\documentclass[11pt]{article}
\usepackage{times}
\input amssym.def
\input amssym.tex
\usepackage{epsfig,psfig}
\setlength{\textwidth}{6.2in}
\setlength{\textheight}{9in}
\setlength{\oddsidemargin}{.2in}
\setlength{\topmargin}{-0.25in}
\setlength{\headheight}{0in}
\makeatletter
\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\normalsize\bf}}
\makeatother
\makeatletter
\def\subsection{\@startsection {subsection}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\normalsize\bf}}
% put a period after section or subsection number in header
\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip .75em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
          \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
        \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #7}\else
        \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
% put a period after theorem and theorem-like numbers
\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\bf #1\ #2.}]}
\makeatother
\thispagestyle{empty}
\begin{document}
\begin{center}
{\Large {\bf The size and growth rate of the Internet}} \\
\vspace{\baselineskip}
K. G. Coffman \\
A. M. Odlyzko \\
\vspace{0.5\baselineskip}
AT\&T Labs - Research \\
kgc@research.att.com, amo@research.att.com \\
\vspace{\baselineskip}
Revised version, October 2, 1998.
\vspace{.5\baselineskip}
\end{center}
\setlength{\baselineskip}{1.5\baselineskip}

\paragraph{Abstract.}

The public Internet is currently far smaller, in both capacity
and traffic, than the switched voice network.  The private line networks
are considerably larger in aggregate capacity than the Internet.
They are
about as large as the voice network in the
U.S., but carry less traffic.  On the other hand, the growth rate
of traffic on the public Internet, while lower than is often cited,
is still about 100\% per year, much higher than for traffic on
other networks.
Hence, if present growth trends continue,
data traffic in the U.S. will overtake voice traffic
around the year 2002 and will be dominated by the Internet.

\section{Introduction}

There are many predictions of when data traffic will overtake voice.
It either happened yesterday, or will happen today, tomorrow, next
week, or perhaps only in 2007.  There are also wildly differing estimates
for the growth rate of the Internet.  The number of Internet users
is variously given as increasing at 20 or 50 percent per year,
and the traffic on the Internet is sometimes reported as doubling
every three months, even in sober government reports such as [DOC].  
Often the same source contains seemingly contradictory
information.  For example, John Sidgmore, the chief operating
officer for WorldCom, and the person in charge of all its Internet
activities, gave an interview (apparently held in early 1998)
that was published in [Sidgmore].  He stated that revenues from 
Internet operations at
WorldCom were about doubling each year.  Later in the interview,
he said that the bandwidth of
UUNet's Internet links was increasing 10-fold each year.  Since the prices
that UUNet charges have not decreased recently, certainly not
by a factor of 5,
both of these claims can be correct only if something
unusual is happening to the WorldCom network.

Since there is no comprehensive source for information
on the size and growth rate of the Internet, it seemed worthwhile 
to do as careful an
analysis as the fragmentary publicly available data allows.
This is especially important because, as we point out below, the 
growth rate of the Internet has not been stable.

In this study we focus on the
sizes of networks (measured by their transmission capacity)
and the traffic they carry (measured in bytes).  We find that
the public Internet (the part of the Internet that is not
restricted to users from any single organization) is still
small, whether measured in capacity of links or in traffic,
when compared to the voice telephone network.  (This may
not be true for all routes.  There are frequent reports, for
example, that there is more Internet traffic than voice
traffic between the U.S. and Scandinavia.)  In contrast,
the private parts of the Internet (largely corporate
private line networks) already have capacity close to that of
the voice network.  On the other hand, traffic on private
line networks is still much smaller than that on the voice
network, possibly not much bigger than traffic
on the public Internet.

In modeling the transition to a network dominated by
data it appears important to recognize three distinct
growth rates:  

(i) Interstate voice traffic (which carries 
some fax and modem data) has been growing recently
about 8\% a year when measured in minutes of use.
This is an acceleration from 
the 4\% rates of the
early 1990s, but not as fast as the record 23\% increase in 1984,
or the average of 10.3\% per year that was observed during
the 1980s.  (See Table 12.1 in [FCC2] or [FCC3] for precise numbers.
Revenue growth has been far lower as prices have dropped, which
was undoubtedly the major reason for the increase in calls.)

(ii) Capacity and presumably traffic
on private line networks have been growing 15\% to 20\%
per year in the last few years [VS].  

(iii) Traffic and capacity of the public Internet grew at rates of about
100\% per year in the early 1990s.  There was then a brief
period of explosive growth in 1995 and 1996.  During those
two years, traffic grew by a factor of about 100, which is
about 1,000\% per year.
In 1997, it appears that traffic growth has slowed down to
about 100\% per year.  

Traffic on the Frame Relay semi-public
data networks is also growing about 100\% per year.  (We refer to
Frame Relay and ATM networks as semi-public, since they carry
traffic from many sources, but almost universally from a source
within an organization to a destination within the same organization.
In contrast, public networks like the voice network and the Internet
allow connections of any source to any destination.)

Reports, such as [DOC], which claim 1,000\% growth rates for the Internet,
appear to be inaccurate today, since they are
based on a brief period of anomalously
rapid growth a short while ago.  
(The claim in [DOC] is based on the report [Inktomi]
that uses data no more recent than the end of 1996, the end of the period of
abnormally fast growth.)  Still, even a doubling each year is fantastically
fast by the standards of the communications industry.

If traffic on the Internet continues to double each year,
data should exceed voice on U.S. long distance
networks around the year 2002.  (We are using data here to refer
to packet traffic, and voice to the circuit switched traffic,
whether those are used to carry voice or data.)
There are obvious uncertainties
in making such projections, but in Section 8 we discuss the
long historical trend of consistently rapid growth of the
Internet, and the reasons we expect it to continue. 

Our estimates of the transition date from domination by
voice to domination by data differ from many published ones.
Most of the claims (such as that of [Thyfault], which says that
the bandwidth of data networks will equal that devoted to
voice in 2000) are not substantiated by detailed analysis
and appear incorrect, as that transition is occurring about
now, it appears.
The analysis of [MutooniT]
appears to go astray by assuming utilization
rates of data and voice networks are about the same.  However,
as is shown in the companion paper [Odlyzko1] and discussed
at greater length in Section 7 below, data networks
typically are used much less intensively
than voice networks.  Thus network capacities do not
represent the amount of traffic those networks carry.
Finally, there are claims (such as in some of the presentations
of Vint Cerf [Cerf]) which may agree with our prediction
of a transition around 2002, but they are not accompanied
by detailed arguments.




