\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} \def\tm{\raise5pt\hbox{{\rm\tiny TM~}}} \newcommand{\hsp}{\hspace*{\parindent}} \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 {Internet growth: Is there a ``Moore's Law'' for data traffic?}} \bigskip \\ K. G. Coffman and A. M. Odlyzko \smallskip \\ AT\&T Labs - Research \smallskip \\ kgc@research.att.com, amo@research.att.com \medskip\\ Revised version, June 4, 2001 \\ \vspace*{2\baselineskip} {\bf Abstract} \\ \end{center} Internet traffic is approximately doubling each year. This growth rate applies not only to the entire Internet, but to a large range of individual institutions. For a few places we have records going back several years that exhibit this regular rate of growth. Even when there are no obvious bottlenecks, traffic tends not to grow much faster. This reflects complicated interactions of technology, economics, and sociology, similar to, but more delicate than those that have produced ``Moore's Law'' in semiconductors. A doubling of traffic each year represents extremely fast growth, much faster than the increases in other communication services. If it continues, data traffic will surpass voice traffic around the year 2002. However, this rate of growth is slower than the frequently heard claims of a doubling of traffic every three or four months. Such spectacular growth rates apparently did prevail over a two-year period 1995-6. Ever since, though, growth appears to have reverted to the Internet's historical pattern of a single doubling each year. Progress in transmission technology appears sufficient to double network capacity each year for about the next decade. However, traffic growth faster than a tripling each year could probably not be sustained for more than a few years. Since computing and storage capacities will also be growing, as predicted by the versions of ``Moore's Law'' appropriate for those technologies, we can expect demand for data transmission to continue increasing. A doubling in Internet traffic each year appears a likely outcome. If Internet traffic continues to double each year, we will have yet another form of ``Moore's Law.'' Such a growth rate would have several important implications. In the intermediate run, there would be neither a clear ``bandwidth glut'' nor a ``bandwidth scarcity,'' but a more balanced situation, with supply and demand growing at comparable rates. Also, computer and network architectures would be strongly affected, since most data would stay local. Programs such as Napster would play an increasingly important role. Transmission would likely continue to be dominated by file transfers, not by real time streaming media. \clearpage \begin{center} {\Large\bf {Internet growth: Is there a ``Moore's Law'' for data traffic?}} \bigskip \\ K. G. Coffman and A. M. Odlyzko \smallskip \\ AT\&T Labs - Research \smallskip \\ kgc@research.att.com, amo@research.att.com \medskip\\ Revised version, June 4, 2001. \vspace*{2\baselineskip} \end{center} \setlength{\baselineskip}{1.5\baselineskip} \section{Introduction} \hsp An earlier paper \cite{CoffmanO} estimated the sizes of telecommunications networks in the U.S. and the traffic they carried. (We concentrated on the U.S. because of lack of data about other countries, and because the disparate development stages of their communications infrastructures make cross-country comparisons difficult.) Our conclusion was that by year-end 1997, the voice network was still the largest in terms of bandwidth, although data networks were almost as large. On the other hand, the traffic carried by the voice network was far larger than that of the data networks. These estimates are summarized in Table 1.1, with the units of measurement being terabytes per month. (A voice call for the purposes of this measurement was counted as two 64 Kb/s streams of data, and fax and modem calls carried on the switched long distance network were counted as voice. For details, see \cite{CoffmanO}.) \\*[1ex] \begin{table}[htb] \begin{center} Table 1.1. Traffic on U.S. long distance networks, year-end 1997. \\ ~ \\ \begin{tabular}{ll} network & traffic (TB/month) \\ \hline US voice & 40,000 \\ Internet & 2,500 - 4,000 \\ other public data networks & 500 \\ private lines & 3,000 - 5,000 \\ \end{tabular} \end{center} \end{table} Table 1.2 is an update of Table 1.1, showing our estimates for traffic on U.S. long distance networks around December 2000. As before, the estimates for the voice, private line, and other public data networks (primarily ATM and Frame Relay) are uncontroversial, consistent with other publicly available sources. On the other hand, the estimates for the public Internet are much less certain, less certain than those we made for year-end 1997. We explain this in greater detail below. \\*[1ex] \begin{table}[htb] \begin{center} Table 1.2. Traffic on U.S. long distance networks, year-end 2000. \\ ~ \\ \begin{tabular}{ll} network & traffic (TB/month) \\ \hline US voice & 53,000 \\ Internet & 20,000 - 35,000 \\ other public data networks & 3,000 \\ private line & 6,000 - 11,000 \\ \end{tabular} \end{center} \end{table} In the earlier paper \cite{CoffmanO} we also considered the growth rates of various networks. While reliable information had long been available for most networks (with increases on the order of 10\% a year for the voice network), very little was known about the Internet. There were many claims of huge growth rates, usually of a doubling of traffic every three or four months, which corresponds to annual growth of around 1,000\%. We confirmed that such growth rates did hold during 1995 and 1996. (More precisely, the traffic carried by the Internet backbones grew by a cumulative factor of 100 between year-end 1994 and year-end 1996. We did not obtain precise estimates for traffic during those two years, so do not know how growth was distributed within those two years.) However, we also showed that growth had slowed down to about 100\% during 1997. Remarkably enough, that was almost exactly the growth rate registered by the Internet backbone in the early 1990s (see \cite{CoffmanO} for data), and is close to other measures of growth rates during earlier periods (cf. \cite{CoffmanO, Paxson}). In fact, if we assume that the traffic on the initial ARPANET links that were activated in the summer of 1969 amounted to a few thousand bytes per month, we find that the average growth rate in traffic has been very close to 100\% a year for the entire 30-year history of the Internet and its predecessors. However, growth rates varied substantially over that period as the initially small research networks evolved. The steady annual doubling of traffic only appeared in the early 1990s, when the NSFNet backbone grew to a significant size in both traffic and number of participants. Table 1.3 shows our estimates for traffic on U.S. Internet backbones. The data through the end of 1994 are based on careful measurements of the NSFNet backbone (and neglect what were thought to be much smaller private backbones and research networks). For the late 1990s, the figures are less certain. As we explain in Section 3, there is less information today than was available a couple of years ago about different carriers' IP networks, either about their sizes or the traffic they carry. Therefore our current estimates are based less on solid data than those of \cite{CoffmanO}, and more on extrapolating from the circumstantial evidence we have accumulated. \\*[1ex] \begin{table}[htb] \begin{center} Table 1.3. Traffic on Internet backbones in U.S.. For each year, shows estimated traffic in terabytes during December of that year. \\ ~ \\ \begin{tabular}{lr} year & TB/month \\ \hline 1990 & 1.0 \\ 1991 & 2.0 \\ 1992 & 4.4 \\ 1993 & 8.3 \\ 1994 & 16.3 \\ 1995 & ? \\ 1996 & 1,500 \\ 1997 & 2,500 - 4,000 \\ 1998 & 5,000 - 8,000 \\ 1999 & 10,000 - 16,000 \\ 2000 & 20,000 - 35,000 \\ \end{tabular} \end{center} \end{table} Much of this chapter is devoted to a study of historical growth rates in Internet traffic. We find that for a variety of institutions, some with abundant bandwidth, others with congested links, traffic tends to about double each year. Even when the bandwidth of congested links is increased, in most cases traffic does not explode in the much-feared ``tragedy of the commons'' phenomenon \cite{GuptaSW}. Instead, it continues growing at about 100\% per year. Malicious behavior is a smaller problem than is often feared. What dominates is the time it takes for new applications and processes to be widely adopted. That, and technological progress, combine to produce the ``Moore's Law'' of data traffic, in a process similar to that operating in other areas. In considering prospects for future growth, one approach is to simply look at the historical record. Since the Internet has been growing at about 100\% a year for its entire history, one can then extrapolate this growth rate into the future, and predict that traffic will continue to double each year. We prefer to do more than that, and consider how fast supply and demand are likely to grow. Those considerations lead us to the same conclusion as the simple extrapolation, namely that traffic is likely to about double each year. (By an approximate doubling we mean growth rates of between 70\% and 150\% per year.) Much is written about the near infinite capacity of fiber, and of the upcoming bandwidth glut (or at least the overabundance of available fiber). For example, the introduction to \cite{Gilder2} talks of ``the coming world of cheap, unlimited bandwidth.'' In the US alone there are now over half a dozen long haul carriers that either have or will have very substantial national fiber networks. The conventional wisdom is that the exploding increase in Internet traffic is the main driver for the expansion of these networks. It also seems to be implied that the ``ever increasing'' capacities of WDM (wavelength division multiplexing) systems (both in terms of the number of channels and the individual channel rates) coupled with this forecasted ``fiber glut'' will result in the national networks being easily able to accommodate whatever growth rate the Internet throws at it. We do not think the carrying capacity of the network, at least the long haul national backbone network(s), can or will grow to accommodate arbitrary traffic growth rates. In fact we believe that if traffic grows by factors of more than two or three a year for any sustained period, the transport backbones are likely to become a very serious bottleneck. However, 100\% annual growth rates appear to be realizable without unusually large new investments for the foreseeable future (which means at least five years). We explore this issue in detail in Section 5. The demand for data transmission is potentially insatiable. As we show in Section 6, there is already so much data stored on hard disks (and much more on magnetic tapes and optical drives) that only a small fraction of it can traverse the long distance networks without saturating them. Furthermore, data storage capacities are about doubling each year. Hence the evolution of computer and network architectures will come from the subtle interaction of supply and demand, which will be mediated by economics and sociology. It appears that an approximate doubling of Internet traffic each year is a reasonable course of evolution for the Internet, even though there may be brief periods of higher or lower growth rates. A doubling of Internet traffic each year is not the doubling every 100 days that is often claimed. However, it is extremely rapid by comparison with older communication technologies. Still, since other technologies (storage and processing power) will also be growing, many expectations for radical changes will not be realized. For example, there have been predictions that the growing bandwidth of long distance networks would lead to dramatic changes. \begin{quote} [The] change in the relationship between the bandwidth of networks and the bandwidth of computers will transform the architecture of information technology. As Robert Lucky of Bellcore [recently renamed Telcordia] puts it, ``Perhaps we should transmit signals thousands of miles to avoid even the simplest processing functions.'' \hspace*{+3in}[Gilder2] \\ \end{quote} The projections of this chapter show that this is very unlikely. Bandwidth will continue to be in short supply compared to storage. Further, the delays forced by speed of light limitations as well as communications overheads mean that most data will be processed locally. We will have to take processing to the data, not vice versa. For decades, the most frequent predictions for data networks were that eventually they would be dominated by traffic such as voice and video. That has not happened yet. If the doubling of traffic each year continues, it will not be true in the long run either, simply since there will be far more data traffic than needed to handle real time streaming transmissions. % There are also arguments, discussed in later sections, as to % why such real time traffic may not even be dominant in the % intermediate run, as transmission modes such as those of % Napster, with local storage and replay, dominate. Section 2 outlines the wide range of commonly expressed opinions about the growth rate of the Internet. Section 3, the bulk of this chapter, is then devoted to an examination of the historical data we have been able to find. Section 4 discusses the disruptive innovations of the past, such as browsers, and of the present (primarily Napster and related programs), and the effects they have on traffic statistics. Section 5 outlines the history and projections for advances in photonic transmission. Section 6 discusses the potential demand for data bandwidth. Section 7 concludes that growth in data traffic is determined by factors similar to those that produce the standard ``Moore's laws'' in other areas. % such as processors and storage. Section 8 has some final concluding remarks. \section{Skeptics and cheerleaders} \hsp There continue to be voices skeptical of the growth prospects of the Internet. In particular, A. Michael Noll has been a persistent naysayer. Back in 1991, he estimated what the maximal feasible volume of data transfers could be (pp.