BBC Home

Explore the BBC

Front Page

Life | The Universe | Everything | Advanced Search
 
Front PageReadTalkContributeHelp!FeedbackWho is Online

Click here to complete your registration.

 
3. Everything / Maths, Science & Technology / Mathematics

Little's Result

There are few ideas that are common over all types of system modelling, in all places, but Little's Result, otherwise known as Little's Law, or Little's Theorem, is one of them. In plain English, it says:

The average number of customers in a system (over some time interval) is equal to their average arrival rate, multiplied by their average time in the system.

This requires no assumptions about how people arrive, how they leave, and whether handbag wielding OAPs always get to the front of the queue. It's actually a comparatively recent result - it was first proved by JDC Little in 1961.

Handily, his result applies to any system, and it particularly applies to systems within systems. So in a bank, the queue might be one subsystem and each of the tellers another subsystem; within such a structure, Little's Result could be applied to each one, as well as the whole thing. The only requirement is that the system is stable - it can't be in some transition state such as just starting up or just shutting down.

A Small Example

Imagine a small shop with a single counter and an area for browsing where only one person can be at the counter at a time, so the system is roughly:

Entrance -> Browsing -> Counter -> Exit

The three important measures are the average time people take at the counter, the utilisation of the counter, and the rate at which people move through the system. The rate is what the shop wants to maximise.

So all we do is apply Little's Result to the counter. This shows that the number of people on average at the counter is the rate at which they move through the system, multiplied by the time it takes to serve them. Since the number of people at the counter is just the utilisation, it can therefore be shown that the rate is given by the utilisation, divided by the time per customer.

Therefore, to create a really productive shop you should strive to take as little time as possible ringing up the bill and you should try to keep your counter as busy as possible. In practice, the latter means walking up to people who seem to be taking their time browsing and saying 'Can I help you' in an annoying fashion. Other ways to increase the counter utilisation might be to have more people in the shop browsing or to have a queue.


Discuss this Entry  People have been talking about this Guide Entry. Here are the most recent Conversations:

But is it useful?
(Last Posting: May 22, 2001)




Add your Opinion!

There are tens of thousands of h2g2 Guide Entries, written by our Researchers. If you want to be able to add your own opinions to the Guide, simply become a member as an h2g2 Researcher. Tell me More!

 
Entry Data
Entry ID: A516782 (Edited)

Written and Researched by:
U129960

Edited by:
U276


Date: 16   March   2001


Text only
Like this page?
Send it to a friend


Most of the content on this site is created by h2g2's Researchers, who are members of the public. The views expressed are theirs and unless specifically stated are not those of the BBC. The BBC is not responsible for the content of any external sites referenced. In the event that you consider anything on this page to be in breach of the site's House Rules, please click here to alert our Moderation Team. For any other comments, please start a Conversation below.
 


Front PageReadTalkContributeHelp!FeedbackWho is Online

Most of the content on h2g2 is created by h2g2's Researchers, who are members of the public. The views expressed are theirs and unless specifically stated are not those of the BBC. The BBC is not responsible for the content of any external sites referenced. In the event that you consider anything on this page to be in breach of the site's House Rules, please click here. For any other comments, please start a Conversation above.


About the BBC | Help | Terms of Use | Privacy & Cookies Policy