queueing theory: part 1
This post is part of a series on Queueing Theory. The other articles can be found here:
- Queueing Theory: Part 1
- Queueing Theory: Part 2
- Queueing Theory: Part 3
- Queueing Theory: Part 4
- What is Waste?
- On Time-Traps and Waste
- Call Centers as Queueing Systems
- Travel Time & Waste
- Little’s Law for Product Development
a queueing system is a model with the following structure: customers arrive and join a queue to wait for service given by n servers. after receiving service, the customer exits the system. a fundamental result of queueing theory is little’s law.
theorem: for a queueing system in steady state, the average length of the queue is equivalent to the average arrival rate multiplied by the average waiting time. in other words,
L = λW
at amazon, i used little’s law all the time. in dynamic systems with n+ dependencies, it is very helpful to know where the bottlenecks of the system are and how to increase efficiencies, reduce time traps, and eliminate waste in order to increase material flow. in other words, we want product to flow as fast as possible: click-to-ship.
here’s an example:
say there’s a warehouse with 4000 pallets of product that turns ~4 times per year. do we have enough labor to support these transactions? using little’s law, we get
4,000 = λ(.25year)
so,
λ = 16,000 pallets/year
assuming a 10 hour shift per day of about 250 working days per year, there is roughly 2,000 working hours. this means, then,
λ = 8 pallets/hour
the analysis above is critically important to estimate the labor force required to move pallets, receive product, move product, and get work done, in general.
there are many more applications of queueing theory that i will explicate and share in the next while. queueing theory is a critical, underused, but very valuable principle in business.
www.comp-nerds.co.nr said,
May 20, 2006 @ 3:37 pm
If you found this article interesting, please digg it at: http://digg.com/technology/queueing_theory so more people will find it.
shmula » queueing theory: part 2+ said,
June 15, 2006 @ 6:34 am
[...] June 15, 2006 at 6:03 am · Filed under business Earlier, we discussed Queueing Theory and Little’s Law. [...]
Mark Graban said,
June 15, 2006 @ 7:51 am
Little’s Law is an incredbly helpful tool for operations. I highly recommend the Hopp and Spearman book “Factory Physics”, which spends a lot of time on Little’s Law.
Another way of thinking about this is:
Throughput = WIP / CT
WIP = Work in Process
You have to be careful with Little’s Law and resist the temptation to think “all I have to do to increase Throughput is to increase WIP”. It doesn’t work that way, not that Peter was implying that. I’m just saying that’s a common mis-application of Little’s Law.
When you start with zero WIP, you will have zero throughput. Makes sense, right? At first, as WIP increases, your throughput will increase somewhat linearly. But, as capacity utilization reaches 80% or so, throughput levels out and Cycle Time explodes. That’s why really busy systems (factories, emergency rooms, etc.) have very long waiting times. The Cycle Time explosion is made worse with variation. The more variation you have in customer demand and service time, the worse the Cycle Time explosion is. That’s why leveling (heijunka) is key…. on to Peter’s second post, I’m looking forward to reading it.
This Industrial Engineer is just happy to see anyone discussing Little’s Law.
Mark Graban said,
June 15, 2006 @ 7:53 am
One problem with your analysis there is that you’re assuming demand (and labor needs) are constant throughout the year. I’m certain that wouldn’t be the case for Amazon or any retailer.
shmula » Queueing Theory: Part 3 said,
August 14, 2006 @ 3:22 pm
[...] I previously wrote on Queueing Theory and titled those posts as Queueing Theory: Part 1 and Queueing Theory: Part 2. Today, I’ll briefly explain how to set-up a model in Microsoft Excel to simulate a Single-Server Queue. [...]
YAMAHA MOTORCYCLE AFTERMARKET PART » shmula queueing theory: part (Yamaha motorcycle aftermarket part) 1 said,
September 20, 2006 @ 1:12 pm
[...] shmula queueing theory: part 1a queueing system is a model with the following structure: customers arrive and join a queue to wait for service given by n servers. after receiving service, the customer exits the system. a [...]
shmula » What is Waste? said,
October 18, 2006 @ 12:00 pm
[...] queueing theory: part 1 [...]
shmula » Call Centers as Queueing Systems : business, operations management, technology, and stuff in between said,
October 20, 2006 @ 4:07 pm
[...] queueing theory: part 1 [...]
shmula » Travel Time & Waste : business, operations management, technology, and stuff in between said,
October 31, 2006 @ 11:04 am
[...] queueing theory: part 1 [...]
shmula » queueing theory: part 2+ : business, operations management, technology, and stuff in between said,
November 1, 2006 @ 11:27 am
[...] queueing theory: part 1 [...]
shmula » Queueing Theory: Part 4 : business, operations management, technology, and stuff in between said,
November 1, 2006 @ 11:40 am
[...] queueing theory: part 1 [...]
shmula » On Time-Traps and Waste : business, operations management, technology, and stuff in between said,
November 1, 2006 @ 1:50 pm
[...] queueing theory: part 1 [...]
shmula » Little’s Law for Product Development : Business, Technology, and Stuff in Between said,
December 28, 2006 @ 3:27 pm
[...] An Ajax-y Google The Pareto Principle “The Long Tail” Ad Naseaum Lean for Software On Time-traps and Waste All Articles on Operations Agile & Team Size Featuritis & The Customer Click-to-Ship Optimization On Game Theory & Digg Queueing Theory, #1 Amazon.com Insider Stories Totalitarian Powerpoint Rejecting Google’s Job Offer Disruptive Company Interviews The State of the Craposphere M&A Mashup: Google, Yahoo, Microsoft Theory of Constraints & Drum, Buffer, Rope Root Cause Analysis [...]
shmula » Shmula Goes Camping: Drum-Buffer-Rope : Business, Technology, and Stuff in Between said,
December 30, 2006 @ 4:35 pm
[...] Company Interviews The State of the Craposphere M&A Mashup: Google, Yahoo, Microsoft Theory of Constraints & Drum, Buffer, Rope Root CauseAnalysis [...]
Richard Karpinski said,
November 23, 2007 @ 11:48 am
“assuming a 10 hour shift per day of about 250 working days per year, there is roughly 2,000 working hours.”
This works only if the 10 is in octal notation.
Customer Service: an iPhone Case Study | shmula said,
April 9, 2008 @ 6:28 pm
[...] Queueing Theory: Part 1 [...]
On Customer Obsession | shmula said,
April 15, 2008 @ 10:56 am
[...] Queueing Theory: Part 1 [...]
Customers Feel the Difference, Not the Average | shmula said,
April 23, 2008 @ 1:26 am
[...] Queueing Theory: Part 1 [...]