~171--175 of \cite{Noll1}). Since that time, the volume of data traffic has surged far beyond his original prediction. The main reason for this development is that he did not foresee the arrival of graphics-rich content, such as Web pages. His estimates assumed only text would be transmitted, and all of it would be processed by people. While that prediction has turned out to be wrong, he continues predicting that data traffic will not exceed voice traffic unless multimedia begins dominating the Internet \cite{Noll2}. While our estimates do confirm that there is still more voice traffic than data traffic, Noll's estimates for data traffic are far too conservative. As an example, we examined the publicly available statistics for data traffic at the University of Southern California, where Noll is a professor. These statistics were available at $\langle$http://foo.usc.edu/netstats$\rangle$, and in early 1999 showed a considerably higher volume of data flow than Noll estimated in \cite{Noll2}. (By early 2000, the volume of data flow at USC had grown by about 70\%, from an average of about 20 Mb/s to the campus and 10 Mb/s out from the campus to about 30 Mb/s in and 20 Mb/s out. Unfortunately, between late 2000 and early 2001, those traffic statistics stopped being updated, so we do not have data about more recent growth patterns.) While there are some skeptics about the prospects for the Internet, there are vastly larger ranks of people who claim astronomical growth rates. However, they invariably talk only of rates of increase, and never cite precise verifiable figures. The most common claim one hears is that ``Internet traffic is doubling every three or four months.'' As was pointed out in \cite{CoffmanO}, many of these claims appear to trace back to statements of John Sidgmore of MCI WorldCom's UUNet or his colleagues. A March 2000 news report \cite{Howe}, for example, cites MCI WorldCom president Bernard J. Ebbers as saying that his company ``has recently had to add capacity to its global network at a rate of 800 percent annually to keep up with soaring demand for Net traffic.'' Yet the February 10, 2000 press release by MCI WorldCom that accompanied the earnings report for the fourth quarter of 1999 refers to ``[g]ains in data services ... measured by an 87 percent increase in Voice Grade Equivalents (VGEs), which capture the volume of local data circuits.'' The two statements may refer to different parts of the MCI WorldCom data network. However, eventually capacities of long distance links are unlikely to grow much faster than those of local ones. Hence we are inclined to believe that the ``87 percent increase'' of the official press release describes overall growth more accurately. Revenue increases from data services for MCI WorldCom (reported in their audited financial statements) are also far more consistent with annual growth rates of 100 percent than 800 percent. It could be that the phrase ``doubling of Internet traffic every three [or four] months'' has lost its literal meaning. Perhaps it is being used as a figure of speech, in the way that many people use ``exponential growth'' (which in mathematics has a precise meaning) to describe any fast growth. There are just too many examples where such statements are either implausible or even demonstrably incorrect. For example, Keith Mitchell, executive chairman of LINX, the London Internet Exchange, Ltd., is quoted in \cite{Jander} as saying in March, 2000, that ``[LINX] traffic doubles every hundred days or so.'' This rate of growth would increase traffic over a year by a factor of 12. Yet an examination of the publicly available statistics for LINX as well as discussions with technical staff at LINX showed that traffic had grown by a factor of about 4 between March 1999 and March 2000. That is certainly fast, but corresponds to a doubling of traffic every 180 days, not every 100 days. (Current traffic statistics for LINX are available at $\langle$http://ochre.linx.net/$\rangle$. There is further discussion of LINX in the next section.) Whether Internet traffic doubles every three months or just once a year has huge consequences for network design as well as the telecommunications industry. Much of the excitement about and funding for novel technologies appear to be based on expectations of unrealistically high growth rates (cf. \cite{Bruno}). Yet it should have been obvious that such growth rates cannot be sustained for long, and in particular could not have been going on for long. A doubling of Internet traffic every three months would produce an increase by a factor of 16 in one year. Hence, from the end of 1994 to the end of 2000, it would have grown by a factor of almost 17 million. Until the end of 1994, the Internet backbone was funded by the National Science Foundation, and was well instrumented. Hence we know that it carried about 15 TB (terabytes) of traffic each month. Had that traffic grown by a factor of 16 million in the intervening 6 years, we would now have about 240 exabytes (exabyte is $10^{18}$ bytes) of traffic on Internet backbones each month. If we generously assume that there are 500 million Internet users in the world today, that volume of traffic would translate into about 1.5 Mb/s of U.S. backbone traffic for each user around the clock! This is enough for reasonably high quality video (if one uses appropriate compression). Yet most Internet users have access only to modems that transmit at best at 28 Kb/s. Moreover, those modems are in use typically for less than an hour per day, and on average transmit about 5 Kb/s while they are connected to the Internet. Even the vast majority of enterprises as well as some universities have links to the Internet that run no faster than T1 speeds (i.e., maximal rates of 1.5 Mb/s). The bottom line is that current user behavior falls well short of the usage levels one would expect had Internet traffic been doubling every three months since the end of 1994. Assuming a doubling of Internet traffic every four months produces traffic estimates that are only slightly less absurd. Actual traffic at well-wired institutions in the U.S. (primarily corporations and some universities) tends to average out to something between one and three thousand bits per second per person (averaged over a complete week). \section{Historical record} \hsp The online data for LINX in April 2001 showed growth of about 300\% from early 2000 to early 2001. Earlier versions of those same online statistics as well as conversations with LINX technical personnel show that LINX has been experiencing those growth rates for several years. One can find other examples of such high growth rates, and sometimes even higher ones. However, there are also numerous examples of much more slowly growing links. In this section we present growth rates from a variety of sources, and attempt to put them into context. Our general conclusion is that Internet traffic appears to be growing at about 100\% a year. By this we mean that the growth rate appears to be between 70\% and 150\% per year, as we cannot be more precise given the limitations of the data. Although our paper \cite{CoffmanO} appears to have been the first one to point out the slowing down of Internet traffic growth, others observed the same phenomenon soon afterwards. For example, there is an article by Peter Sevcik \cite{Sevcik} from early 1999, as well as reports from market researcher firms such as Probe that also pointed out that the claims of a doubling every three or four months were not correct. An important example that supports our thesis of Internet traffic doubling about once each year is that of Telstra, the dominant Australian telecommunications carrier. A January 15, 2001 news story \cite{Cochrane} cited official Telstra figures as follows: \begin{quote} Australia's biggest ISP, Telstra Big Pond, says total daily traffic grew from about 4 TB a day in November 1999 to more than 9 TB a day at the same time last year. It continued the 1998-99 growth rate of 225 per cent, when traffic demand rose from 1.8 TB to about 4 TB in November. Consumption first broke the 1 TB a day barrier in 1997. \end{quote} Disregarding the obvious mistake (an increase from 4 TB to 9 TB represents growth by 125\%, not 225\%), we find annual growth rate for Telstra falling in the range we derive for each of several consecutive years. (The printed version of the story, but not the online one, has a detailed chart, showing daily Telstra Internet traffic from beginning of 1997 to November 2000. It shows that traffic grew at about 100\% a year over that full 4-year period.) There is further discussion of Telstra later in this section. Our presentation in this section follows the pattern of the above paragraph for Telstra, and is largely in terms of a narrative. It would be much more effective to have a table or chart combining data for a variety of institutions. Unfortunately the statistics we have collected are not sufficiently systematic to do this. They come from a variety of sources in many formats and for different periods. We concentrate on large and stable institutions for which we have more than a year's worth of data. For some links, one can obtain detailed statistics going back some years from the Web page we indicate. For most, though, the public Web page shows only the graphs produced by the MRTG (multi-router traffic grapher) tool \cite{MRTG}. (At some institutions, MRTG is beginning to be partially displaced by a more modern program, RRDtool \cite{RRD}.) This excellent program displays the exact averages of in and out traffic over the previous day, week, month, and year, and also produces graphs with the traffic profiles for those periods. This means that by downloading one of the MRTG pages, one can estimate the average traffic a year earlier. % , but not get its exact values. It is in principle possible to decode the .gif files produced by MRTG to obtain more precise values, but we have not done so, and have relied on ``eye-balling'' the graphs to estimate traffic. As an example, consider Onvoy, the main ISP in Minnesota. Its growth trends are discussed later in this section. We have exact MRTG readings and graphs from October 1999 and June 2000. That means we have exact traffic data for those two months, and can estimate traffic back to October 1998, but no further. In a few cases we have obtained more precise statistics from network administrators. As a brief note on conversion factors, traffic that averages 100 Mb/s is equivalent to about 30 TB/month. (It is 32.4 TB for a 30-day month, but such precision is excessive given the uncertainties in the data we have.) When the NSF Internet backbone was phased out in early 1995, it was widely claimed that most of the Internet backbone traffic was going through the Network Access Points or NAPs, which tended to provide decent statistics on their traffic. Currently it is thought that only a small fraction of backbone traffic goes through the NAPs, while most goes through private peering connections. Furthermore, NAP statistics are either no longer available, or not as reliable. Here we just mention a few cases. The data for the Chicago NAP from the summer of 1996 through May of 1999 is available at $\langle$http://nap.aads.net/$\sim$nap-stat/$\rangle$. From August of 1996 to very early in 1997 (February) the traffic profile was moderately flat. However, from February 1997 until May 1999 there was a fairly consistent growth that resulted in about a 12 fold increase in traffic, to a final level of about 1.2 Gb/s. A twelve-fold increase in a little over 2 years implies an annual growth rate of around 3.5. On the other hand, a different picture emerges when we examine the statistics for MAE-East (which a few years ago was often claimed to handle a third of all Internet traffic). They are available at $\langle$http://www.mae.net/east/stats.html$\rangle$. In March of 2000, the average traffic there was about 1.5 Gb/s. That is the same traffic as this NAP handled in March 1998 (and twice what it handled in March 1997). Thus practically nothing can be concluded about current growth rates of Internet traffic by examining the statistics of the public NAPs in the U.S. LINX, the London Internet exchange, was mentioned already in Section 2. A July 1999 LINX press release announced that it had achieved a traffic level of 1.0 Gb/s, up from 180 Mb/s a year earlier, for a growth rate of 455\%. However, no definition was offered how these ``traffic levels'' were defined. An examination of the MRTG graphs obtained from $\langle$http://www2.linx.net/info/$\rangle$ (which are unreliable towards the end of the period they cover due to counter overflows in the routers and the more recent statistics available at $\langle$http://ochre.linx.net$\rangle$) showed that the average traffic (averaged over a whole month) went from about 200 Mb/s in September 1998 to 360 Mb/s in March 1999, to 1.1 Gb/s by the end of 1999, and 4.5 Gb/s by May 2001. Thus the growth rate has been fairly steady at about 300\% per year. AMS-IX, the Amsterdam Internet Exchange, $\langle$http://www.ams-ix.net/$\rangle$, has shown growth by a factor of 4.6 from June 1999 to May 2000, to a level of about 800 Mb/s, then a further growth by a factor of 2.5 to April 2001, to a level of 2 Gb/s. Several smaller exchanges, especially in countries that used to lag in Internet penetration, sometimes show similarly high growth rates. For example, the Slovak Internet eXchange, $\langle$http://www.six.sk/mrtg/switch.six.sk.b.html$\rangle$, increased its traffic approximately 4-fold in the year ending June 2000, to an average level of about 40 Mb/s. However, by May 2001, traffic grew only about 80\% during the intervening 11 months, to a level of 73 Mb/s. HKIX, a commercial exchange created by The Chinese University of Hong Kong, $\langle$http://www.hkix.net$\rangle$ (with aggregate statistics available more directly at $\langle$http://www.cuhk.edu.hk/hkix/stat/aggt/hkix-aggregate.html$\rangle$), doubled its traffic in 1999, and then tripled it in the first six months of 2000 to an average of about 250 Mb/s. By May 2001, traffic had grown to about 600 Mb/s, for a growth rate of about 150\% per year. (Total Internet bandwidth from Hong Kong to other countries tripled between September 1999 and September 2000, and then doubled in the next six months, according to statistics compiled by Hong Kong telecommunications regulators.) Even BNIX, $\langle$http://www.belnet.be/bnix/$\rangle$, located in Belgium, a country that already has extensive Internet deployment, experienced a 5-fold rise from middle of 1999 to the middle of 2000, to a level of 120 Mb/s, and a further rise to about 300 Mb/s by May 2001. INEX, an Irish exchange, $\langle$http://www.inex.ie$\rangle$, saw its traffic increase from about 3 Mb/s in June 1999 to about 5 Mb/s in June 2000, and 10 Mb/s in May 2001. SIX, the Seattle Internet Exchange, $\langle$http://www.altopia.com/six$\rangle$, saw approximately 150\% growth in the 12 months to June 2000, to a level of about 50 Mb/s, and a further approximately 100\% growth in the 12 months to May 2001, to a level of about 100 Mb/s. FICIX, the Finnish exchange, $\langle$http://www.ficix.fi/$\rangle$, tripled its traffic in a bit less than two years, from an average of about 70 Mb/s in September 1998 to about 210 Mb/s in June 2000, for an annual growth rate of about 70\%. By May 2001, though, its traffic had grown to about 450 Mb/s, for a growth rate of slightly more than 100\%. (The statistics of traffic for individual FICIX members tend to show similar growth rates to that of the exchange aggregate.) VIX, the Vienna Internet Exchange, $\langle$http://www.vix.at/$\rangle$, approximately doubled its traffic between May 2000 and May 2001, to a level of about 450 Mb/s. Traffic interchange statistics are hard to interpret, unless one has data for most exchanges, which we do not. Much of the growth one sees can come from ISPs moving from one exchange to another, moving their traffic from one exchange to another, or else coming to an exchange in preference to buying transit from another ISP. At LINX, a large part of its growth is almost surely caused by more ISPs exchanging their traffic there. Between March 1999, and March 2000, the ranks of ISPs that are members of LINX have grown by about two thirds, based on the data on the LINX home page. Hence the average per-member traffic through LINX may have increased only around 120\% during that year. On the other hand, FICIX membership appears to have been much more stable. Unfortunately the largest ISPs do not release reliable statistics. This situation was better even a couple of