\section{What to measure and how}

Many studies of the Internet look at the number of users (cf. [Nua]).
This is the most relevant measure for some purposes, although it
is inadequate for others, as it does not say anything about
the intensity of usage.
Other studies measure the Internet's size by the number 
of computers connected to it
(cf. [ITU] and Table 7 in this paper, both based on data from [NW]).
In this study we focus on the
sizes of networks and the traffic they carry.  

Since the Internet
is a loose collection of networks, it is hard to decide what
to include in estimating its size. See Fig. 1 for a sketch of
the universe of data networks and the role that the public
Internet plays in it.  A key point is that what is commonly
thought of as the Internet, namely the public backbones
connecting all the local networks, is only a small part of the
data networking universe.  Most data traffic, just like most voice phone
traffic, is local.  Also, most of the cost of data and voice
communications is associated with local facilities.  For example,
universities tend to devote between 10\% and 20\% of their
network budget (counting the cost of people as well as
equipment and services obtained from carriers) to Internet
connections.  In voice telephony, of the approximately
\$200 billion that is spent in the USA each year, only about \$80
billion is for long-distance (inter-LATA) calls.  Moreover,
of that \$80 billion, about \$30 billion is paid to the local
carriers in access charges, so the true long-distance component of
the cost to the public is
around \$50 billion, only about a quarter of the total for the
voice system.

Although most of the cost of telecommunications networks
is for local facilities, we consider long-distance transport only.
The economics and patterns of usage of local facilities are
different (see [Odlyzko2] for more extensive discussion of
this point).  Studies of data
as well as voice communications have historically concentrated
on long haul circuits.  They are the most heavily utilized
and also the most difficult or expensive to upgrade,
so sophisticated
engineering and pricing approaches are most appropriate there.
We will follow this precedent, and will not consider the LANs and WANs.  
Similarly, we will not consider local access links, such as the 
phone lines used
by residential Internet users to connect to their ISPs or to make
local voice calls. 
While we cannot avoid comparing apples to oranges, we
try not to compare apples to orange trees.

Unlike
most studies of the Internet, we consider not only the public
Internet, but also the long-distance private line networks.  
These networks are estimated to mostly use IP (Internet Protocol), and,
as we show,
are far larger in both cost and bandwidth (but not necessarily in
traffic carried) than the public Internet.
The evolution of the Internet in the next few years is likely
to be determined by those private networks, especially by
the rate at which they are replaced by VPNs (Virtual Private
Networks) running over the public Internet.
Thus it is important to understand how large they are and
how they behave.

In this study,
we consider only U.S. networks.  These networks still account for between
60\% and 70\% of users and host computers in the world [ITU, Nua], and
almost surely a higher fraction of capacity and
traffic, since transmission costs much less in the U.S. than in most
of the world [ITU].  It is also easier to obtain data for
North America.  Further, most countries are striving to
lower their telecommunications costs, and so the patterns
we observe in the USA are likely to be replicated elsewhere
in the next few year.  The
geographical restriction does mean, however, that the equality
of data and voice traffic we predict for 2002 applies
only to the U.S., and the crossover is likely to be
somewhat later in most other countries.

Even in the U.S., we exclude government networks from consideration.
We also do not consider research networks such as vBNS, 
since they carry little
traffic, although they do have substantial capacity (as we will
mention).

We consider only lines that are used for carrying
voice and data traffic.  The capacities of the underlying
fiber networks (cf. [FCC1]) are far higher than those we
will be listing.  It would take us too far afield to try
to explain the disparity in the estimates, but they
have to do with differences between air distances and
fiber route distances, presence of dark fiber,
restoration capacity, and other factors.




\section{Costs and prices and the decline of distance}

We study capacities of networks and the traffic they carry.
We measure these in Gbps (gigabits per second, $10^9$ bits per
second) and TB/month
(terabytes per month, $10^{12}$ bytes per month).  However, 
it seems intuitive that
a terabyte carried between Baltimore and Philadelphia is not
equivalent to a terabyte between Baltimore and San Francisco.
Thus a more complete description of communications traffic
should incorporate a measure of how far that traffic travels.  Distance 
does play an important role in the evolution
of networks.  For example, an important reason cited for the migration
of corporate data traffic to the public Frame Relay networks
is that charging for Frame Relay is insensitive to distance,
making it much less expensive for long distance communications
[Cavanagh].  

While distance does play a role in telecommunications, it is a decreasing role.
(See the book [Cairncross] for general discussions of this
phenomenon, and its likely effects.)
The monthly tariffs for interstate T1 leased
lines from MCI (quoted from [Leida]) consist of a fixed fee
of \$3,234 and \$3.87 for each mile.  (The corresponding figures
for a T3 are \$22,236 and \$52.07, respectively, so the
distance dependence is stronger for higher capacity links,
a phenomenon we expect to continue.) 
For the typical 300-mile leased circuit distance, the fixed
fee is 73.6\% of the cost of a T1, and 58.7\% for a T3, 
and a more representative
cost estimate would show much greater share for fixed costs,
since it would include local connections and lease of
terminating equipment.  (The figures in Table 3
are for all-inclusive costs of private lines of various speeds,
and for a 56 Kbps line include 57\% for local access costs.
It should be noted, as is detailed in [Leida], for example,
that customers typically lower their costs by up to 50\% through
long-term contracts and bulk purchase discounts.)
The historical trend in pricing of a T1 connection is
shown in Fig. 2, which displays the tariffed rates
for a T1 line of 700 miles, broken down 
into fixed and mileage-sensitive components, from the time
this service was first offered until the end of 1997.  
Even at such a large distance, the distance-sensitive part
of the price has decreased rapidly.

The decreasing role of distance can also be seen in the
voice telephony price structure.  As is shown in Table 14.2
of [FCC2], in the early 1980s there were many rates
for interstate calls, depending on both distance and
time of day.  Today there is still some variation
depending on time of day, even though that is
also decreasing (see [Odlyzko2] for a discussion),
but calls are priced independently of distance (within
the U.S.).  This reflects the decreasing fraction of
the price that goes to cover network costs.  It is
estimated that of the 12 cents a minute
that carriers collect on average for a voice call within
the U.S., only about 1.5 cents is needed to pay for the
network.  (By far the largest component of cost is the approximately
5 cents a minute of access charges paid to local carriers
largely to subsidize local service.)

