Grosch's law
Encyclopedia
Grosch's law is the following observation about computer
performance made by Herb Grosch
in 1965:
This adage
is more commonly stated as
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 might have prompted Thomas J. Watson
to predict at the time a total global computing market of five mainframe computer
s.
To provide a modern example: this law states, that to have a computer one hundred times as powerful as a modern PC
the owner would need to pay only ten times as much.
cloud computing, [but] he was correct in his assumption that significant economies of scale and efficiencies could be achieved by relying on massive, centralized data centers rather than an over-reliance on storage in end units."
, 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.
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
performance made by Herb Grosch
Herb Grosch
Herbert Reuben John Grosch was an early computer scientist, perhaps best known for Grosch's law, which he formulated in 1950. Grosch's Law is an aphorism that states "economy is as the square root of the speed."...
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
Adage
An adage is a short but memorable saying which holds some important fact of experience that is considered true by many people, or that has gained some credibility through its long use....
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.
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 might have prompted Thomas J. Watson
Thomas J. Watson
Thomas John Watson, Sr. was president of International Business Machines , who oversaw that company's growth into an international force from 1914 to 1956...
to predict at the time a total global computing market of five mainframe computer
Mainframe computer
Mainframes are powerful computers used primarily by corporate and governmental organizations for critical applications, bulk data processing such as census, industry and consumer statistics, enterprise resource planning, and financial transaction processing.The term originally referred to the...
s.
To provide a modern example: this law states, that to have a computer one hundred times as powerful as a modern PC
Personal computer
A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...
the owner would need to pay only ten 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." 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." 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. However, some scholars have recently rehabilitated Grosch's law, looking at the history of cloud computing and claiming that "Grosch was wrong about the cost model ofcloud computing, [but] he was correct in his assumption that significant economies of scale and efficiencies could be achieved by relying on massive, centralized data centers rather than an over-reliance on storage in end units."
Law applied to clusters
For clustersCluster (computing)
A computer cluster is a group of linked computers, working together closely thus in many respects forming a single computer. The components of a cluster are commonly, but not always, connected to each other through fast local area networks...
, 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
Google
Google Inc. is an American multinational public corporation invested in Internet search, cloud computing, and advertising technologies. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program...
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.