years ago. For example, MCI used to publish precise data about the traffic volumes on their Internet backbone. Even though they were among the first ISPs to stop providing official network maps, one could obtain good estimates of the MCI Internet backbone capacity from Vint Cerf's presentations. These sources dried up when MCI was acquired by WorldCom, and the backbone was sold to Cable \& Wireless. As was noted in \cite{CoffmanO}, the traffic growth rate for that backbone had been in the range of 100\% a year before the change. Today, one can obtain some idea of the sizes (but not traffic) of various ISP networks through the backbone maps available at \cite{Boardwatch}. They may not be too reliable, but provide some indication of capacity and capacity growth. Although networks appear to have been growing at faster rates than the doubling of traffic we estimate, even they have not been growing at anything like the mythological doubling every three months. The only large U.S. ISP to provide detailed network statistics is AboveNet, at $\langle$http://www.above.net/traffic/$\rangle$. We have recorded the MRTG data for AboveNet for March 1999, June 1999, February 2000, June 2000, November 2000, and April 2001. The average utilizations of the links in the AboveNet long-haul backbone during those 6 months were 18\%, 16\%, 29\%, 12\%, 11\%, and 10\%, respectively. (The large drop between February and June 2000 was caused by deployment of massive new capacity, including four OC48s. By the middle of 2001, there were even some OC192 links. One of the reasons we concentrate on traffic and not network sizes in this chapter is that extensive new capacity is being deployed at an irregular schedule, and is often lightly utilized. Thus it is hard to obtain an accurate picture of the evolution of network capacity.) If we just add up the volumes for each link separately, we find that traffic quadrupled in 15 months between March 1999 and June 2000. (Similarly, it grew by a factor of slightly over 3 between June 2000 and April 2001.) These increases represent annual growth rates of about 200\%. However, this figure has to be treated with caution, as actual traffic almost surely increased somewhat more slowly. During these periods, AboveNet expanded geographically, with links to Japan and Europe, so that at the end it probably carried packets over more hops than before. In this chapter we count only bytes that are delivered to customers, and count them once, no matter how many backbone links they traverse. Hence the sum of the traffic figures for the AboveNet links has to be deflated by the average number of hops that a packet makes over the backbones. (In particular, the sum of the volumes over all the links in the AboveNet network in June 2000, which comes to 1,400 TB, has to be deflated by this average number of hops if one desires to compare it to the volumes in Table 1.2.) Even when we do have data for a single carrier, such as AboveNet, some of the growth we see there may be coming from gains in market share, both from gains within a geographical region, and from greater geographical reach, and not from general growth in the market. More interesting examples are those of Telstra and Onvoy, since their geographical reach did not change. We discuss them next. Telstra, the dominant Australian carrier, has operated within the same geographical region, and its traffic growth rate may be an approximation to that of the entire Australian market. The only traffic statistics that Telstra has provided are those in \cite{Cochrane}, cited at the beginning of this section. (In addition to an approximate doubling of Internet traffic over several years, that reference also provides some data about Telstra ATM and Frame Relay traffic, which just about doubled during the year 2000.) In addition, Telstra does present network maps at $\langle$http://www.telstra.net$\rangle$. In January 1998, the total bandwidth to the U.S., including some provided over a satellite link, was 146 Mb/s. (The bandwidth to other countries has historically been almost negligible compared to that to the U.S..) In March 2000, that bandwidth had grown to 592 Mb/s. By late June 2000, it had shrunk to 515 Mb/s. However, by September 2000, it was up to 980 Mb/s, and by April 2001, it was 1245 Mb/s. Thus the growth rate of international bandwidth was close to 100\% per year over three consecutive years, closely paralleling the growth of Internet traffic, as disclosed by Telstra in \cite{Cochrane}. On the other hand, domestic Australian Internet bandwidth grew much faster. Whereas in September 1999, the highest capacity domestic links were 155 Mb/s (OC3), during 2000 several were upgraded to 2488 Mb/s (OC48). The Telstra data provides a rough check on our estimates for Internet backbone traffic. According to public statements by Telstra officials \cite{Taggart}, 60\% of Telstra Internet traffic is with the U.S. Let us assume that the links from the U.S. to Australia are run at an average of 60\% of capacity. (This is rather heavy loading, but not unprecedented on expensive links, cf. Table 3.3.) Let us assume that the reverse direction is operated at an average of 20\% of capacity, which seems reasonable by comparison with the data in Table 3.2. Then we find that at year-end 2000, Telstra was probably receiving about 200 TB/month from the U.S., and transmiting about 70 TB/month. If this represents 60\% of Telstra's Internet traffic (and this fits reasonably well with the data in \cite{Cochrane}), then (without making allowances for other carriers or for the likelihood that some of the traffic on the link to the U.S. is destined for or comes from other countries) we obtain an estimate of about 500 TB/month for all of Australia's Internet traffic. Since the U.S. has about 15 times as many inhabitants as Australia, is somewhat richer on a per capita basis, and has better developed Internet infrastructure and lower prices, the estimates in Table 1.2 appear in the right range. Onvoy, $\langle$http://www.onvoy.net$\rangle$ has evolved from the research and educational MRNET to the largest commercial ISP in Minnesota. Its traffic statistics were available at $\langle$http://graphs.onvoy.com/infrastructure$\rangle$ and over the two years from June 1998 to June 2000 showed an annual growth rate in traffic of only about 50\%, to a level in June 2000 of 155 Mb/s from the Internet and 100 Mb/s towards the Internet. (More recent statistics are not available any more.) IP-Plus, the ISP operated by Swisscom, the dominant carrier in Switzerland, has extensive statistics about their network at $\langle$http://www.ip-plus.net$\rangle$. As of May 2001, they showed only very moderate growth over the preceding year, almost surely under 100\%, for the domestic links. For the general market, the growth in usage by residential customers, at least in the U.S., has slowed down. Their ranks are growing at only about 20\% per year, and the time spent online is growing at under 20\% per year (cf. \cite{Odlyzko3}). Thus the traffic they generate (about 5 Kb/s from the Internet towards their PCs when they are online) is increasing less than 50\% a year. In other countries, the pattern is different. For example, in France in 1999, the number of residential Internet users grew by almost 150\%, just as it had done the previous year, while the average time online stayed constant \cite{Odlyzko3}. Therefore it is likely that French residential traffic grew by a factor of 2.5 in 1999. Around the world, the number of residential customers appears to be growing at about 50\% per year, but their usage tends to be static as a result of per-minute charging (cf. \cite{Odlyzko3}). The traffic from residential U.S. customers may very well increase at a faster rate in the near future. The growth in the number of users is likely to diminish, as we reach saturation. (You cannot double the ranks of subscribers if more than half the people are already signed up!) However, broadband access, in the shape of cable modems and DSL (digital subscriber line), and to a lesser extent fixed wireless links, will stimulate usage. The evidence so far is that users who switch to cable modem or DSL access increase their time online by 50 to 100\%, and the total volume of data they download per month by factors of 5 to 10. A 5 or 10-fold growth in data traffic would correspond to a doubling of traffic every four months if everyone were to switch to such broadband access in a year. However, that is not going to happen. At the end of 1999, there were about 3 million households in the U.S. with broadband access. At the end of 2000, it is estimated there were about 6 million, and as of May 2001, the estimates for year-end 2001 were for about 11 million. That is approximately a doubling each year. (Not all of this growth will be even. The ranks of DSL subscribers apparently grew about four-fold in 2000, but in early 2001, with the bankruptcy of several DSL providers, growth appears to have slowed down dramatically.) The traffic from a typical residential broadband customer is likely to grow beyond the level we see today, as more content becomes available, and especially as more content that requires high bandwidth is produced, and as people learn to exploit high bandwidth links for their own communication needs. Still, it is hard to see average traffic per customer among those with broadband connections growing at more than 50\% a year. Together with a doubling in the ranks of such customers, this might produce a tripling of traffic from this source. Since the ranks of customers with regular modems are unlikely to decrease much, if any, and since their traffic dominates, it appears that we most likely will see total residential customer traffic growing no faster than 200\% per year, and probably closer to 100\% per year. (Access from information appliances, which are forecast to proliferate, is unlikely to have a major impact on total traffic, since the mobile radio link will continue to have small bandwidth compared to wired connections. There may be much greater traffic to mobile gateways, but it appears unlikely that such traffic will be huge.) Growth in traffic can be broken down into growth in the number of traffic sources, and growth in traffic per source. For LINX, much of the increase in traffic may be coming from an increase in member ISPs and increased peering among those ISPs. For individual ISPs, much of the increase in traffic may also be coming from new customers. Yet in the end, that kind of growth is limited, as the market gets saturated. We will concentrate in the rest of this section on rates of growth in traffic from stable sources. Now nothing is completely stable, as the number of devices per person is likely to continue growing, especially with the advent of information appliances and wireless data transmission. Hence we will consider growth in traffic from large institutions that are already well wired, such as corporations and universities. Most corporations do not publicize information about their network traffic, and many do not even collect it. However, there are some exceptions. For example, Lew Platt, the former CEO of Hewlett-Packard, used to regularly cite the HP Intranet in his presentations. The last such report, dated September 7, 1998, and available at $\langle$http://www.hp.com/financials/textonly/personnel/ceo/rules.html$\rangle$, stated that this network carried 20 TB/month, and a comparison with previous reports shows that this volume of traffic had been doubling each year for at least the previous two years. (As an interesting point of comparison, the entire NSFNet Internet backbone carried 15 TB/month at its peak at the end of 1994.) Several other corporations have provided us with data showing similar rates of growth for their Intranet traffic, although some indicated their growth has slowed down, and a few have had practically no growth at all recently. Internal corporate traffic appears to be growing more slowly than the public Internet traffic. Data for retail private lines (i.e., those sold to corporate and government entities for their own internal use, not for connecting to the Internet, and not for use by ISPs) as well as for Frame Relay and ATM services show aggregate growth in bandwidth (and therefore most likely also traffic) in a a range of 30 to 40\% per year. (Growth is slow for retail private lines, and faster for Frame Relay and ATM.) This is remarkably close to the growth rate observed in the late 1970s in the U.S., which was around 30\% per year \cite{deSolaPITH}, as well as to the growth rate of total private line data bandwidth, local and long distance, through most of the 1990s \cite{Galbi}. Thus it is the corporate traffic to the public Internet that is growing at 100\% per year. (Currently over two thirds of the volume on the public Internet appears to be business to business.) Thus the acceleration in the overall growth rate of data traffic to the range of 100\% per year from the old 30\% or so a year appears to be a reflection of the advantages of the Internet, with its open standards, and any-to-any connectivity. In the rest of this section we concentrate on publicly available information, primarily about academic, research, and government networks. These might be thought of as unrepresentative of the corporate or private residential users. Our view is just the opposite, that these are the institutions that are worth studying the most, since they normally already have broadband access to the Internet, tend to be populated by technically sophisticated users, and tend to try out new technologies first. The spread of Napster through universities is a good example of the last point. We suggest (see Section 6 for more detail) that Napster and related tools, such as Gnutella and Wrapster, are just the forerunners of other programs for sharing of general information, and not just for disseminating pirated MP3 files. As we explain in Section 6, there is already much more digital data on hard disks alone than shows up on today's Internet. Further, this situation is likely to continue. \\*[1ex] \begin{table}[htb] \begin{center} ~~Table 3.1. Growth in data traffic at Library of Congress. For each year, shows total traffic in gigabytes during February of that year and the rate of increase over the previous year. % \begin{center} ~ \\ \begin{tabular}{lrr} year & GB/month & increase \\ \hline 1995 & 14.0 \\ 1996 & 31.2 & 123\% \\ 1997 & 109.4 & 251\% \\ 1998 & 282.0 & 158\% \\ 1999 & 535.0 & 88\% \\ 2000 & 741.1 & 39\% \\ 2001 & 1202.6 & 62\% \end{tabular} \end{center} \end{table} The growth rates we observe among the institutions that make traffic statistics publicly available vary tremendously. For example, Table 3.1 presents data for the Library of Congress, taken from the online statistics at $\langle$http://lcweb.loc.gov/stats/$\rangle$. There was a pronounced slowdown in the growth rate of traffic, followed by a noticeable by not huge increase. On the other hand, other sources show no such effect. The AT\&T Labs - Research public Web server has experienced a consistent growth rate in the volume of downloads of about 50\% a year until the beginning of 2000, and then more than a doubling of traffic during 2000. This growth continued even though this server contains primarily high quality technical material, that is of interest primarily to people who are already well-connected. Table 3.2 shows statistics for the transatlantic