Grosch's law

Grosch's law is the following observation about computer performance made by Herb Grosch in 1965:

There is a fundamental rule, which I modestly call "Grosch's law", giving added economy only as the square root of the increase in speed -- that is, to do a calculation 10 times as cheaply you must do it 100 times as fast.

This adage is more commonly stated as

Computer performance increases as the square of the cost. If computer A costs twice as much as computer B, you should expect computer A to be four times as fast as computer B.cite book
author=Lobur, Julia; Null, Linda
title=The Essentials of Computer Organization And Architecture
publisher=Jones & Bartlett Pub
year=2006
isbn=0-7637-3769-0
url=http://books.google.pl/books?id=QGPHAl9GE-IC
pages=pp. 589
accessdate=2008-04-02]

The law can also be interpreted as meaning that computers present economies of scale: the more costly is the computer, the price-performance ratio linearly becomes better. This implies that low-cost computers cannot compete in the market. In the end, a few huge machines would serve all the world's computing needs. Supposedly, this could prompt Thomas Watson to predict at the time a total global computing market of five mainframe computers.

To provide a modern example: this law states, that to have a computer 100 times as powerful as a modern PC the owner would need to pay only 10 times as much.

Debates

The relevance of Grosch's law today is a debated subject. Paul Strassmann asserted in 1997, that Grosch's law is now "thoroughly disproved" and serves "as a reminder that the history of economics of computing has had an abundance of unsupported misperceptions." [ [http://www.strassmann.com/pubs/datamation0297/ Will big spending on computers guarantee profitability?] , Paul Strassmann - Excerpts from The Squandered Computer.] Grosch himself has stated that the law was more useful in the 1960s and 1970s than it is today. He originally intended the law to be a "means for pricing computing services." [ [http://www.techweb.com/wire/networking/160701379/ Author Of Grosch's Law Going Strong At 87] , W. David Gardner, TechWeb News, April 12, 2005 - article discussing Grosch's Law and Herb Grosch's personal career.] Grosch also explained that more sophisticated ways of figuring out costs for computer installations mean that his law has limited applicability for today's IT managers.

Law applied to clusters

For clusters, the original Grosch's law would imply that if a cluster contains 50 machines, and it has another 50 added (twice the cost), the resulting 100-machine cluster has a quadruple processing power, which is clearly false. On the contrary, even a linear advance—100-machine cluster twice as powerful as 50-machine—would be a challenge.

When Google was deciding on the architecture for its Web search service, it concluded that scaling up clusters of large or medium-sized computers as the business grew would be too expensive, and opted for arrays of cheap processors and disk drives. [ [http://www.wired.com/wired/archive/14.10/cloudware.html The Information Factories - George Gilder's Article on Cloudware] ]

ee also

*List of eponymous laws
**Metcalfe's law
**Moore's law

References