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Queuing Theory Articles

Queueing Theory is is the mathematical study of waiting lines, or queues. Queueing Theory enables mathematical analysis of several related processes, including the following:

On average, how many will arrive at the (back of the line) queue?
On average, how long will one wait in the queue?
On average, how long will one wait until being served at the front of the queue?

Below are several posts on Queueing Theory. I’ll be adding to this page periodically — applications, best practices, and general items:

Psychology of Queueing & Disneyland

by Pete Abilla on March 26, 2007

I went on vacation last week to Disneyland. We had a lot of fun. It was also a time to learn how organizations like Disneyland deal with queueing challenges, especially with systems under high stress and load. In this post, I want to cover the Psychology of Queueing and how Disneyland satisfies several of the [...]

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YouTube’s Queueing Properties

by Pete Abilla on March 1, 2007

YouTube has many intriguing queueing properties. This article will primarily look at the mpeg-to-swf conversion and study out the queueing properties of that process. I’ll show the basic process of how to upload a video on Youtube, explain the Queueing mechanics that goes on behind-the-scenes, propose a few books in case you’re interested in Queueing [...]

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Little’s Law for Product Development

by Pete Abilla on November 27, 2006

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 [...]

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Recognizing Constraints & Bottlenecks

by Pete Abilla on November 13, 2006

All dynamic systems — online or offline — consists of discrete and dependent processes. Each step in the system has a finite capacity. When one step is feeding more than what the next step can handle, you’ll have yourself a constraint. Constraints or Bottlenecks aren’t bad, they’re expected and are found in any process. The [...]

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Psychology of Queueing & Build-A-Bear Workshop

by Pete Abilla on November 10, 2006

Last Saturday, we celbrated my daughter’s birthday. For her birthday, we took her and 13 of her friends to Build-A-Bear Workshop, which is a business that where you can: Choose your Bear Create a voice for your Bear Stuff the Bear Stitch the Bear Fluff the Bear Dress the Bear Name the Bear Then go [...]

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Travel Time & Waste

by Pete Abilla on October 31, 2006

There are 3 types of activities, 2 of which produce waste: Steps that definitely create value. Steps that create no value, but are necessary given the current state of the system. Steps that create no value and can be eliminated. (2) & (3) naturally create wastes, of which there are 7 types: Over-Production: Producing more [...]

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Call Centers as Queueing Systems

by Pete Abilla on October 20, 2006

It’s clear that a Call Center is a Queue. The flow of calls begins with K trunk lines that connect to the Call Center. There are w ≤ k work stations, or seats, at which N ≤ w agents serve incoming calls. An arriving call that finds all k trunk lines occupied (let’s assume there [...]

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