link of the JANET network, which provides connectivity to British academic institutions. (More complete data is available at $\langle$http://bill.ja.net/$\rangle$.) There are several interesting features of this data. One is that for a long time, there was increasing asymmetry of the traffic, with the preponderance of traffic from the U.S. over that to the U.S. growing. (There are some signs of a reversal of this trend, starting in 2001.) Another is that traffic with the U.S. is increasing faster than with the LINX exchange. Perhaps even more interesting is that the growth rate of this traffic shows no signs of exploding, even though the link capacity has grown, and so the average utilization has decreased. In March 1999, JANET had two T3s across the Atlantic, for an aggregate capacity of 90 Mb/s. By March 2000, these were replaced by two OC3s, providing 310 Mb/s. In January 2001, a third OC3 was added. Hence the utilization of the U.S. to U.K. link decreased from 64.8\% in March 1999 to 47.0\% in March 2000 and remained at about that level in March 2001. The increased capacity was not filled up immediately. (JANET links within the U.K. are about to be upgraded to OC48 or OC192, and it will be interesting to see what effect this has on the load on the transatlantic link.) \\*[1ex] \begin{table}[htb] \begin{center} Table 3.2. Growth in JANET traffic. Shows terabytes transmitted on the link from the U.S. to the British JANET academic network in March of each year, and the rate of increase from previous year. \\ ~ \\ \begin{tabular}{lrrl} year & \multicolumn{1}{c}{US to UK} & \multicolumn{1}{c}{UK to US} & \multicolumn{1}{c}{increase in} \\ & \multicolumn{1}{c}{TB/month} & \multicolumn{1}{c}{TB/month} & \multicolumn{1}{c}{US to UK traffic} \\ \hline 1997 & 3.73\hspace*{+.19in} & 2.95\hspace*{+.19in} \\ 1998 & 8.79\hspace*{+.19in} & 4.44\hspace*{+.19in} & \hspace*{+.3in}136\% \\ 1999 & 19.52\hspace*{+.19in} & 9.51\hspace*{+.19in} & \hspace*{+.3in}122 \\ 2000 & 48.76\hspace*{+.19in} & 14.90\hspace*{+.19in} & \hspace*{+.3in}150 \\ 2001 & 75.18\hspace*{+.19in} & 28.94\hspace*{+.19in} & \hspace*{+.3in}54 \end{tabular} \end{center} \end{table} The prevalent opinion appears to be that in data networks, ``if you build it, they will fill it.'' Our evidence supports this, but with the important qualification that ``they'' will not fill it immediately. That certainly has been the experience in local area networks, LANs. The prevalence of lightly utilized long distance corporate links was noted in \cite{Odlyzko1}. That paper also discussed the vBNS research network, which was extremely lightly loaded. Here we cite another example of a large network with low utilizations and moderate growth rates. Abilene is the network created by the Internet2 consortium of U.S. universities \cite{Dunn}. Its backbone consists of 13 OC48 (2.4 Gb/s) links. % Moreover, most of the consortium members had OC3 links to it. The average utilization in June 2000 was about 1.5\%, and by April 2001 it had grown to 4.1\%, for an annual growth rate of somewhat under 300\%. (That also appears to have been the growth rate over the year ending June 2000.) Yet most members had OC3 or OC12 links to the Abilene backbone. Thus in spite of the uncongested access and backbone links, traffic did not explode. (Moreover, the 300\% growth rate in traffic may be partially a reflection of some of the growth that would normally have gone over the commercial ISP links being redirected over Abilene instead. A substantial fraction of the traffic growth appears to have come from additional members joining the consortium.) Access to vBNS was restricted to certain research projects. On the other hand, Abilene is open to any traffic between the member universities, and thus it does not have the same limits to growth. The research networks cited above have low utilizations. It should be emphasized that this is not a sign of inefficiency. Many novel applications require high bandwith to be effective. That (together with some additional factors, such as high growth rates, lumpy capacity, and pricing structure) contributes to the generally much lower utilization of data networks than of the long distance voice network, \cite{Odlyzko1}. Even on more congested links, it often happens that an increase in capacity does not lead to a dramatic increase in traffic. This is illustrated by several examples. Figure 3.1 shows statistics for the traffic from the public Internet to the University of Waterloo over a period of 7 years, through the end of 1999. (This is the longest such time series that we have been able to obtain.) Detailed statistics for the Waterloo network are available at $\langle$http://www.ist.uwaterloo.ca/cn/\#Stats$\rangle$, but Fig. 3.1 is based on additional historical data provided to us by this institution.) Just as for the JANET network discussed above, for the SWITCH network to be discussed later, as well as for most access links, there is much more traffic from the public Internet to the institution than in the other direction. Hence we concentrate on this more congested link, since it offers more of a barrier. We see that even substantial jumps in link capacity did not affect the growth rate much. Traffic during most of that period kept about doubling each year. This growth rate slowed down substantially in the last two years, to about 55\% from early 1999 to early 2000, and about 33\% from then to early 2001. (We do not include most of that period in our graph, since it is hard to provide comparable data, as new connections to research networks were opened up, which, however, are not available for general Internet access.) This was primarily the result of a budget-driven limitation on the capacity of the public link. It led to an imposition of official limits on individual users, limits we will discuss later. Even with those limits, usage has been rising, and the link is completely saturated for large parts of the day. (There has been growth in connections to research networks, but those links are much more lightly utilized. Hence it is hard to say precisely what the growth rate of the entire Internet traffic at Waterloo has been recently. This is also a problem at many other institutions. That is why we do not show traffic statistics for 2000 and early 2001 in Figure 3.1.) \begin{figure} \centerline{\psfig{file=Pwat3,width=5in,height=3.5in}} Figure 3.1. Traffic on the link from the public Internet to the University of Waterloo. The line with circles shows average traffic during the month of heaviest traffic in each school term. The step function is the full capacity of the link. \end{figure} The same phenomenon of traffic that just about doubles each year, no matter what happens to capacity, can be observed in the statistics for the SWITCH network, which provides connectivity for Swiss academic and research institutions. The history and operations of this network are described in \cite{Harms, ReichlLS}, and extensive current and historical data is available at $\langle$http://www.switch.ch/lan/stat/$\rangle$. The data used to prepare Table 3.3 was provided to us by SWITCH. As is noted in \cite{ReichlLS}, the transatlantic link has historically been the most expensive part of the SWITCH infrastructure, and at times was more expensive than the entire network within Switzerland. It is therefore not surprising that this link tends to be the most congested in the SWITCH network. Even so, increasing its capacity did not lead to a dramatic change in the growth rate of traffic. If we compare increases in volume of data received between November of one year and January of the following year, there was an unusually high jump from Nov. 1998 to Jan. 1999, by 42\%. This was in response to extreme congestion experienced at the end of 1998, congestion that produced extremely poor service, with packet loss rates during peak periods exceeding 20\%. However, over longer periods of time, the growth rate has been rather steady at close to 100\% per year and independent of the capacity of the link. Especially noteworthy was the large increase in capacity in the year 2000, caused partially by the dramatic declines in prices of transatlantic transmission. It allowed SWITCH to have two OC3 links, providing redundancy. Utilization dropped noticeably, to a low level of about 10\% (and a level of about 3\% in the less heavily utilized direction from Switzerland to the U.S.), but traffic continued growing at about the same pace as before. \clearpage \begin{table}[htb] \begin{center} Table 3.3. Growth in SWITCH traffic. Average traffic flow from the U.S. to SWITCH, the Swiss academic and research network. \\ ~ \\ \begin{tabular}{l@{~}lrrr@{}l} \multicolumn{2}{c}{month} & \multicolumn{1}{c}{traffic flow} & \multicolumn{1}{c}{link capacity} & \multicolumn{2}{c}{average} \\ \multicolumn{2}{c}{~} & \multicolumn{1}{c}{Mb/s} & \multicolumn{1}{c}{Mb/s} & \multicolumn{2}{c}{utilization} \\ [+.15in] May&1996 & 1.51\hspace*{+.2in} & 3\hspace*{+.4in} & ~~~~50&.4\% \\ Jul&1996 & 1.90\hspace*{+.2in} & 3\hspace*{+.4in} & 63&.3 \\ Sep&1996 & 1.99\hspace*{+.2in} & 3\hspace*{+.4in} & 66&.3 \\ Nov&1996 & 2.21\hspace*{+.2in} & 3\hspace*{+.4in} & 73&.6 \\ Jan&1997 & 2.37\hspace*{+.2in} & 3\hspace*{+.4in} & 67&.6 \\ Mar&1997 & 2.62\hspace*{+.2in} & 4\hspace*{+.4in} & 65&.4 \\ May&1997 & 2.86\hspace*{+.2in} & 4\hspace*{+.4in} & 71&.4 \\ Jul&1997 & 3.17\hspace*{+.2in} & 8\hspace*{+.4in} & 39&.7 \\ Sep&1997 & 2.87\hspace*{+.2in} & 8\hspace*{+.4in} & 35&.9 \\ Nov&1997 & 3.24\hspace*{+.2in} & 8\hspace*{+.4in} & 40&.5 \\ Jan&1998 & 3.88\hspace*{+.2in} & 8\hspace*{+.4in} & 48&.5 \\ Mar&1998 & 4.20\hspace*{+.2in} & 8\hspace*{+.4in} & 52&.5 \\ May&1998 & 5.05\hspace*{+.2in} & 8\hspace*{+.4in} & 63&.1 \\ Jul&1998 & 5.14\hspace*{+.2in} & 8\hspace*{+.4in} & 64&.3 \\ Sep&1998 & 5.66\hspace*{+.2in} & 8\hspace*{+.4in} & 70&.7 \\ Nov&1998 & 6.20\hspace*{+.2in} & 8\hspace*{+.4in} & 77&.5 \\ Jan&1999 & 8.78\hspace*{+.2in} & 24\hspace*{+.4in} & 36&.6 \\ Mar&1999 & 9.41\hspace*{+.2in} & 24\hspace*{+.4in} & 39&.2 \\ May&1999 & 10.63\hspace*{+.2in} & 32\hspace*{+.4in} & 33&.2 \\ Jul&1999 & 10.03\hspace*{+.2in} & 32\hspace*{+.4in} & 31&.3 \\ Sep&1999 & 11.62\hspace*{+.2in} & 32\hspace*{+.4in} & 36&.3 \\ Nov&1999 & 13.26\hspace*{+.2in} & 32\hspace*{+.4in} & 41&.4 \\ Jan&2000 & 15.52\hspace*{+.2in} & 56\hspace*{+.4in} & 27&.7 \\ Mar&2000 & 17.81\hspace*{+.2in} & 56\hspace*{+.4in} & 31&.8 \\ May&2000 & 15.92\hspace*{+.2in} & 64\hspace*{+.4in} & 24&.9 \\ Jul&2000 & 19.94\hspace*{+.2in} & 155\hspace*{+.4in} & 12&.9 \\ Sep&2000 & 24.86\hspace*{+.2in} & 155\hspace*{+.4in} & 16&.0 \\ Nov&2000 & 28.37\hspace*{+.2in} & 155\hspace*{+.4in} & 18&.3 \\ Jan&2001 & 28.75\hspace*{+.2in} & 310\hspace*{+.4in} & 9&.3 \\ Mar&2001 & 32.00\hspace*{+.2in} & 310\hspace*{+.4in} & 10&.3 \\ \end{tabular} \end{center} \end{table} More detailed data about other types of SWITCH traffic can be found at $\langle$http://www.switch.ch/lan/stat/$\rangle$, through the ``Public access'' link. The listings available there as of early 2001, as well as those from previous years, show that various transmissions tended to grow at 100 to 150\% per year. (Some of the growth has come from growth in the number of institutions. For example, for the largest SWITCH customer, traffic between June 1992 and June 2000 grew by a factor of 90, for an annual growth rate of 75\%.) Occasionally there have been bigger jumps, such as the explosion in the category of traffic ``leaving SWITCHlan'' in early 2000, caused by the installation of an Akamai server that provides data to many European educational and research institutions. The NORDUNet network connects research and educational institutions in the Nordic countries. It has detailed traffic statistics online, at $\langle$http://www.nordu.net/stats/$\rangle$, that go back to November 1996. Over this period, adding up the traffic over all the interfaces shown in the data, we find that total traffic has been growing at about 130\% a year. The link to the U.S. went from 56 Kb/s in 1990 to 1.4 Gb/s in January 2001, for a compound annual growth rate of bandwidth over 10 years of about 150\%. Over the last few years, the bandwidth to the U.S. has been growing at about 100\% a year; the first OC3 (155 Mb/s) link was installed in February 1998, the second in January 1999, and by February 2000 there were four OC3 links. The fifth OC3 was put into service in June 2000, and in January 2001, four more were installed. Traffic on the main U.S. links (ignoring the 45 Mb/s connection from Iceland) grew from 54 and 30 Mb/s in March 1998 (54 Mb/s from the U.S. to NORDUNet, and 30 Mb/s in the reverse direction) to 237 and 122 Mb/s in March 2000, almost exactly a 100\% growth rate over those two years. The traffic statistics for the European TEN-155 research network (which consists largely of OC3, 155 Mb/s, links) are available at $\langle$http://stats.dante.org.uk/mystere/$\rangle$. Some of the links were heavily congested in the middle of 2000, while overall utilization has been moderate. Some of the historical traffic data for TEN-155 has been lost. However, DANTE (the organization that runs it) has provided us with data for the access link to the German national research network DFN, one of the largest contributors to TEN-155 traffic. This data, covering the period from the end of January 1999 to the beginning of July 2000, shows annual growth rates of about 70 and 90\% (for the two directions of traffic). Merit Network is a non-profit ISP that serves primarily Michigan educational institutions. It has some statistics available online at $\langle$http://www.merit.net/michnet/statistics/direct.html$\rangle$ that goes back to January 1993. This data was used to construct the graph in Fig. 3.2. The information for January 1993 through June 1998 shows only the number of inbound IP packets. The data for months since July 1998 is more complete, but it is so complete, with details of so many interfaces, that we have not yet figured out how to utilize it fully and obtain figures comparable to those for the earlier periods. Hence we have used only the earlier information for January 1993 through June 1998. The resulting time series is a reasonable although imperfect representation of a straight line, modulated by the periodic variations introduced by the academic calendar. The growth rate is almost exactly 100\% per year. \begin{figure} \centerline{\psfig{file=Pmich,width=5in,height=3.5in}} \begin{center} Figure 3.2. Traffic from Merit Network to customers. \end{center} \end{figure} We conclude by presenting data traffic growth rates for three universities. The University of Toronto in the spring of 1998 had an 8 Mb/s connection to the Internet. By the spring of 2000, the bandwidth had been increased to 25 Mb/s. At both times, the link was run at about a 50\% utilization (average of both directions), so it was very congested. (For current data and that of the previous year, see $\langle$http://www.noc.utoronto.ca/netstats/index.html$\rangle$.) Thus the compound annual growth rate for both traffic and bandwidth was about 70\%. By the spring of 2001, the link capacity had only been increased to 30 Mb/s, and the average utilization was 65\%. Thus even in the face of deteriorating quality of transmission, users had increased their traffic by about 55\%. Princeton University had two standard connections to the Internet in the springs of both 1998 and 2000. Their combined bandwidth was 31 Mb/s all this