The discussion above was intended to show that
while our analysis does ignore important factors of
distance, it is reasonable to do so as a first
approximation.  In further defense of our approach, let 
us mention that most communication is still local.
This was apparently first noted in the 19th century by 
Carey and others (see Chapter 11 of [Isard]), 
but is best known from the work of
Zipf [Zipf], who collected
a variety of statistics on communication and transportation
patterns.  Zipf observed that whether one measured phone calls,
car travel, or mail usage, the interaction between two
cities with populations A and B at distance D appeared to
be proportional to $A \ast B/D^\alpha$, with $\alpha = 1$.  Other
investigators since that time have found better fit
for other values of $\alpha$, typically with $1 \le \alpha \le 2$.
Even services with distance-insensitive fees, such
as mail, appear to be closely tied to social interactions,
and are mostly local.  That is certainly the case for
usage of the telephone network.
Interstate voice calls on average go over 500 air miles,
while private lines are on average about 300 air miles
in length.

A fascinating topic for further research is whether
Zipf's observations will apply to the Internet.
In voice telephony, the last 20 years have seen a growth
in interstate and intrastate toll calls from 8 minutes per line 
per day to 14 minutes, while local calling has stayed about
constant at 40 minutes (Table 12.2 of [FCC2]).  This was presumably caused by
the decline in long-distance prices and the greater mobility
of the population.  Still, most calls are local, and even
in the interstate calling case, the intensity of calls drops
off with distance, as Zipf observed.  The Internet is a world-wide network,
and much traffic comes from downloading from popular Web servers,
many of which appear to be located in California.  On the other
hand, a disproportionate share of Internet traffic is within
California in any event (as is seen by examining the backbone
maps in [Boardwatch]), so it could be that most traffic is local
even on the Internet.
Even if that is not the case now, the penetration of the
Internet into everyday life may mean that Internet traffic
will again follow patterns of our everyday social and
economic interactions, and be largely local in the future.
Further, even if there is no trend towards local information sources,
the spread of caching may mean that most packets will be
transported over short distances.
Additional investigation is clearly desirable, especially since
the speed with which it is economical to deploy  
some novel transport technologies depends on the 
distances over which
traffic is to be carried.



\section{Units of measurement}

It will be convenient to state some conversion factors
between different units and between the bandwidth of a connection and
the traffic carried by that connection.  Since there is substantial
uncertainty about many estimates, we will not attempt to achieve
precision, and will often not worry about 10\% differences.

Voice on phone networks is carried in digitized form at 64,000 bits
per second.  Each voice call
occupies two channels, one in each direction, so takes up 128,000
bps of network bandwidth.  Thus one minute of a voice call takes 60*128*1000
bits, or 937.5 KB (kilobytes, units of $1024 = 2^{10}$ bytes).  
Rounding this off, we get
\begin{quote}
   1 minute of switched voice traffic $\stackrel{=}{\sim} 1$ MB.
\end{quote}
(There is a discrepancy between the meaning of the ``$k$'' or ``$K$''
prefixes, which commonly denote 1000 in communication and
$1024 = 2^{10}$ in computing.  Given the lack of precision in most
of the estimates we will be dealing with, this difference will
be immaterial and will be ignored.)
Compression can reduce that to a much smaller figure, and is used to
some extent on high-cost international circuits, as well as on some
corporate private line networks.  As far as the network is concerned,
though, it is carrying almost 1 MB of digital data for each minute of a voice
call.  Further, most data traffic can also be compressed, so we
will ignore this factor.

A T3 (or DS3) line operates at 45 Mbps (actually, closer to 43 Mbps,
but again we won't worry about this discrepancy) in each direction, so that if
it were fully loaded, it would carry 90 Mbps.  Over a full month of 30
days, that comes to 29 TB (terabytes, which are $10^{12}$ bytes).  We will say that
\begin{quote}
  full capacity of a T3 link $\stackrel{=}{\sim} 30$ TB/month.
\end{quote}
A T1 line (1.5 Mbps) is 1/28-th of a T3, and we will say that
\begin{quote}
  full capacity of a T1 link $\stackrel{=}{\sim} 1$ TB/month.
\end{quote}


\section{Voice networks}

The FCC collects and publishes comprehensive statistics
on long-distance switched voice networks.  They show that
at the end of 1997, U.S. carriers had about 40 billion voice minutes
per month of interstate traffic on their public networks (Table 11.1
of [FCC2]), which
is about 40,000 TB/month.  This number has recently been growing at about
8\% per year (Table 12.1 of [FCC2] and [FCC3]).  Including local and intrastate
toll traffic boosts the estimate to about 275,000 TB/month.  (Table 12.1
of [FCC2] also shows that since 1980, intrastate and interstate toll
calls have grown from 7\% and 8\%, respectively, of switched voice
minutes, to 11\% and 15\%, another sign of the declining role of
distance.)

The 40,000 TB/month figure for long distance switched network
traffic includes a large but unknown fraction of fax
and modem calls, which carry data.  However, since they appear
on the network as switched calls, they will be counted as voice.

Defining long distance traffic is easy compared to defining what
is meant by long distance network capacity.  There are various
special connections for operator services, 800 number services,
and the like.  We consider just the long distance lines between
large switches.  Then known distributions of traffic over
a week, achievable busy hour utilizations, and reserve capacity
rules of thumb (all described in the literature, for example
in Figure 1.13, Table 1.8, and discussion on p. 49 of [Ash])
show that the average utilization of such links is around 33\%.
Combined with the traffic estimates above, this shows that
all the switched voice networks in the U.S. had capacity of
around 350 Gbps at the end of 1997.



\section{The public Internet}

There are many estimates of the size and growth rate of the
Internet that are either implausible, or inconsistent, or
even clearly wrong.  We already cited the Sidgmore interview
[Sidgmore] as an example.  In a somewhat different vein,
the article [Gareiss] claimed that one third of Internet
traffic went through the MAE East peering point.  While
it is probably true that at the time [Gareiss] was written,
about one third of the traffic that went through public
peering points went through MAE East, this traffic was
only a part of total Internet backbone traffic.

The major reason for the uncertainties in measuring the
Internet is that carriers do not release detailed
information about their networks.  
As a result, any estimates made from publicly
available data will necessarily have a large error margin.

