IP: Erlang's Forumla in the Digital Age

[Dave Farber <farber () cis upenn edu>]

We, in the field knew this for a long time, now it is press feed. djf


From: The Old Bear <oldbear () arctos com> 
Subject: Erlang's Forumla in the Digital Age

INNOVATION
Old rule doesn't apply in new age: Experts find Erlang phone formula 
fails to explain digital traffic jams
by 
Lee Dye 
LA Time Syndicate
Armed with little more than a stopwatch and a good understanding 
of statistics, A. K. Erlang went to a small village shortly after 
the turn of the century and began timing phone calls on the local 
switchboard. His goal was to figure out which percentage of 
callers had to wait for an available line.
Out of that simple project came the basis for something called 
queuing theory and a formula that is still used to help 
communications companies design their systems to meet the needs 
of everything from small communities to global networks.
While it still works for voice calls, Erlang's formula began to 
crumble with the advent of the fax machine and data communications, 
including the Internet.
Much to their astonishment, scientists have learned that Erlang's 
simple formula -- based on the assumption that there is an average 
length for phone calls and a mean traffic rate -- isn't going to 
work for anything but voice communications. Instead of the low 
rumble of the telephone, scientists grappling with Internet 
traffic have found themselves faced with a Gatling gun.
"Erlang's formula started to break down when computers started 
talking to computers," said Robert Calderbank, a vice president 
for research at AT&T Labs in Florham Park, N.J. "When fax 
machines and computers started using the network instead of just 
people, the statistics of traffic started to change."
Calderbank heads an AT&T research project set up to study how 
digital traffic flows through the Internet and what role users 
play in that process. Until they understand that, they don't have 
a prayer of designing systems that will meet the needs of the 21st 
century.
The first discovery was a whopper. Traffic on the World Wide Web 
comes in bursts, rather than in steady flows, and the same 
patterns of bursts are repeated regardless of whether the time 
interval studied is a few seconds long or a millionth of a second.
"It's a true fractal," said Walter Willinger, a member of Calderbank's 
team. By that he means patterns that repeat themselves, regardless of 
the time interval. Such "self-similar" patterns have been found 
throughout nature, giving rise to a new field of mathematics called 
fractals.
"With fractals you look at a coastline and it looks wiggly, 
and then you look at a smaller piece of the coastline and it still 
looks wiggly, and then you look at an even smaller segment, and 
it's still wiggly," Calderbank said. "It looks the same at all 
distance scales." 
Similarly, the same "bursty" patterns of Web traffic appear over 
and over again, regardless of whether the time studied is a 
millisecond or a second. That "bursty" pattern is one of the 
chief reasons networks experience those irritating delays familiar 
to all Web users, Willinger said. 
"The network can be filled up in short periods of time during 
which the user will get very bad performance," Willinger said. 
"If you try to go to a Web server and download a document, you 
might have to wait a couple of seconds or even longer just to get 
connected. One of the links along the Web server can be so 
congested for a small period of time that when you try to use it 
you don't get any response." 
Those delays will surely increase as traffic on the Internet 
continues to grow.
"Once you understand" the bursting effect "you can start dealing 
with questions like, 'How can I control it, how can I manage it, 
what can I do with it?'" Willinger said.
But why would digital traffic be that different from voice 
communications, especially in today's global networks? Why don't 
the peaks and valleys offset each other, since peak demands in Los 
Angeles are at different times than in London, for example?
The answer, Calderbank said, lies in how we use the Net. In voice 
communications, we make short phone calls and long phone calls, 
and they tend to average out. But differences in the amount of 
data we ship over the Internet are far more extreme, ranging from 
very short, such as email, to "incredibly long," such as sending a 
portfolio of high-resolution images, Calderbank said.
Anna Gilbert has been using "a kind of microscope to study the 
level of traffic on AT&T's network over the last six years. 
"It allows you to zoom in on particular times," she said. 
Through a technique called "wavelet decomposition," Gilbert can 
break down the packets of digital information at any point in 
time.
It was by plotting that information that scientists discovered the 
fractal nature of Internet traffic.
Network designers want to know precisely what is causing the 
bursting so they can build better systems for the future. And for 
that, the researchers are concentrating on analyzing very short 
periods of time, down to fractions of a millionth of a second
It's a tattle like analyzing earthquakes in Southern California," 
Calderbank said. "Something very interesting happened in a very 
short period of time, and it's important to understand exactly 
what happened in that very small amount of time."