time. (They were lightly utilized in 1998, and only moderately heavily in 2000.) By 2000, Princeton also had a 155 Mb/s connection to the vBNS research network. (MRTG data for all these links is available at $\langle$http://wwwnet.princeton.edu/monitoring.html$\rangle$.) The combined traffic increased from 4.2 and 1.9 Mb/s in 1998 to 14.7 and 11.4 Mb/s in 2000. If we combine the data rates for the two directions, we find a growth rate of about 100\% per year. By spring 2001, the bandwidth of the two commercial connections to the Internet had been increased to 41 Mb/s, while the vBNS connection remained at 155 Mb/s. Combined traffic had grown to 27.0 and 20.4 Mb/s, for an almost exact doubling since spring of 2000. The connection between the University of California at Santa Cruz and the Internet is currently dominated by traffic from student residences. Thus it shows very strong seasonal effects. If we consider total Internet traffic during the first 7 days in June (before the start of the summer vacation), we find 143\% growth from 1998 to 1999, and 205\% growth from 1999 to 2000, to a final average level of 22.7 Mb/s. Much of the recent increase was caused by Napster (and will be discussed in the next section). % Much of the growth from 1998 to 1999 may have been caused by % completing the connection of all the student residences to the campus network. Many more examples can be cited, such as that of USC that was mentioned in Section 2, or that of Utah State University, with traffic statistics available at $\langle$http://thingy.usu.edu/network-stats/uen-ds3.html$\rangle$. There is also data about some of the campuses of the University of California at \\ $\langle$http://www.calren2.net/router-stats/$\rangle$. (CalREN2 provides external connectivity to most campuses in this system.) The article \cite{McCredie} mentions that the Berkeley campus has seen its traffic to the outside grow by a factor of 40 in 7 years, for a compound annual growth rate of 70\%. Some of the other average growth rates appear higher. An interested reader can find pointers to other universities, corporations, as well as exchanges that make their traffic statistics available in the listing of MRTG users at \cite{MRTG}. % $\langle$http://ee-staff.ethz.ch/$\sim$oetiker/webtools/mrtg/users.html$\rangle$. In addition, there is an increasing number of gigapops that are being formed, and they usually show their traffic statistics on the Web. For URLs, see \cite{Dunn}. (It should be mentioned, though, that most of the institutions connecting to the gigapops continue to have other connections to the Internet. Thus growth rates of their traffic at the gigapops by themselves may sometimes be misleading.) The general conclusion we draw from the examples listed above, as well as from numerous others, is that data traffic has a remarkable tendency to double each year. There are slower and faster growth rates. Overall, though, they tend to cluster in the vicinity of 100\% a year. We have not seen any large institutions with traffic doubling anywhere close to three or even four months. The growth rates noted above are often affected strongly by restrictions imposed at various levels. We will discuss this question further in Section 7, and at this stage just remark on some of the explicit limits imposed by network administrators. We noted that at the University of Waterloo, the growth rate slowed down to 55\% from early 1999 to early 2000, and to 33\% over the following year. This was probably caused largely by the congestion on the Internet link, and the explicit limits on individual student download rates, described at $\langle$http://www.ist.uwaterloo.ca/cn/\#Stats$\rangle$. The arrival of Napster (discussed in the next section) led many institutions to either ban its use, or limit traffic rates to some parts of the campus (typically student dormitories), or else to limit rates of individual flows. Push technologies were stifled at least partially because enterprise network administrators blocked them at their firewalls. Email often has size restrictions that block large attachments (and in some cases all attachments are still banned). Teleconferencing is only slowly being experimented with on corporate intranets, and even packetized voice sees very limited (although growing) use. Even spammers exercise some control. One of us has been collecting all the spam messages that have made it through the AT\&T Labs - Research spam filter to his email account. They total several thousand over the last four years. An interesting observation is that the average size of these spam messages has increased over this period, but not rapidly, namely from 4900 bytes to 7600 bytes, for a compound annual growth rate of only 12\%. Spammers want to send many messages from their connections, so have an interest in keeping them short (especially if they are attempting to avoid being recognized as spammers and shut down). At the same time, most of their customers are probably not ready to process complicated attachments in any case, and, connected by slow modems, would not have the patience to download large files. (Hardly any spam messages contain Microsoft Office attachments, the main reason corporate email messages are much larger.) This provides an informal but apparently effective limitation on how big spam messages get. There appears to be an increase in large spam messages in html format, but this process started in a serious way only in 2000. Even now, in early 2001, relatively few html spam messages show up, although the Web has been prominent for many years. Similar constraints apply to most of the content seen on the Web. As long as a large fraction of potential users have limited bandwidth, such as through dial modems, managers of Web servers will have an incentive to keep individual pages moderate in size. The general conclusion from the above discussion is that Internet traffic is subject to a variety of constraints and feedback loops, at different levels and operating on different time scale. Some are applied by network managers, others by individual users. The interaction of these constraints with rising demands is what produces the growth rates we see. To sustain the high growth rate of Internet traffic will require the creation of new applications that will generate huge traffic volumes. We estimate that as of year-end 1999, U.S. Internet backbone traffic was about a quarter to a third of voice traffic. At current growth rates (100\% per year for the Internet, 10\% for voice), by year-end 2004 there will be 8 times as much Internet as voice traffic. If voice is packetized at that stage, it will likely be compressed as well, and even at very moderate 4:1 compression, would then amount to just 3\% of Internet traffic. Thus voice will not fill the pipes that are likely to exist, and neither will traditional Web surfing. Thus we have the dilemma of service providers, network administrators, and equipment suppliers: to sustain the growth rates that the industry has come to depend on, and to accommodate the progress in technology (to be discussed more extensively later), we need new applications. Such applications are likely to appear disruptive to network operations today, and so often have to be controlled. In the long run, though, they have to be encouraged. \section{Disruptive innovations: browsers, Napster, ...} \hsp It is often said that everything changes so rapidly on the Internet that it is impossible to forecast far into the future. The next ``killer app'' could disrupt any plans that one makes. Yet there have been just two ``killer apps'' in the history of the Internet: email and the Web (or, more precisely, Web browsers, which made the Web usable by the masses). Many other technologies that had been widely touted as the next ``killer app,'' such as push technology, have fizzled. Furthermore, only the Web can be said to have been truly disruptive. From the first release of the Mosaic visual browser around the middle of 1993, it apparently took under 18 months before Web traffic became dominant on Internet backbones. It appears overwhelmingly likely that it was the appearance of browsers that then led, in combination with other developments, to that abnormal spurt of a doubling of Internet traffic every three or four months in 1995 and 1996. What were the causes of the 100-fold explosion in Internet backbone traffic over the two-year period of 1995 and 1996? We do not have precise data, but it appears that there were four main factors, all interrelated. Browsers passed some magic threshold of usability, so many more people were willing to use computers and online information services. Users of the established online services, primarily AOL, CompuServe, and Prodigy, started using the Internet. The text-based transmissions of those services, which probably averaged only a few hundred bits per second per connected user, were replaced by the graphics-rich content of the Web, so transmission rates increased to a few thousand bits per second. Finally, flat rate access plans led to a tripling of the time that individual users spent online \cite{Odlyzko3}, as well as faster growth in number of users. The Internet was able to support this explosion in traffic because it was utilizing the existing infrastructure of the telephone network. At that time, the Internet was tiny compared to the voice network. % There are no precise figures, but It is likely that the data network that handles control and billing for the AT\&T long distance voice services by itself was carrying more traffic than the NSF Internet backbone did at its peak at the end of 1994. Today, by contrast, the public Internet is rapidly moving towards being the main network, so quantum jumps in traffic cannot be tolerated so easily. In late 1999, a new application appeared that attracted extensive attention and led to many predictions that network traffic would see a major impact. It was Napster. Numerous articles in the press have cited Napster's ability to ``overwhelm Internet lines'', and have claimed that it has forced numerous universities to ban or limit its use. The impression one got from these press reports was that Napster was causing a quantum jump in Internet traffic, and was driving the traffic growth rates well beyond the normal range. However, upon close examination this does not appear to be completely accurate, and the use of Napster has not increased growth rates much beyond the annual doubling or tripling rates, even within university environments, where Napster is most popular. That is not to say that is has not resulted in huge amounts of traffic, nor that it has not had serious impact on several major networks. Napster provides software that enables users connected to the Internet to exchange and/or download MP3 music files. The Napster (web) site matches users seeking certain music files with other users who have those files on their computer. The Napster system preferentially uses as sources of files machines that have high bandwidth connections. This means that universities are the primary sources, since other organizations with fast dedicated links, mainly corporations, do not allow such traffic. The result is that although college students are often cited as the greatest users of MP3 files, it is the traffic from universities that gets boosted the most. (Since that direction of traffic is typically much less heavily used than the reverse one, the impact of Napster is much less severe than if the dominant direction of traffic were reversed.) Regular modem users are usually not affected, since their connections are too slow and evanescent. However, the proliferation of cable modems and DSL connections that have ``always-on'' high bandwidth connectivity is leading to problems for some residential users and their ISPs, especially since the uplink is the one that invariably has the more limited bandwidth. Napster has attracted huge attention because of its perceived potential to facilitate violations of copyright. This threat has led to litigation, and several universities have blocked access to the central Napster server as a result. (Whether such bans can be effective is questionable, as there are ways to bypass them. Some universities have adopted an attitude of watchful waiting, cf. \cite{Plonka}.) While the legal aspects of Napster and their implications for the music business are important questions, we will not deal with them in this chapter. A key reason that Napster is of great interest to us is that similar types of sharing applications effectively turn consumers of information into providers of information. (The World Wide Web was designed for such information sharing, but for some types of files Napster and its kin are preferable.) These applications will effectively turn the traditional consumer PCs into Internet servers which will output large amounts of traffic to other users. In Napster's case this has been predominantly MP3 music files, but other programs, such as Gnutella, work with more general data. It is highly probable that such applications could be one of the key factors that fuel the continued annual doubling or tripling of data traffic. \begin{figure} \centerline{\psfig{file=Pucsc5,width=5in,height=3.5in}} \begin{center} Figure 4.1. Traffic between UCSC and the Internet. \end{center} \end{figure} Napster first became noticeable in the summer of 1999. Its share of the total Internet traffic on many of the university networks has grown from essentially nothing to around 25\% of the total traffic. The amount of Napster traffic that is reported by several university networks (such as UC Santa Cruz, University of Michigan, University of Michigan, Indiana, UC Berkeley, Northwestern University, and Oregon State University to name a few) range from around 20\% at some as high as 50\%. However, the reported numbers are often very preliminary, and in some cases they compare Napster traffic to total traffic, while in others it appears that the high values may represent a comparison only to the out traffic. In any event this is a phenomenal growth rate for any single application. % Since it started from zero less than a year ago, it is % a little % risky to extrapolate this initial explosion out indefinitely. % Of more importance is that we do not have good values for how much (if any) of % the other types of traffic Napster is cannibalizing. With the caveat that the numbers are approximate and preliminary, we did a quick estimate of the impact of Napster on growth rates for some of these university networks. For example, prior to the introduction of Napster, UC Berkeley's network traffic appeared to be growing at roughly 70\% annually (i.e., doubling every 15 to 16 months), \cite{McCredie}. It was reported that by the spring of 2000, Napster traffic had grown to 50\% of the total. (It is not clear whether this is a percentage of the total traffic or only the out traffic). If we assume that the non-Napster traffic continued to grow at this rate, and assume that Napster traffic is now 50\% of the total, then the overall annual growth rate (since the introduction of Napster) is around 4x per year. If, however, Napster only makes up 30\% of the total then it works out to an annual growth rate of about 3.2x per year. We have detailed data for the University of California at Santa Cruz (UCSC). Its traffic reporting system is at $\langle$http://noc.ucsc.edu/mrtg/data/routers/to\_campus:\_commcat-comm-g.html$\rangle$. In