As a first step, to provide a "sanity check" on other estimates,
we consider the traffic generated by residential users accessing
the Internet with a modem.  There are about 20 million of them
(or, more precisely, there are about 20 million active accounts)
and according to the latest information from America Online and
other services, on average an account is
connected about 25 hours each month.
These users download data at a rate of about 5 Kbps when
they are online (with considerably smaller average upload rates), which
generates traffic load of just about 1,000 TB/month.  (To the
voice phone network, which dedicates 128 Kbps for each connection, the
load appears as 26,000 TB/month, about 10\% of the total load
of voice calls, local and long distance.)  
Since there are more PCs in corporate environments than at home,
we should expect to see total Internet
traffic of at least twice that, or 2,000 TB/month.

We next consider traffic through the public peering points.
Statistics for them are available through the links at [CAIDA, NLANR],
often going back a year or more.  The 5 largest ones are 
shown in Table 1.  The traffic estimates are for the early
part of December 1997 (to avoid the Christmas and New Year holiday
effects).  The other public peering points are much smaller.
Total traffic through all the public peering points is dominated
by that through the 5 points in Table 1, and comes to about
4 Gbps, or 1,200 TB/month.
For comparison, in mid-1996, traffic through these points
was about 1.6 Gbps, or 500 TB/month.  Growth has been uneven,
with especially rapid increase in traffic at the Chicago NAP.
That peering point had traffic of only around 0.2 Gbps
as late as October 1997, but by April 1998 was carrying about
0.7 Gbps.  Overall, though, aggregate traffic through 
the NAPs and MAEs appears to have been growing at about
100\% per year from late 1996 through April 1998.
This agrees with the 100\% growth rates for 1997 for MCI and an
unnamed ISP that are cited in [Schulzrinne].

We assume that little traffic goes through more than a single
peering point.  That assumption appears reasonable, especially
in view of the congestion at the NAPs and MAEs.  What we do
not know how to evaluate with high confidence is the fraction
of Internet traffic that goes through the public peering points.
A substantial part of backbone traffic, which we estimate to
be about 50\%, stays within a single ISP.
(This estimate could easily be too high, and is almost
surely too high for traffic from residential users.  On
the other hand, corporations are increasingly moving
their internal traffic to the Internet, and they appear to
try to stay with a single provider.  Also, many hosting services
have connections to several ISPs, and so much of their traffic
does not have to go through exchange points.)
Even of the traffic
crossing ISP boundaries, some fraction, which we estimate
to be 40\%, goes through a private peering point.  With
these assumptions, we find that about 30\% of all backbone
traffic goes through the NAPs and MAEs.  This leads to
an estimate of backbone traffic of 13 Gbps, or 4,000 TB/month
at the end of 1997.
By comparison, in mid-1996, the estimate was 5.7 Gbps, or 1,800 TB/month.

Another way to measure the Internet is to look at particular
carriers.  MCI is regarded as carrying between 20\% and 30\%
of the backbone traffic.  In mid-1996, MCI press releases
claimed their network was carrying 250 TB/month.  Around
November 1997, Vint Cerf stated that the MCI network was
carrying 140 TB/week (and was growing about 100\% per year)
[Schulzrinne].  In December 1997, the MCI "white paper" [MCI]
said that MCI was carrying 170 TB/week.  A weekly load of
170 TB/week corresponds to about 740 TB/month, and depending
on whether we assume the 20\% or 30\% figure for the MCI
share of backbone traffic, we obtain an estimate of between
2,500 and 3,700 TB/month for all the backbones.

To determine the size of the Internet,
we examined all of the major NSPs (National Service Providers,
the large carriers with backbones extending across the U.S.)
and obtained a bandwidth
capacity for each of these carriers.  Typically, the actual networks
are composed of combinations of T1s, T3s, OC3s, and OC12s.  For
consistency we chose to express the bandwidth capacity in terms of
equivalent T3s.  We realize that a more appropriate metric would be
in terms of circuit miles.  As mentioned earlier in this document a
shorter 100 mile T3 link is much different than a 700 mile T3. In
fact several of the smaller carriers have a large number of short
T3 links (as compared to say MCI and the other large NSPs).
In many cases, it appears that the average lengths
of the T3s in the smaller networks are between 1/3 and 1/5 of that
for the larger NSPs.  Nevertheless, we simply counted the number of
equivalent T3s, and compared.

The data for Internet backbones was obtained from a variety of
sources.  There are extensive listings for many NSPs at [CAIDA],
and we relied on those to a large extent.  However, we often had to
adjust the data there.  For example, the listing for UUNet in
the [CAIDA] files in April 1998 (when we completed our study)
listed the equivalent of about 380 T3s.  A count of the UUNet
backbone links on the UUNet map at [UUNet] showed about 480 T3s
at that time, and if the map were current, that would represent
the state of the UUNet network 
in April 1998.  Since the 4 months between December 1997 and
April 1998 represents about 25\% growth when traffic doubles
each year (as it appears to be doing currently), we assumed
that UUNet had the equivalent of about 400 T3s in their
network at the end of 1997.

In mid-1996 
we estimated the total number of equivalent
backbone T3s to be around 400.  (This may have been an underestimate, and
the value was probably closer to 500.)   At that time we obtained detailed
information on the key carriers, specifically:  AGIS, BBN, PSINET,
UUNet, MCI, Sprint, ANS, and AT\&T.  These eight accounted for about
75\% of the total number.  For December 1997, we  
examined 35 commercial backbone
providers (such as internetMCI and UUNet), and 8 research networks
(such as MAGIC and vBNS).
We found about 2,100 equivalent T3s in the
commercial networks and about 500 equivalent T3s in the research networks,
giving a total of 2,600 equivalent DS3s.  This was the estimate
based on data available in April 1998.  Much of that information
was several months old.  On the other hand, we were trying to measure 
the Internet at the end of 1997, at which point it was probably some 20\%
smaller.  Thus we assume that the two sources of error cancel each
other out, and that the commercial Internet backbones had
the equivalent of about 2,100 T3s in December 1997.  

Table 2 gives some of equivalent T3 counts for several of the
major NSPs (both commercial and R\&D).  We note that 
2,100 T3s represents a 100-fold increase from the 20 or so
in the NSFNet backbone at the end of 1994.  Traffic of
2,500 to 4,000 TB/month at the end of 1997 represents more than a 100-fold
increase from the 15 TB/month carried by NSFNet at its
peak.

