Wednesday, March 16, 2005

A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections

A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections

Abstract. Metcalfe's Law states that the value of a communications network
is proportional to the square of the size of the network. It is widely accepted
and frequently cited. However, there are several arguments that this rule is a
signi¯cant overestimate. (Therefore Reed's Law is even more of an overestimate,
since it says that the value of a network grows exponentially, in the mathemat-
ical sense, in network size.) This note presents several quantitative arguments
that suggest the value of a general communication network of size n grows like
n log(n). This growth rate is faster than the linear growth, of order n, that,
according to Sarnof's Law, governs the value of a broadcast network. On the
other hand, it is much slower than the quadratic growth of Metcalfe's Law, and
helps explain the failure of the dot-com and telecom booms, as well as why net-
work interconnection (such as peering on the Internet) remains a controversial
issue.