Fig. 4.1 we show the monthly traffic between UCSC and the Internet during the crucial period when Napster made its appearance. There were no controls on this traffic in 1999, other than email warnings to owners of machines with large data transfers. There are huge variations from month to month, caused by the academic calendar, but one can see that traffic basically doubled from the spring semester of 1999 to the fall one. By early 2000, Napster traffic was about 50\% of outgoing transmissions, and 10\% of incoming ones. In March 2000, a rate limitation was imposed on the traffic from the dormitories, which has limited the impact of Napster. Napster is the obvious culprit in the increase in outgoing traffic to about 60\% of that of incoming traffic in February 2000. The limits did result in the drop in the ratio of outgoing to incoming traffic to about 40\% in April 2000, but then this ratio crept up to over 50\% in May and June. \begin{figure} \centerline{\psfig{file=Pwisc4,width=5in,height=3.5in}} \begin{center} Figure 4.2. Change in volume and composition of traffic between the University of Wisconsin in Madison and the Internet. Average transmission rates in spring 1999 and spring 2000. \end{center} \end{figure} The University of Wisconsin-Madison has done the most to carefully monitor Napster and its kin, has high bandwidth on campus and to the Internet, and as of mid-2000 has not as yet taken any steps to limit Napster traffic \cite{Plonka}. (For current analysis of their traffic by protocol, application, and so on, see $\langle$http://wwwstats.net.wisc.edu/$\rangle$. Several other universities are using this software, developed by Dave Plonka at the University of Wisconsin, for analyzing their traffic as well.) Fig. 4.2 shows the effect of Napster. This campus is very unusual in that even before Napster made its appearance, there was about as much outgoing as incoming traffic. Napster has led to a disproportionate increase in outgoing traffic. (At some times it apparently led to this traffic reaching capacity limit for the link.) Fig. 4.2 compares the average rates for data traffic during the week starting May 7, 1999 to those for the week starting May 12, 2000. Both were exam weeks at the end of the regular school year. (Transmissions dropped dramatically in the following weeks.) Outgoing traffic increased 157\%, and total traffic 138\%. If we exclude Napster, the other traffic increased by 81\%. Thus Napster has had a noticeable effect on the growth rate of traffic on this campus, but not an outlandish one. Several networks % , such as that of the University of Wisconsin-Madison that report Napster traffic of as much as 30\% are not doing anything to limit Napster since they claim that they still have plenty of bandwidth. Others have imposed limits on the total bandwidth available to the dormitories, or else are limiting rates of individual flows. Note that if your traffic doubles each year, a one-time 30\% increment is noticeable when it occurs, but becomes minor in a couple of years. A much more serious problem arises if a new application continues growing. % The big question for % many campuses is whether Napster traffic will surge again in % the fall of 2000. Even if Napster does not grow much more, either because of legal action or because of music demand being met by other sources. video files are likely to become increasingly common, and the question is how fast that will drive the growth of total traffic. % It is also interesting to note that some % networks are reporting that Napster, HHTP, and FTP % traffic all make up roughly the same amount of traffic (around 20\% % each). This is a bit similar to what happened with respect to the % HTTP/web traffic. Prior to the wide spread introduction of browsers % such as Netscape (and perhaps its predecessor Mosiac), web/HTTP traffic % made up essentially a negligible amount of the traffic. However, within % a year or two it became a substantial fraction (around 20-30\%) of the % total traffic. Aside from Napster, occasionally even a large institution will experience a local perturbation in its data traffic patterns caused by one particular application. For example, the SETI@home distributed computing project, $\langle$http://setiathome.ssl.berkeley.edu$\rangle$, uses idle time on about three million PCs (as of mid-2001) to search for signs of extraterrestrial intelligence in signals collected by radio telescopes. This project is run out of the Space Sciences Institute at the University of California at Berkeley, and within a year of inception accounted for about a third of the outgoing campus traffic \cite{McCredie}. (Moreover, this was extremely asymmetrical traffic, with large sets of data to be analyzed going out to the participating PCs, and small final results coming back. That most of the data went away from campus made this application less disruptive than it would have been otherwise.) Its disruptive effect is moderated by limiting its transmission rate to about 20 Mb/s. At the University of California at Santa Cruz, a complete copy of the available genome sequence was made available for public download in early July 2000. This, combined with coverage in the popular press and on the popular Slashdot online discussion list, led to an immediate surge in traffic, far exceeding the effects of Napster. If the interest in this database continues, it will require reengineering of the campus network. The SETI@home project is interesting for several reasons. It is cited in \cite{McCredie} as a major new disruptive influence. Yet it contributes only about 20 Mb/s to the outgoing traffic. An increasing number of PCs and workstations are connected at 100 Mb/s, and even Gigabit Ethernet (1,000 Mb/s) is coming to the desktop. This means that for the foreseeable future, a handful of workstations will in principle be capable of saturating any Internet link. Given the projections for bandwidth (discussed in Section 5), a few thousand machines will continue to be capable of saturating all the links in the entire Internet. Thus control on user traffic will have to be exercised to prevent accidental as well as malicious disruptions of service. However, it seems likely that such control could be limited to the edges of the network. In fact, such control will pretty much have to be exercised at the edges of the network. QoS will not help by itself, since a malicious attacker who takes over control of a machine will be able to subvert any automatic controls. Finally, after considering current disruptions from Napster and SETI@home, we go back and consider browsers and the Web again. They were cited as disruptive back in 1994 and 1995. (Mosaic was first released unofficially around the middle of 1993, officially in the fall of 1993, and took off in 1994.) However, when we consider the growth rates for the University of Waterloo (Fig. 3.1), for MichNet (Fig. 3.2), or for SWITCH (for which Table 3.3 only covers the period since early 1996, but which apparently had regular growth throughout the 1990s, according to \cite{Harms}), we do not see anything anomalous, just the steady doubling of traffic each year or so. If we consider the composition of the traffic, there were major changes. For example, Fig. 4.3 shows the evolution of traffic between the University of Waterloo and the Internet. (It is based on analysis of traffic during the third week in each March, and more complete results are available at $\langle$http://www.ist.uwaterloo.ca/cn/Stats/ext-prot.html$\rangle$.) The Web did take over, but much more slowly than on Internet backbones. There are no good data sets, but it has been claimed that by the end of 1994, Web traffic was more than half of the volume of the commercial backbones. On the other hand, the data for the NSFNet backbone, available at $\langle$http://www.merit.edu/merit/archive/nsfnet/statistics/.index.html$\rangle$, show that Web traffic was only approaching 20\% there by the end of 1994, a level similar to that for the University of Waterloo. Thus at well-wired academic institutions such as the University of Waterloo and others that dominated NSFNet traffic, the impact of the Web was muted. \begin{figure} \centerline{\psfig{file=Pwat9,width=5in,height=3.5in}} \begin{center} Figure 4.3. Composition of traffic between the University of Waterloo and the Internet. Based on data collected in March of each year. \end{center} \end{figure} Perhaps the main lesson to be drawn from the discussion in this section is that the most disruptive factor is simply rapid growth by itself. A doubling of traffic each year is very rapid, much more rapid than in other communication services. Fig. 4.3 shows email and netnews shrinking as fractions of the traffic at the University of Waterloo, from a quarter to about 5\%. Yet the byte volume of these two applications grew by a factor of 12 during the 6 years covered by the graph, for a growth rate of over 50\% per year, which is very rapid by most standards. If we are to continue the doubling of traffic each year, new applications will have to keep appearing and assuming dominant roles. An interesting data point is that even at the University of Wisconsin in Madison, which analyzes its data traffic very carefully, about 40\% of the transmissions escape classification. That is consistent with information from a few corporate networks, where the managers report that upwards of half of their traffic is of unknown types. (A vast majority of network managers do not even attempt to perform such analyses.) This shows how difficult coping with rapid growth is. \section{Technology trends: Growth in bandwidth} \hsp Bandwidth is growing rapidly, primarily through the introduction of WDM systems of increasing capacity, and to a much lesser extent through installation of additional fiber. However, this increase is not as fast as some would have us believe. For example, George Gilder has predicted that ``bandwidth will triple each year for the next 25'' \cite{Gilder2}. While he was right in predicting rapid growth, the actual rate of increase has so far been somewhat more modest. In Table 5.1 we show the progress that has occurred so far, and is likely to occur in the next few years. This table was generated by using a variety of vendor release dates along with our detailed technical understanding of such high-speed transport systems. We are considering commercial systems and not research hero experiments. Historically, there was a lag of three years or more between the lab demonstration of a given transmission capacity, and its introduction into the commercial environment. Recently, however, this time lag appears to have diminished, but this is very debatable. There is much hype about commercial transmission capacities, and it is still a bit unclear as to how early a given high capacity transmission system will become widely deployed. Even the rate of increase for the maximum capacity achieved within lab experiments has slowed down considerably. For example, the first 1 Tb/s experiments were done in late 1995 to early 1996, and it appears that at year's end 1999 % to beginning 2000 the maximum rate was only around 3 Tb/s. This is a growth of ``only'' three times in roughly 4 years, a rate much less than what was demonstrated in the previous several years. Even when a system does become commercially widely available, it takes a while for it to affect the available bandwidth of a network. It has to be installed and tested, which all takes time. Further, not all old systems get replaced right away. This is similar to the PC situation, in which machines tend to be replaced on a three or four year cycle. \\*[1ex] \begin{table}[htb] \begin{center} Table 5.1. Widespread deployment of WDM systems. ~ \\ [+.2in] \begin{tabular}{ccc} system description & fiber capacity & wide deployment \\ [+.1in] 8 $\times$ 2.5 Gb/s & 20 Gb/s & 1996 \\ 16 $\times$ 2.5 Gb/s & 40 Gb/s & 1997 \\ 32 $\times$ 2.5 Gb/s & 80 Gb/s & 1999 \\ 80 $\times$ 2.5 Gb/s & 200 Gb/s & 2000 \\ 40 $\times$ 10 Gb/s & 400 Gb/s & mid to late 2000 \\ 160 $\times$ 2.5 Gb/s & 400 Gb/s & mid to late 2000 \\ 80 $\times$ 10 Gb/s & 800 Gb/s & late 2001 \\ 160 $\times$ 10 Gb/s & 1.6 Tb/s & late 2002 \\ 40 $\times$ 40 Gb/s & 1.6 Tb/s & late 2002 \\ 80 $\times$ 40 Gb/s & 3.2 Tb/s & late 2003 to early 2004 \\ 100 $\times$ 40 Gb/s & 4 Tb/s & 2005 \\ 160 $\times$ 40 Gb/s & 6.4 Tb/s & 2007 \\ \end{tabular} \end{center} \end{table} The projections in Table 5.1 only go out to 2007. Beyond that point there appear to be serious barriers to improvements in the current technologies. For example, the erbium-doped fiber amplifiers that are crucial for the current systems cover only a limited range of wavelengths. It could be that those barriers will be overcome in time, just as similar barriers to Moore's Law for semiconductors have repeatedly been overcome. However, that does not affect our arguments. Given the time lags between research experiments and deployment, it appears that for the next half a dozen years at least we will be limited to the progress shown in Table 5.1, which corresponds to approximately a doubling of capacity each year for each fiber. The effective transport capacity can be increased by measures other than boosting the capacity of each fiber. One can ``light up'' existing fibers that are presently not used. (Much of the capacity, especially among the new carriers, is ``dark,'' not used for any transmission yet.) One can also ``light up'' more channels on installed DWDM systems. (Today it is rare for all channels to be in use.) The currently dominant SONET technologies can be abandoned in favor of service restoration at the IP level. (SONET rings typically use fiber with three times the transport capacity of the circuits that provide actual service.) Private lines, which are used at low fractions of their capacity, can be replaced by virtual private networks (VPNs) over the public Internet, which is run at higher average utilization. All these measures together, combined with advances in DWDM, could allow an increase in the traffic carried by long distance network by factors of three or so each year for the next decade. However, substantially faster growth rates would require deploying new fiber. This is increasingly easy to do, as much of the new construction provides empty conduits in addition to the one carrying the fiber that is installed. However, there are limits to how fast new fiber could be installed. If network capacity were to grow by 200\% per year, and the DWDM allowed the capacity of each fiber to grow only 100\%, eventually we would need to increase the volume of fiber by 50\% a year. Compound interest is very powerful, and a 50\% annual growth rate results in growth by a factor of almost 60 over a decade. As a result, we do not expect that growth rates of even 300\% per year in traffic could be sustained over many years. Although technology will be providing increasing transport capacity, and also ways to use that capacity more efficiently, there will also be countervailing tendencies that are hard to estimate. One is that of the distance dependence of traffic. This subject is treated in \cite{CoffmanO} and in somewhat more detail in \cite{Odlyzko3}. Voice telephone and private line data traffic are strongly local. On the other hand, it appears that Internet traffic at present is not. Will that change? We do not know enough to predict this yet, although there are some signs of increasing