Our estimates show considerably greater growth in the sizes
of backbones than in traffic through the NAPs and MAEs between
mid-1996 and end of 1997.  This could be caused by more
traffic bypassing the public peering points.  It could also
be that the rapid growth in traffic during 1995 and 1996
led NSPs to project faster growth than materialized in 1997.
(It takes close to a year to obtain a T3 private line,
since capacity is short at present.)  Another possibility
is that the NSPs were responding to complaints about congestion
and decreasing utilization rates of their networks.  There
are also stories that they may have put in more capacity,
especially of very fast links, than
was absolutely required in order to win battles for
business customers, for whom ability to burst to high speeds and low
utilization rates are attractions.

A network of 2,100 T3s has a bandwidth of 190 Gbps.  However,
that is the total bandwidth of all the links, and could only
be utilized fully if every packet 
went from the node where it enters the backbone to an
adjacent node and exited the network right at that point.
There are studies (see [Schulzrinne] for links) which
show that the average number of hops that a
packet makes on the Internet is around 15.  However, those
studies measure 
all the hops a packet makes, and most of them are in the access part of
the network.  We are looking only at the backbones.
There do not appear to be any comprehensive studies of how many
backbone hops a packet makes.
Statistics for the NSFNet
backbone (available at [NSFNet]) show that towards the end of its
existence, in late 1994, its T3 links were running
around 5\% of capacity.
Next, NSFNet data show transport of about 15 TB/month at that
time.  Since there were 19 T3s in service, a
5\% utilization rate should have led to total traffic of 28.5 TB/month
on all the T3s. This is consistent with NSFNET moving 15 TB/month if
each packet on average traveled over two T3s.  

For the current public Internet, an average of 2.5 hops on the
backbone links per packet appears reasonable.  Experts we have
consulted thought it was about right, and it is also the figure
used in [Leida].  Further, it agrees with some recent
routing data provided by Ramon Caceres (private communication) for various 
Internet connections in the U.S..  If we assume this estimate
of 2.5 hops per packet, the effective bandwidth of the public
Internet becomes 75 Gbps.



\section{Private line networks}

Many private lines are leased by one carrier from another to
carry voice.  Others carry Internet traffic or the traffic
on the semi-public Frame Relay and ATM networks, or else
government traffic.  If we
consider just the so-called retail market, in which lines are
leased to private non-carrier organizations, then industry
statistics (collected by the Vertical Systems Group, [VS])
give the estimates of Table 4.  There are several noteworthy
features of these numbers.  One is that the bulk of the
bandwidth will soon be in T3 lines, yet these lines bring in
only 7\% of the industry revenue.  This explains how bandwidth
has been exploding while leased line revenues have been increasing
at modest rates.  
% Another is that growth has been fastest in
% the high-bandwidth lines.

Adding up the bandwidths in Table 4, we obtain an estimate
of total bandwidth of the private line networks of 630 Gbps,
substantially more than the bandwidth of the voice network.
However, as for the Internet, we have to consider
the effective bandwidth.  Users care just about getting 
a message or a file from point A to point B, and not how it
gets there.  What we don't know is how many private line
links a typical message in a corporate networks traverses.
In the early days of data networking, most corporate networks
appear to have been star-shaped, with branch locations
communicating with a central facility.  In those networks,
usually just a single hop is involved in a message.  However,
recent years have seen development of mesh networks, especially
among the large corporations that are the primary customers
for the T1 and T3 lines that contain the bulk of the bandwidth.
For those networks, it appears reasonable to assume that
on average a message will make two hops.  (Even in star
networks, some fraction of the traffic is between points
on the periphery, which again requires two hops.)
With that two-hop assumption (justified by data from two large
corporate networks)
the effective bandwidth of the private line networks reduces
to about 330 Gbps.

Just as the voice network carries substantial but unknown
proportion of data calls, private line networks are not
all dedicated to data.  Large organizations often use them
to transmit voice calls, especially on international links.
However, the general opinion seems to be that although
at one point this was the main use of private lines,
today it is a minor factor.  We will therefore ignore it.

Traffic on private line networks is much harder to estimate
than their capacity.  The key point of the companion
paper [Odlyzko1] is that conventional capacity utilization
estimates, such as those of [Leida], are almost an order of
magnitude too high.  It is impossible to obtain precise
estimates, since no measurements are taken on many lines,
and even when there are statistics, those are not released.
However, both direct and circumstantial evidence
is presented in [Odlyzko1] for the claim that
private lines are used at
3\% to 5\% of their capacity, when averaged over a full week.
These estimates produce estimates of traffic on private
line networks between 3,000 and 5,000 TB/month.

Finally, we should mention the semi-public Frame Relay and
ATM networks.  No firm figures are available, but industry
estimates (partially based on data in [VS]) suggest the
capacity and traffic estimates in Tables 5 and 6.

\section{Rates and sources of growth}

Voice traffic is currently growing about 8\% per year.
Private line capacity, and presumably also traffic, is
growing at about 15\% to 20\% per year.  The semi-public Frame Relay
and ATM networks are growing about 100\% a year.  (It is
noteworthy that although Frame Relay is sometimes claimed
to be cannibalizing
the leased line business, it is not doing it fast enough
yet to affect the growth of the latter.  Most of the growth
in Frame Relay appears to be coming from new applications.)  Internet
traffic on the NSFNet backbone was doubling each year
between early 1991 and the end of 1994, when the
impending phaseout of NSF support led traffic to shift
to private backbones.  (The growth in NSFNet traffic is shown in Table 8.
The Dec. 1990 entry in that table is extrapolated
from data starting in March 1991.  Otherwise all the numbers
through 1994 are taken from [NSFNet].)

We do not have precise traffic statistics for NSFNet
before 1991.  However, the project overview (available
at [NSFNet]) does mention 
that the number of packets transmitted increased by a factor of 62.5
in the 30 months between July 1988 and January 1992, 
for an annual growth rate 400\%.  
Internet host counts (see Table 7, based on
statistics at [NW]) show slower growth, with
regular doubling each year
throughout the 1980s and 1990s.  Host measurements are unreliable
and hard to interpret, but in general we might expect 
their growth rates to be at least slightly indicative of those of network
traffic.  An extensive study of data traffic through
1993 by Paxson [Paxson] found many volume measures showing
about a doubling each year.

