JoeC3 1y ago
It is a great PM book. Thanks for linking to my write up!

vismit2000 2y ago

Little's law comes up in the beautiful book 'Programming Pearls' by Jon Bentley in 'Back of the Envelope' calculations: - `Little’s Law`: The average number of objects in a queue is the product of the entry rate and the average holding time - Response-time formula for a multi-user system: - Assume n users of average think time z are connected to an arbitrary system with response time r. - Each user cycles between thinking and waiting-for-response, so the total number of jobs in the meta-system (consisting of users and the computer system) is fixed at n. - If you cut the path from the system's output to the users, you see a meta-system with average load n, average response time z + r, and throughput x (measured in jobs per time unit). - Little’s Law says n = x × (z + r), and solving for r gives r = n/x – z.