locality. Caching and content distribution networks will be pushing content towards the edges. However, only a fraction (usually estimated at well under half) of the Web traffic is cachable. There is also likely to be a growth in non-Web traffic, as we explain later. This, combined with the continuing growth in the volume of data on the Internet (to be discussed later) may be such that these measures will have little effect. In addition, it is desire for low transaction latency that is driving the development of data networks, and this is what underlies the low average utilizations we observe. It is possible that as transmission capacity becomes less expensive, users will demand lower utilizations. This would be analogous to what appears to have happened, and to still be happening, in LANs. A decade ago, average utilizations appear to have been perhaps 10 times as high as those we see today. (We do not have solid data on this subject, unfortunately.) Yet there is a rapid movement towards gigabit Ethernet, and soon towards ten gigabit Ethernet, although average utilizations are low, on the order of 1\%. % George Gilder has predicted that the transmission capacity % of a single fiber would triple each year through at least % 2022 \cite{Gilder2}. The difference between doubling and % tripling each year quickly becomes immense through the % power of compound interest. Over 10 years, doubling each % year increases capacity by a factor of 1,024, whereas % a tripling each year increases that capacity by 59,049, % almost 60 times more. As a final remark, we should note that the bandwidth we discuss here is not directly comparable to the bandwidths of data and voice networks discussed in \cite{CoffmanO}. That paper considered only circuits that are actually used to carry customer traffic. It ignored all the redundancy that is present to provide fault tolerance, as well as the dark fiber. It also ignored the differences between air distance and actual distance along fibers, the loss of capacity from various framing schemes, and many other factors. \section{Technology trends: Growth in demand} \hsp The approximate doubling of transmission capacity of each fiber that is shown in Table 5.1 is analogous to the famous ``Moore's Law'' in the semiconductor industry. In 1965, Gordon E. Moore, then in charge of R\&D at Fairchild Semiconductor, made a simple extrapolation from three data points in his company's product history. He predicted that the number of transistors per chip would about double each year for the next 10 years. This prediction was fulfilled, but when Moore revisited the subject in 1975, he modified his projection for further progress by predicting that the doubling period would be closer to 18 months. (For the history and fuller discussion of ``Moore's Law'', see \cite{Schaller}.) Remarkably enough, this growth rate has been sustained over the following 25 years. There have been many predictions that progress was about to come to a screeching halt (including some recent ones), but the most that can be said is that there may have been some slight slowdown recently. (For example, according to the calculations of \cite{ElderingSE}, the number of transistors in leading-edge microprocessors doubles every 2.2 years. On the other hand, the doubling period is lower for commodity memories.) Experts in the semiconductor area are confident that Moore's 1975 prediction for rate of improvement can be fulfilled for at least most of the next decade. Predictions similar to Moore's had been made before in other areas, and in \cite{Licklider} (which was written before Moore made his famous prediction) they were made for the entire spectrum of computing and communications. However, it is Moore's Law that has entered the vernacular as a description of the steady and predictable progress of technology that improves at an exponential rate (in the precise mathematical sense). Moore's Law results from a complex interaction of technology, sociology, and economics. No new laws of nature had to be discovered, and there have been no dramatic breakthroughs. On the other hand, an enormous amount of research had to be carried out to overcome the numerous obstacles that were encountered. It may have been incremental research, but it required increasing ranks of very clever people to undertake it. Further, huge investments in manufacturing capacity had to be made to produce the hardware. Perhaps even more important, the resulting products had to be integrated into work and life styles of the institutions and individuals using them. For further discussions of the genesis, operations, and prospects of Moore's Law, see \cite{ElderingSE, Schaller}. The key point is that Moore's Law is not a natural law, but depends on a variety of factors. Still, it has held with remarkable regularity over many decades. While Moore's Law does apply to a wide variety of technologies, the actual rates of progress vary tremendously among different areas. For example, battery storage is progressing at a snail's pace, compared to microprocessor improvements. This has significant implications for mobile Internet access, limiting processor power and display quality. Display advances are more rapid than those in power storage, but nowhere near fast enough to replace paper as the preferred technology for general reading, at least not at any time in the next decade. (This implies, in particular, that the bandwidth required for a single video transmission will be growing slowly.) DRAMs are growing in size in accordance with Moore's Law, but their speeds are improving slowly. Microprocessors are rapidly increasing their speed and size (which allows for faster execution through parallelism and other clever techniques), but memory buses are improving slowly. For some quantitative figures on recent progress, see \cite{GrayS}. From the standpoint of a decade ago, we have had tidal waves of just about everything, processing power, main memory, disk storage, and so on. For a typical user, the details of the PC on the desktop (MHz rating of the processor, disk capacity) do not matter too much. It is generally assumed that in a couple of years a new and much more powerful machine will be required to run the new applications, and that it will be bought for about the same price as the current one. In the meantime, the average utilization of the processor is low (since it is provided for peak performance only), compression is not used, and wasteful encodings of information (such as 200 KB Word documents conveying a simple message of a few lines) are used. The stress is not on optimizing the utilization of the PC's resources, but on making life easy for the user. To make life easy for the end user, though, clever engineering is employed. Because the tidal waves of different technologies are advancing at different rates, optimizing user experience requires careful architectural decisions \cite{GrayS, HennessyP}. In particular, since processing power and storage capacity are growing the fastest, while communication within a PC is improving much more slowly, elaborate memory hierarchies are built. They start with magnetic hard disks, and proceed through several levels of caches, invisibly to the user. The resulting architecture has several interesting implications, explored in \cite{GrayS}. % The fraction of information % that is actually accessed during a month, say, is diminishing. For example, mirroring disks is becoming preferable to RAID fault tolerant schemes that are far more efficient but slower. \\*[1ex] % It makes sense to cache just about everything that is processed. % George Gilder was a pioneer in predicting that data transmission % would explode \cite{Gilder1, Gilder2}. It has, and is continuing % to explode. % Table 1 of \cite{FishburnO} shows Intel microprocessors increasing % in power in line with Moore's Law, prices staying about constant, % but Intel revenues growing 20-fold between 1986 and 1997. \begin{table}[htb] \begin{center} Table 6.1. Worldwide hard disk drive market. (Based on Sept. 1998 and Aug. 2000 IDC reports.) ~ \\ [+.2in] \begin{tabular}{ccc} year & revenues (billions) & storage capacity (terabytes) \\ [+.1in] 1995 & \$21.593 & 76,243 \\ 1996 & 24.655 & 147,200 \\ 1997 & 27.339 & 334,791 \\ 1998 & 26.969 & 695,140 \\ 1999 & 29.143 & 1,463,109 \\ 2000 & 32.519 & 3,222,153 \\ 2001 & 36.219 & 7,239,972 \\ 2002 & 40.683 & 15,424,824 \\ 2003 & & 30,239,756 \\ 2004 & & 56,558,700 \end{tabular} \end{center} \end{table} The density of magnetic disk storage increased at about 30\% per year from 1956 to 1991, doubling every two and a half years \cite{Economist}. (Total deployed storage capacity increased faster, as the number of disks shipped grew.) In the 1990s, the growth rate accelerated, and in the late 1990s increased yet again. By some accounts, the densities in disk drives are about doubling each year. For our purposes, the most relevant figure will be the total storage capacity of disk drives. Table 6.1 shows data from IDC reports, which shows capacity shipped each year slightly more than doubling through the year 2003, and then slowing down somewhat. An interesting comment is that in the earlier 1998 report, the slowing of the growth rate was expected to occur already in 1999. Similar projections from Disk/Trend ($\langle$http://www.disktrend.com/$\rangle$) also suggest that the total capacity of disk drives shipped will continue doubling through at least the year 2002. Given the advances in research on magnetic storage, it seems that a doubling each year until the year 2010 might be achievable (with some contribution from higher revenues, as shown in Table 6.1, but most coming from better technology). After about 2010, it appears that magnetic storage progress will be facing serious limits, but by then more exotic storage technologies may become competitive. It seems safest to assume that total magnetic disk storage capacity will be doubling each year for the next decade. However, even if there is a slowdown, say to a 70\% annual growth rate, this will not affect our arguments too much. The key point is that storage capacity is likely to grow at rates not much slower than those of network capacity. Furthermore, total installed storage is already immense. Table 6.1 shows that at the beginning of the year 2000, there were about 3,000,000 TB of magnetic disk storage. If we compare that with the estimates of Table 1.2 for network traffic, we see that it would take between 250 and 400 months to transmit all the bits on existing disks over the Internet backbones. This comparison is meant as just a thought exercise. The backbones considered in Table 1.2 are just those in the U.S., whereas disks counted in Table 6.1 are spread around the world. A large fraction of the disk space is empty, and much of the content is duplicated (such as those hundreds of millions of copies of Windows 98), so nobody would want to send them over the Internet. Still, this thought exercise is useful in showing that there is a huge amount of digital data that could potentially be sent over the Internet. Further, this pool of digital data is about doubling each year. An interesting estimate of the volume of information in the world is presented in \cite{Lesk}. (For a recent update of Lesk's study, with more detail as well as with more current data, see the report prepared at University of California at Berkeley under the leadership of Peter Lyman and Hal Varian \cite{LymanV}.) It shows that already in the year 1997 we were on the threshold of being able to store all data that has ever been generated (meaning books, movies, music, and so on) in digital format on hard disks. By now we are well past that threshold, so future growth in disk capacities will have be devoted to other types of data that we have not dealt with before. Some of that capacity will surely be devoted to duplicate storage (such as a separate copy of an increasingly bloated operating system on each machine). Most of the storage, though, will have to be filled by new types of data. The same process that is yielding faster processors and larger memories is also leading to improved cameras and sensors. These will yield huge amounts of new data, that had not been available before. It appears impossible to predict precisely what type of data this will be. Much is likely to be video storage, from cameras set up as security measures, or else ones that record our every movement. There could also be huge amounts of data from medical sensors on our bodies. What is clear, though, is that ``[t]he typical piece of information will {\em never} be looked at by a human being'' \cite{Lesk}. There will simply not be enough of the traditional ``content'' (books, movies, music), nor even of the less formal type of ``content'' that individuals will be generating on their own. Huge amounts of data that is generated by machines use by other machines suggests that data networks will also be dominated by transfers of such data. This was already predicted in \cite{deSolaPITH}, and more recently in \cite{Odlyzko2, StArnaud, StArnaudCFM}. Given an exponential growth rate in volume of data transfers, it was clear that at some point in the future most of the data flying through the networks would be neither seen nor heard by any human being. Thus we can expect that streaming media with real-time quality requirements will be a decreasing fraction of total traffic at some point within the next decade. There will surely be an increase in the raw volume of streaming real-time traffic, as applications such as videoconferencing move onto the Internet. However, as a fraction of total traffic, such transmissions will not only decrease eventually, but may not grow much at all even in the intermediate future. (Recall that at the University of Waterloo over the last 6 years, the volume of email grew about 50\% a year, but as a fraction of total traffic it is almost negligible now.) The huge imbalance in volume of storage and capacities of long distance data networks strongly suggests that even the majority of traditional ``content'' will be transmitted as files, and not in streaming form. For more detailed arguments supporting this prediction, see \cite{Odlyzko2}. This development (in which ``content'' is sent around as files for local storage and playback) is already making its appearance with MP3, Napster, and related programs. The huge hard disk storage volumes also mean that most data will have to be generated locally. There will surely also be much duplication (such as operating systems, movies, and so on that would be stored on millions of computers). Aside from that, there will likely be huge volumes of locally generated data (such as from security cameras and medical sensors) that will be used (if at all) only in highly digested form. \section{Is there a ``Moore's Law'' for data traffic?