The rapid growth spurt in traffic in 1995 and 1996
was presumably caused by several closely related phenomena.
One was that the Internet caught the public's attention, with
millions of new users signing up for home accounts
or getting access at work.  The other was that user-friendly
Web browsers made the Internet more valuable even than
it would have been otherwise.  (General growth of the
Internet can be ascribed to Metcalfe's Law, which says
that the value of a network is proportional to the square
of the number of users.)  Also, the graphical user interface
of the popular Web browsers led to the creation and use of
illustrations, which consume far more bandwidth than text.
(Some projections for amount of data traffic that in
retrospect can be seen to have been far too conservative, 
such as that on pp. 171-175
of [Noll], erred primarily by not anticipating the growth
of rich graphical content.)
What is remarkable, though, is
that in some networks, the Web did not appear to have
a noticeable effect on the growth rate of traffic.
For example, the Swiss SWITCH network for
academic and research and research institutions
has seen growth in IP traffic by a factor of about
2.5 each year in the 1990s ([Harms] and private communication
with J. Harms covering the period since 1994).

As we explain in Section 6, 
most indications are that after the anomalous
period of 1995 and 1996, when Internet backbone traffic
increased by a factor of 100, it appears that it has
slowed down to a growth rate of about 100\% a year.
The big question is whether this growth rate can be
sustained for long.  We feel that there is no reason
to expect a slowdown in the next decade, and there
could even be periods of more rapid growth.

The 100\% annual growth rates for the Internet
were a result of increase in number of users as
well as increased traffic from existing users.
While there will surely continue to be growth in
users of the Internet, it will not be by a factor
of 100 or even close to it over the next decade,
since that would require more people than live on the Earth.
However, rapid growth has been observed even from
small communities.
The Swiss SWITCH network
was mentioned above.  The University of Waterloo
[Waterloo] also appears to have experienced roughly
a doubling of traffic to and from the Internet each year for
the last five years.  The statistics for their traffic
are shown in Table 9.  (Data is available only for the
month in each school term that had the greatest traffic
during that term.)
The Library of Congress statistics
(Table 10 below, based on data at [LOC]) also show more than
a doubling each year.  Nortel has seen 80\% growth in its
IP traffic volume for the last three years (private communication
from Terry Curtis of Nortel).  Press releases of presentations
by Lew Platt of HP in 1996 and 1997 show that HP's IP traffic
doubled during that year.  Thus it appears that organizations
find IP sufficiently attractive that they double their
traffic each year, although the sources of demand may
change.

Where will future growth come from?  Unlike voice phone traffic,
for which there is a natural limit, since people are not willing
to spend all their time talking to others, there is no obvious
bound on data traffic demand.  For residential
customers, there is a serious current limiting factor in the modems
they have.  However, even without deployment
of new technologies, substantial further growth of the Internet
can come from that source.  America Online reports that its customers
have tripled the time they stay connected, to 45 minutes per
day, in the year and a half that their flat-rate pricing
plan has been in effect.  There is room for
further expansion in this area.  About half the households
in the U.S. have PCs, and of these only half have
residential Internet service.
Further, 45 minutes per day is a small fraction of the time
that American families watch TV.  As more people join the
network, they create more content, and make it more attractive
for others to create content for the Internet, which draws
in more users, and so on, as predicted
by Metcalfe's Law.

Once broadband technologies such as cable modems, various DSL
technologies, or wireless data links are deployed, residential
customers will be able to substantially increase their
traffic per household.  In the very near future, though,
rapid growth is most likely to come from institutions
such as corporations, which have the broadband communication
infrastructure to increase increased traffic.  
Costs of providing local access at T1 speeds to the Internet from
corporate WANs are dropping rapidly with the deployment
of HDSL (although that is not reflected in prices yet),
and fiber will be increasingly feasible for higher speeds. 
Even without novel applications, such as
packet telephony and videoconferencing, ordinary Intranet
and Extranet applications could lead to continued growth
at historic rates.  We could also see spurts of growth
even faster than 100\% per year if some of the novel
applications start growing.  The public Internet could
also grow at high rates if more of the growth in internal
private line networks shifts to it.

It is worth remarking that packet telephony may cause
a spurt in Internet traffic.  However, this is likely
to be just one of many spurts powering the growth of the
Internet, just as streaming audio, for example, is doing
today.
The reason not to expect packet telephony to be a gigantic
influence is that there is not that much
voice traffic to lead to a major change in Internet
traffic statistics.  This may seem paradoxical in view
of the evidence we have presented that there is much more
voice than data traffic.  However, packetization of
voice offers natural opportunities for compression.  The switched
voice network devotes 128 Kbps to each conversation,
whereas decent quality can be obtained with rates of
8 Kbps.  Even if we do not pursue the most aggressive
compression schemes, say in order to keep latencies low,
and digitize voice calls at 32 Kbps, the 40,000 TB/month
of voice traffic becomes 10,000 TB/month, a level
that at present rates of growth the Internet is likely to reach in
less than two years.  Thus the fears about lack
of bandwidth for packet voice transmission, 
such as those in [GMLCOBRS], appear to be unwarranted.



\section{Conclusions}

We have shown that in the U.S., traffic on the public Internet
is under 10\% and bandwidth is around 20\% of the switched
long distance network.  On the other hand, the bandwidth
of the private line networks is already comparable to that
of the voice network, although traffic on them is probably
not much higher than on the public Internet.  Also, the
Internet appears to be growing at 100\% per year, compared
to 15-20\% for private line networks and under 10\% for
the voice network.  Thus if current trends continue, and
there seems to be no reason they should not, data traffic
will overtake voice traffic around the year 2002, and
will be going primarily over the public Internet.

The 100\% annual growth rate of the Internet forces new
ways of thinking about telecommunications.  As one simple
example, the estimates we made are primarily for December 1997.
However, this paper was written four months later, at
which point all the estimates for the Internet in the
tables already have to be increased by about 25\%.





\paragraph{Acknowledgements:}

We thank Vijay Bhagavath, Ehud Gelblum, Jacek Kowalski,
Clem McCalla, Roger Watt,
and Bill Woodcock 
for comments and enlightening information.


\clearpage
\begin{thebibliography}{MM}

\bibitem[Ash]{Ash}
 G. R. Ash, {\em Dynamic Routing in Telecommunications Networks,}
  McGraw Hill, 1998.

\bibitem[Boardwatch]{Boardwatch}
{\em Boardwatch} magazine, $\langle$http://www.boardwatch.com$\rangle$.

\bibitem[CAIDA]{CAIDA}
Cooperative Association for Internet Data Analysis (CAIDA),
  $\langle$http://www.caida.org/$\rangle$.