} \hsp The examples in Section 3 support the notion that there is a ``Moore's Law'' for data traffic, with transmission volumes doubling each year. Even at large institutions that already have access to state-of-the art technology, data traffic to the public Internet tends to follow this rule of doubling each year. This is not a natural law, but, like all other versions of ``Moore's Law,'' reflects a complicated process, the interaction of technology and the speed with which new technologies are absorbed. A ``Moore's Law'' for data traffic is different from those in other areas, since it depends in a much more direct way on user behavior. In semiconductors, consumer willingness to pay drives the research, development, and investment decisions of the industry, but the effects are indirect. In data traffic, though, changes can potentially be much faster. A residential customer with dial modem access to the Internet could increase the volume of data transfer by a factor of about five very quickly. All it would take would be installation of one of the software packages that prefetch Web sites that are of potential interest, and which fill in the slack between transmissions initiated by the user. Similarly, a university's T3 connection to the Internet could potentially be filled by a single workstation sending data to another institution. Thus any ``Moore's Law'' for data traffic is by nature much more fragile than the standard ``Moore's Law'' for semiconductors, for example. Thus it is remarkable that we see so much regularity in growth rates of data transfers. Links to the public Internet are usually the most expensive parts of a network, and are regarded as key choke points. They are where congestion is seen most frequently at institutional networks. Yet the ``mere'' annual doubling of data traffic even at institutions that have plenty of spare capacity on their Internet links means that there are other barriers that matter. The obvious one is the public Internet itself. It is often (some would say usually) congested. A terabit pipe does not help if it is hooked up to a megabit link, and so providing a lightly utilized link to the Internet does not guarantee good end-to-end performance. Yet that is not the entire explanation either, since corporate Intranets, which tend to have adequate bandwidth, and seldom run into congestion, tend to grow no faster than a doubling of traffic each year. There are other obstructions, such as servers, middleware, and, perhaps most important, services and user interfaces. People do not care about getting many bits. What they care about are applications. However, applications take time to be developed, deployed, and adopted. To quote J. Licklider (who deserves to be called ``the grandfather of the Internet'' for his role in setting up the research program that led to the Internet's creation), \begin{quote} A modern maxim says: ``People tend to overestimate what can be done in one year and to underestimate what can be done in five or ten years.'' \hspace*{+3in}(footnote on p.~17 of \cite{Licklider}) \\ \end{quote} ``Internet time,'' where everything changes in 18 months, has a grain of truth, but is largely a myth. Except for the ascendancy of browsers, most substantial changes take 5 to 10 years. As an example, it is at least five years since voice over IP was first acclaimed as the ``next big thing.'' Yet its impact so far has been surprisingly modest. It is coming, but it is not here today, and it won't be here tomorrow. People take time to absorb new technologies. What is perhaps most remarkable is that even at institutions with congested links to the Internet, traffic doubles or almost doubles each year. Users appear to find the Internet attractive enough that they exert pressure on their administration to increase the capacity of the connection. Existing constraints, such as those on email attachments, or on packetized voice, or video, as well as the basic constraint of limited bandwidth, are gradually loosened. Note that this is similar to the process that produces the standard Moore's Law for PCs. Intel, Micron, Toshiba, and the rest of the computer industry would surely produce faster advances if users bought new PCs every year. Instead, a typical PC is used for three to four years. On one hand there is pressure to keep expenditures on new equipment and software under control, and also to minimize the complexity of the computing and communications support job. On the other hand, there is pressure to upgrade, either to better support existing applications, or to introduce new ones. Over the last three decades, the conflict between these two pressures has produced a steady progress in computers. Similar pressures appear to be in operation in data networking. In conclusion, we cannot be certain that Internet traffic will continue doubling each year. All we can say is that historically it has tended to double each year. Still, trends in both transmission and in other information technologies appear to provide both the demand and the supply that will allow a continuing doubling each year. Since betting against such ``Moore's laws'' in other areas has been a loser's game for the last few decades, it appears safest to assume that data traffic will indeed follow the same pattern, and grow at close to 100\% per year. \section{Conclusions and speculations} \hsp The main conclusion we draw from the data and arguments of the previous sections is that Internet traffic is likely to continue doubling each year for the next decade or so. We next discuss the likely implications of such a growth rate. There have been many predictions that data traffic would grow rapidly, and that this would produce a quantum change in our information environment. That has happened, and is continuing to happen. However, some of the predictions have been too optimistic. Bill Gates predicted in 1994 that we would have ``unlimited bandwidth'' within a decade (see \cite{Gilder1}). That has not happened and will not happen. We are indeed experiencing a ``tidal wave of bandwidth,'' as George Gilder forecast \cite{Gilder1}. However, that tidal wave is accompanied by other tidal waves, of processing power and especially storage. In particular, there is far more stored data than transport capacity, and this will not change materially. At today's Internet traffic rates, it would take over 20 years to transmit all the bits that are on magnetic hard drives. The precedents of Moore's laws suggest that we should expect total capacity of magnetic storage to continue doubling each year, as it has been doing for a while. If it does, and data traffic also doubles each year, as we have shown is likely, then the relation of storage capacity and transport will not change. Even if data traffic triples each year (as it might for a few years, given the spare fiber capacity that exists, and other factors we have discussed in Section 5), at the end of this decade it would still take four months to transmit all the hard disk contents over the Internet. Therefore most data will stay local. Locality of data, as well as speed of light limitations and communication overheads will mean that information architectures will not change radically. Today it already makes sense to cache practically everything \cite{GrayS}. This will be even more true in the future. Caching and content distribution will play major roles. Yet the value of the Net is largely in the mass of data out there, most of which has little value to most people. Thus there will be tremendous value in crawlers and other aids to finding and organizing all that content. Another general conclusion is that there will be neither a ``bandwidth glut'' nor a ``bandwidth shortage.'' It appears that supply and demand will be growing at comparable rates. Thus pricing is likely to play a major role in the evolution of traffic. (As was noted in \cite{CoffmanO, Odlyzko3}, data transmission prices have been increasing through most of the 1990s, and have only recently showed signs of decrease. Once they start declining rapidly, many of the constraints on usage that we see today are likely to be relaxed.) Streaming real time transmission is bound to grow in absolute volume. As a fraction of total traffic, it may increase for a while. However, eventually it is very likely to decline, as demand for this type of traffic will not be growing as fast as network capacity. Repeating what we said in Section 4, if the doubling of traffic each year is to continue, new applications will have to keep appearing and assuming dominant roles. A doubling of traffic each year will mean that network operators will continue to scramble to meet disruptive demands of new applications. We will not have the smooth and predictable growth that has been common in other communication services. % caching and content distribution % premium on finding content % pricing: fiber not the limiting factor % local connections key % can record everything % speed of light % communications overheads to be cut down \paragraph{Acknowledgements.} We thank Mark Boolootian, Michael Bruce, Doug Carson, Kim Claffy, Jim Gray, Jose-Marie Griffiths, Willi Huber, Cheng Jin, Don King, Michael Lesk, Alan McCord, Daniel McRobb, Jeff Ogden, Saverio Pangoli, Jim Pepin, Dave Plonka, Gil Press, Larry Rabiner, Roger Watt, and Dan Werthimer for comments and useful information. \clearpage \begin{thebibliography}{deSolaPITH} \bibitem[Boardwatch]{Boardwatch} {\em Boardwatch} magazine, $\langle$http://www.boardwatch.com$\rangle$. \bibitem[Bruno]{Bruno} L. Bruno, Fiber optimism: Nortel, Lucent, and Cisco are battling to win the high-stakes fiber-optics game, {\em Red Herring,} June 2000. Available at $\langle$http://www.herring.com/mag/issue79/mag-fiber-79.html$\rangle$. \bibitem[Cochrane]{Cochrane} N. Cochrane, We're insatiable: Now it's 20 million million bytes a day, {\em Melbourne Age,} Jan. 15, 2001. Available at $\langle$http://www.it.fairfax.com.au/networking/20010115/A13694-2001Jan15.html$\rangle$. \bibitem[CoffmanO]{CoffmanO} K. G. Coffman and A. M. Odlyzko, The size and growth rate of the Internet. {\em First Monday,} Oct. 1998, $\langle$http://firstmonday.org/$\rangle$. Also available at $\langle$http://www.research.att.com/$\sim$amo$\rangle$. \bibitem[deSolaPITH]{deSolaPITH} I. de Sola Pool, H. Inose, N. Takasaki, and R. Hurwitz, {\em Communications Flows: A Census in the United States and Japan,} North-Holland, 1984. \bibitem[Dunn]{Dunn} L. Dunn, The Internet2 project, {The Internet Protocol Journal,} vol. 2, no. 4 (Dec. 1999). Available at $\langle$http://www.cisco.com/warp/public/759/ipj\_issues.html$\rangle$. \bibitem[Economist]{Economist} Not Moore's Law, {\em The Economist}, July 12, 1997. \bibitem[ElderingSE]{ElderingSE} C. A. Eldering, M. L. Sylla, and J. A. Eisenach, Is there a Moore's Law for bandwidth?, {\em IEEE Communications Magazine}, Oct. 1999, pp. 2--7. \bibitem[FishburnO]{FishburnO} P. C. Fishburn and A. M. Odlyzko, Dynamic behavior of differential pricing and Quality of Service options for the Internet, Proc. First Intern. Conf. on Information and Computation Economies (ICE-98), ACM Press, 1998, pp. 128-139. Extended version to appear in Decision Support Systems (2000). Available at $\langle$http://www.research.att.com/$\sim$amo$\rangle$. \bibitem[Galbi]{Galbi} D. Galbi, Bandwidth use and pricing trends in the U.S., {\em Telecommunications Policy}, vol. 24, no. 11 (Dec. 2000). Available at $\langle$http://www.galbithink.org$\rangle$. \bibitem[Gilder1]{Gilder1} G. Gilder, The bandwidth tidal wave, {\em Forbes ASAP}, Dec. 5, 1994. Available at $\langle$http://www.forbes.com/asap/gilder/telecosm10a.htm$\rangle$. \bibitem[Gilder2]{Gilder2} G. Gilder, Fiber keeps its promise: Get ready, bandwidth will triple each year for the next 25, {\em Forbes}, April 7, 1997. Available at $\langle$http://www.forbes.com/asap/97/0407/090.htm$\rangle$. \bibitem[GrayS]{GrayS} J. Gray and P. Shenoy, Rules of thumb in data engineering, Proc. 2000 IEEE Intern. Conf. Data Engineering. Also available at $\langle$http://research.microsoft.com/$\sim$gray$\rangle$. \bibitem[GuptaSW]{GuptaSW} A. Gupta, D. O. Stahl, and A. B. Whinston, The Internet: A future tragedy of the commons?, available at $\langle$http://cism.bus.utexas.edu/res/wp.html$\rangle$. \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[HennessyP]{HennessyP} J. L. Hennessy and D. A. Patterson, {\em Computer Architecture: A Quantitative Approach,} Morgan Kaufmann, 1990. \bibitem[Howe]{Howe} P. J. Howe, MCI chief sees big outlays to handle net traffic: Ebbers estimates \$100B to upgrade network, {\em Boston Globe}, March 7, 2000. \bibitem[Jander]{Jander} M. Jander, LINX to Cisco: ``Good Riddance'', {\em Light Reading,} March 16, 2000. Available at $\langle$http://www.lightreading.com/document.asp?doc\_id=266$\rangle$. \bibitem[Lesk]{Lesk} M. Lesk, How much information is there in the world?, 1997 unpublished paper, available at $\langle$http://www.lesk.com/mlesk/diglib.html$\rangle$. \bibitem[Licklider]{Licklider} J. C. R. Licklider, {\em Libraries of the Future,} MIT Press, 1965. \bibitem[LymanV]{LymanV} P. Lyman and H. R. Varian, How much information?, available at $\langle$http://www.sims.berkeley.edu/how-much-info/$\rangle$. \bibitem[McCredie]{McCredie} J. McCredie, UC Berkeley must manage campus network growth, {\em The Daily Californian,} March 14, 2000. Available at $\langle$http://www.dailycal.org/article.asp?id=1912\&ref=news$\rangle$. \bibitem[MRTG]{MRTG} The Multi Router Traffic Grapher of Tobias Oetiker and Dave Rand, information and links to sites using it at $\langle$http://ee-staff.ethz.ch/$\sim$oetiker/webtools/mrtg/mrtg.html$\rangle$. \bibitem[Noll1]{Noll1} A. M. Noll, {\em Introduction to Telephones and Telephone Traffic,} 2nd ed., Artech House, 1991. \bibitem[Noll2]{Noll2} A. M. Noll, Does data traffic exceed voice traffic?, {\em Comm. ACM,} June 1999, pp.~121-124. \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 Internet and other networks: Utilization rates and their implications, {\em Information Economics \& Policy}. To appear. (Presented at the 1998 Telecommunications Policy Research Conference.) Available at $\langle$http://www.research.att.com/$\sim$amo$\rangle$. \bibitem[Odlyzko3]{Odlyzko3} A. M. Odlyzko, The history of communications and its implications for the Internet, 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[Plonka]{Plonka} D. Plonka, UW-Madison Napster traffic measurement. Available at $\langle$http://net.doit.wisc.edu/data/Napster$\rangle$. \bibitem[ReichlLS]{ReichlLS} P. Reichl, S. Leinen, and B. Stiller, A practical review of pricing and cost recovery for Internet services, to appear in Proc. 2nd Internet Economics Workshop Berlin (IEW'99), Berlin, Germany, May 28-29, 1999. Available at $\langle$http://www.tik.ee.ethz.ch/$\sim$cati/$\rangle$. \bibitem[RRD]{RRD} RRDtool of Tobias Oetiker, $\langle$http://ee-staff.ethz.ch/$\sim$oetiker/webtools/rrdtool/$\rangle$. \bibitem[Schaller]{Schaller} R. R. Schaller, Moore's law: Past, present, and future, {\em IEEE Spectrum}, vol. 34, no. 6, June 1997, pp. 52-59. Available through Spectrum online search at $\langle$http://www.spectrum.ieee.org$\rangle$. \bibitem[Sevcik]{Sevcik} P. Sevcik, The myth of Internet growth, {\em Business Communications Review,} vol. 29, no. 1, January 1999, pp. 12-14. Available at $\langle$http://www.bcr.com/bcrmag/01/99p12.htm$\rangle$. \bibitem[StArnaud]{StArnaud} B. St. Arnaud, The future of the Internet is NOT multimedia, {\em Network World}, Nov. 1997. Available at $\langle$http://www.canarie.ca/$\sim$bstarn/publications.html$\rangle$. \bibitem[StArnaudCFM]{StArnaudCFM} B. St. Arnaud, J. Coulter, J. Fitchett, and S. Mokbel, Architectural and engineering issues for building an optical Internet. Short version in {\em Proc. Soc. Optical Engineering,} (1998). Full version available at $\langle$http://www.canet3.net$\rangle$. \bibitem[Taggart]{Taggart} S. Taggart, Telstra: The prices fight, {\em Wired News,} $\langle$http://www.wired.com/news/politics/0,1283,32961,00.html$\rangle$. \end{thebibliography} \end{document}