\bibitem[Cairncross]{Cairncross}
F. Cairncross, {\em The Death of Distance: How the Communications
  Revolution will Change our Lives,} Harvard Business School Press, 1997.

\bibitem[Cavanagh]{Cavanagh}
J. P. Cavanagh, {\em Frame Relay Applications: Business and
  Technical Case Studies,} Morgan Kaufman, 1998.

\bibitem[Cerf]{Cerf}
V. Cerf, PowerPoint slides of presentations, available at
  $\langle$http://www.mci.com/aboutyou/interests/technology/ontech/powerpoint.shtml$\rangle$.

\bibitem[DOC]{DOC}
U.S. Department of Commerce, {\em The Emerging Digital Economy,}
  April 1998.  Available from
  $\langle$http://www.ecommerce.gov/emerging.htm\#$\rangle$.

\bibitem[FCC1]{FCC1}
J. M. Kraushaar, {\em Fiber deployment update: End of year 1996,}
  U.S. Federal Communications Commission, 1997.  Available from 
  $\langle$http://www.fcc.gov/ccb/stats$\rangle$.

\bibitem[FCC2]{FCC2}
U.S. Federal Communications Commission, {\em Trends in Telephone Service,}
  Feb. 1998.  Available from $\langle$http://www.fcc.gov/ccb/stats$\rangle$.

\bibitem[FCC3]{FCC3}
J. Zolnierek, K. Rangos, and J. Eisner, {\em Long Distance Market Shares;
  First Qaurter 1998,} U.S. Federal Communications Commission, June 1998.
  Available from 
  $\langle$http://www.fcc.gov/Bureaus/Common\_Carrier/Reports/FCC-State\_Link/comp.html$\rangle$.

\bibitem[Gareiss]{Gareiss}
R. Gareiss, Is the Internet in Trouble?, {\em Data Communications,}
  Sept. 21, 1997.  Available at
  $\langle$http://www.data.com/roundups/trouble.html$\rangle$.

\bibitem[GMLCOBRS]{GMLCOBRS}
V. Granger, C. McFadden, M. Lambert, S. Carrington,
  J. Oliver, N. Barton, D. Reingold, and K. Still, Net benefits:  The
  Internet - A real or virtual threat, Merrill Lynch report, March 4,
  1998.

\bibitem[Harms]{Harms}
J. Harms, From SWITCH to SWITCH* - extrapolating from a case study,
  {\em Proc. INET'94,} pp. 341-1 to 341-6, available at
  $\langle$http://info.isoc.org/isoc/whatis/conferences/inet/94/papers/index.html$\rangle$.

\bibitem[Inktomi]{Inktomi}
Inktomi white paper, {\em Traffic server: Large scale network
  caches provide more bandwidth for your money,} 1997.  Available at
  $\langle$http://www.inktomi.com/Tech/EconOfLargeScaleCache.html$\rangle$.

\bibitem[Isard]{Isard}
W. Isard, {\em Methods of Regional Analysis,} MIT Press, 1960.

\bibitem[ITU]{ITU}
International Telecommunication Union, {\em Challenges to the Network:
  Telecommunications and the Internet,} Sept. 1997.  Can be purchased
  through $\langle$http://www.itu.ch$\rangle$.

\bibitem[Leida]{Leida}
B. Leida, A cost model of Internet service providers: Implications
  for Internet telephony and yield management, M.S. thesis, department
  of Electr. Eng. and Comp. Sci. and Technology and Policy Program, MIT,
  1998.  Available at
  $\langle$http://www.nmis.org/AboutNMIS/Team/BrettL/contents.html$\rangle$.

\bibitem[LOC]{LOC}
Library of Congress, data traffic statistics, available at
  $\langle$http://lcweb.loc.gov/stats/$\rangle$.

\bibitem[MCI]{MCI}
{\em Quality counts,} MCI white paper, available at
  $\langle$ftp://ftp.mci.net/pub/Quality.pdf$\rangle$.

\bibitem[MutooniT]{MutooniT}
P. Mutooni and D. Tennenhouse, Modeling the communication
  network's transition to a data-centric model, available at
  $\langle$http://www.sds.lcs.mit.edu/$\sim$mutooni/telecomms/$\rangle$.

\bibitem[NLANR]{NLANR}
National Laboratory for Applied Network Research,
  $\langle$http://www.nlanr.net/$\rangle$.

\bibitem[Noll]{Noll}
A. Michael Noll, {\em Introduction to Telephones and Telephone Traffic,}
  2nd ed., Artech House, 1991.

\bibitem[NSFNet]{NSFNet}
Historical data for NSFNet, available at 
  $\langle$http://www.merit.edu/nsfnet/$\rangle$.

\bibitem[NW]{NW}
Network Wizards, $\langle$http://www.nw.com$\rangle$.

\bibitem[Nua]{Nua}
Nua, Ltd., resources available at $\langle$http://www.nua.ie/$\rangle$.

\bibitem[Odlyzko1]{Odlyzko1}
A. M. Odlyzko, Data networks are lightly utilized, and 
  will stay that way.  Available at 
  $\langle$http://www.research.att.com/$\sim$amo$\rangle$.

\bibitem[Odlyzko2]{Odlyzko2}
A. M. Odlyzko, The economics of the Internet: Utility, utilization, 
  pricing, and Quality of Service.  Available at 
  $\langle$http://www.research.att.com/$\sim$amo$\rangle$.

\bibitem[Paxson]{Paxson}
V. Paxson, Growth trends in wide-area TCP connections, {\em IEEE Network,}
  8 (no. 4) (July 1994), pp. 8-17.  Available at
  $\langle$http://www-nrg.ee.lbl.gov/nrg-papers.html$\rangle$.

\bibitem[Schulzrinne]{Schulzrinne}
H. Schulzrinne, traffic statistics collected at
  $\langle$http://www.cs.columbia.edu/$\sim$hgs/internet/traffic.html$\rangle$.

\bibitem[Sidgmore]{Sidgmore}
John Sidgmore, interviewed by R. L. Brandt, {\em Upside} 10 
  (no. 5) (May 1998), pp. 78ff.  Available at
  $\langle$http://www.upside.com/texis/mvm/story?id=3512c4520$\rangle$.

\bibitem[Thyfault]{Thyfault}
M. E. Thyfault, Resurgence of convergence, {\em Information
  Week,} April 13, 1998, pp. 50ff.

\bibitem[UUNet]{UUNet}
UUNet backbone map, available at $\langle$http://www.us.uu.net/$\rangle$.

\bibitem[VS]{VS}
Vertical Systems Group, {\em ATM \& Frame Relay Industry Update,} 1997.

\bibitem[Waterloo]{Waterloo}
University of Waterloo network statistics, available at
  $\langle$http://www.ist.uwaterloo.ca/cn/\#Stats$\rangle$.

\bibitem[Zipf]{Zipf}
G. K. Zipf, Some determinants of the circulation of information,
  {\em Amer. J. Psychology} 59 (1946), 401-421.
\end{thebibliography}


\clearpage

\begin{figure}[htb]
\centerline{\psfig{file=Stree2,width=6in,height=4in}}
\caption{The Internet and private line networks.  Artwork by Sue Pope
and Thelma Pickell.}
\end{figure}

\begin{figure}[htb]
\centerline{\psfig{file=Pt1,width=6in,height=4in}}
\caption{The decreasing role of distance.  Top curve shows the total
cost of the monthly lease on a T1 line, the bottom curve the 
distance-insensitive part of the cost (all in current dollars,
without adjusting for inflation).}
\end{figure}

\clearpage

\begin{table}[htb]
\caption{Major public exchange point traffic, end of year 1997.}

\begin{center}
\begin{tabular}{ll}
peering point & traffic in Gbps \\ \hline
Sprint NAP (New York City) & 0.5  \\
Ameritech NAP (Chicago) & 0.7 \\
Pac Bell NAP (San Francisco) & 0.5  \\
MAE East (Washington, DC) & 1.1  \\
MAE West (San Jose) & 1.1  \\
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{National Internet backbones, in T3 equivalents.}

\begin{center}
\begin{tabular}{lll}
network & mid-1996 & year-end 1997 \\ \hline
MCI & 75 & 400 \\
UUNet & $< 50$ & 400 \\
BBN & 30 & 52 \\
AGIS & 35 & 61 \\
PSINET & 20 & 51 \\
Sprint & 50-70 & 137 \\
MAGIC & & 86 \\
vBNS & & 255 \\
\end{tabular}
\end{center}
\end{table}


\begin{table}[htb]
\caption{Leased line prices (300 miles long distance, 5 miles local).}

\begin{center}
\begin{tabular}{lr}
speed & price per month \\ \hline
9.6 Kbps & \$1,150 \\
56 Kbps & \$1,300 \\
1.5 Mbps (T1) & \$7,000 \\
45 Mbps (T3) & \$66,000 \\
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{Retail leased line market in the U.S., end of year 1997.
Bandwidth in Gbps, revenue in billions of dollars.}

\begin{center}
~ \\
\begin{tabular}{lrrrl}
line speed & no. lines & bandwidth & projected 98 growth & revenue \\ 
&& Gbps &&\$ B \\ \hline
56/64 \& lower & 447,530 & 57 & -1\% & 4.87 \\
fractional T1 & 19,880 & 10 & 2\% & 0.26 \\
T1 & 98,850 & 304 & 7\% & 4.58 \\
T3 \& higher & 3,010 & 259 & 34\% & 0.72
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{Effective bandwidth of long distance networks, year-end 1997.}

\begin{center}
\begin{tabular}{lr}
network & bandwidth (Gbps) \\ \hline
US voice & 350 \\
Internet & 75  \\
other public data networks & 40  \\
private line & 330 \\
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{Traffic on long distance networks, year-end 1997.}

\begin{center}
\begin{tabular}{ll}
network & traffic (TB/month) \\ \hline
US voice  & 40,000 \\
Internet & 2,500 - 4,000 \\
other public data networks & 500  \\
private line & 3,000 - 5,000  \\
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{Growth in number of Internet hosts.}

\begin{center}
\begin{tabular}{lr}
Date & Hosts  \\ \hline
08/81 & 213 \\
05/82 & 235 \\
08/83 & 562 \\
10/84 & 1,024 \\
10/85 & 1,961 \\
11/86 & 5,089 \\
12/87 & 28,174 \\
10/88 & 56,000 \\
10/89 & 159,000 \\
10/90 & 313,000 \\
10/91 & 617,000 \\
10/92 & 1,136,000 \\
10/93 & 2,056,000 \\
10/94 & 3,864,000 \\
01/96 & 9,472,000 \\
01/97 & 16,146,000 \\
01/98 & 29,670,000 \\
\end{tabular}
\end{center}
\end{table}


\begin{table}[htb]
\caption{Growth in traffic on Internet backbones.  For each year,
shows estimated traffic in terabytes during December of that year.}

\begin{center}
~ \\
\begin{tabular}{lr}
year & TB/month \\ \hline
1990 & 1.0 \\
1991 & 2.0 \\
1992 & 4.4 \\
1993 & 8.3 \\
1994 & 16.3 \\
1995 &  ? \\
1996 & 1500  \\
1997 & 3000 
\end{tabular}
\end{center}
\end{table}

\begin{table}[htb]
\caption{Growth in traffic between the University of Waterloo
and the Internet.  For each school terms, shows volume of data
transmitted during the month of highest traffic.  By permission
of University of Waterloo.}

\begin{center}
~ \\
\begin{tabular}{lrr}
month & MB/day in & MB/day out\\ \hline
93-03   & 453     & 227 \\
93-07   & 541     & 271 \\ 
93-10   & 648     & 324 \\
94-04   & 977     & 543 \\
94-08   & 1,377   & 915 \\
94-11   & 2,098   & 1,426 \\
95-04   & 2,285   & 1,730 \\
95-07   & 3,229   & 2,588 \\
95-11   & 6,000   & 3,450 \\
96-03   & 7,229   & 4,275 \\
96-07   & 7,823   & 4,572 \\
96-11   & 10,962  & 5,984 \\
97-03   & 11,463  & 6,235 \\
97-07   & 12,087  & 7,223 \\
97-11   & 24,621  & 10,572 \\
98-03   & 24,676  & 9,502 \\
\end{tabular}
\end{center}
\end{table}




\begin{table}[htb]
\caption{Growth in data traffic at Library of Congress.  For
each year, shows total
traffic in gigabytes during February of that year.}

\begin{center}
~ \\
\begin{tabular}{lrr}
year & GB/month & increase from previous year \\ \hline
1995 & 14.0   \\ 
1996 & 31.2 & 123\% \\
1997 & 109.4 & 251\% \\
1998 & 282.0 & 158\%
\end{tabular}
\end{center}
\end{table}

\end{document}
