Network Working Group
Request for Comments: 3439
Updates: 1958
Category: Informational
R. Bush
D. Meyer
December 2002

Some Internet Architectural Guidelines and Philosophy

Status of this Memo

This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited.

Copyright Notice

Copyright © The Internet Society (2002). All Rights Reserved.


This document extends RFC 1958 by outlining some of the philosophical guidelines to which architects and designers of Internet backbone networks should adhere. We describe the Simplicity Principle, which states that complexity is the primary mechanism that impedes efficient scaling, and discuss its implications on the architecture, design and engineering issues found in large scale Internet backbones.

Table of Contents

   1. Introduction . . . . . . . . . . . . . . . . . . . . . . . .  2
   2. Large Systems and The Simplicity Principle . . . . . . . . .  3
   2.1. The End-to-End Argument and Simplicity   . . . . . . . . .  3
   2.2. Non-linearity and Network Complexity   . . . . . . . . . .  3
   2.2.1. The Amplification Principle. . . . . . . . . . . . . . .  4
   2.2.2. The Coupling Principle . . . . . . . . . . . . . . . . .  5
   2.3. Complexity lesson from voice. . . . .  . . . . . . . . . .  6
   2.4. Upgrade cost of complexity. . . . . .  . . . . . . . . . .  7
   3. Layering Considered Harmful. . . . . . . . . . . . . . . . .  7
   3.1. Optimization Considered Harmful . . .  . . . . . . . . . .  8
   3.2. Feature Richness Considered Harmful .  . . . . . . . . . .  9
   3.3. Evolution of Transport Efficiency for IP.  . . . . . . . .  9
   3.4. Convergence Layering. . . . . . . . . . .  . . . . . . . .  9
   3.4.1. Note on Transport Protocol Layering. . . . . . . . . . . 11
   3.5. Second Order Effects   . . . . . . . . . . . . . . . . . . 11
   3.6. Instantiating the EOSL Model with IP   . . . . . . . . . . 12
   4. Avoid the Universal Interworking Function. . . . . . . . . . 12
   4.1. Avoid Control Plane Interworking . . . . . . . . . . . . . 13
   5. Packet versus Circuit Switching: Fundamental Differences . . 13
   5.1. Is PS is inherently more efficient than CS?  . . . . . . . 13
   5.2. Is PS simpler than CS? . . . . . . . . . . . . . . . . . . 14
   5.2.1. Software/Firmware Complexity . . . . . . . . . . . . . . 15
   5.2.2. Macro Operation Complexity . . . . . . . . . . . . . . . 15
   5.2.3. Hardware Complexity. . . . . . . . . . . . . . . . . . . 15
   5.2.4. Power. . . . . . . . . . . . . . . . . . . . . . . . . . 16
   5.2.5. Density. . . . . . . . . . . . . . . . . . . . . . . . . 16
   5.2.6. Fixed versus variable costs. . . . . . . . . . . . . . . 16
   5.2.7. QoS. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
   5.2.8. Flexibility. . . . . . . . . . . . . . . . . . . . . . . 17
   5.3. Relative Complexity  . . . . . . . . . . . . . . . . . . . 17
   5.3.1. HBHI and the OPEX Challenge. . . . . . . . . . . . . . . 18
   6. The Myth of Over-Provisioning. . . . . . . . . . . . . . . . 18
   7. The Myth of Five Nines . . . . . . . . . . . . . . . . . . . 19
   8. Architectural Component Proportionality Law. . . . . . . . . 20
   8.1. Service Delivery Paths . . . . . . . . . . . . . . . . . . 21
   9. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . 21
   10. Security Considerations . . . . . . . . . . . . . . . . . . 22
   11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 23
   12. References. . . . . . . . . . . . . . . . . . . . . . . . . 23
   13. Authors' Addresses. . . . . . . . . . . . . . . . . . . . . 27
   14. Full Copyright Statement. . . . . . . . . . . . . . . . . . 28

1. Introduction

RFC 1958 [RFC1958] describes the underlying principles of the Internet architecture. This note extends that work by outlining some of the philosophical guidelines to which architects and designers of Internet backbone networks should adhere. While many of the areas outlined in this document may be controversial, the unifying principle described here, controlling complexity as a mechanism to control costs and reliability, should not be. Complexity in carrier networks can derive from many sources. However, as stated in [DOYLE2002], "Complexity in most systems is driven by the need for robustness to uncertainty in their environments and component parts far more than by basic functionality". The major thrust of this document, then, is to raise awareness about the complexity of some of our current architectures, and to examine the effect such complexity will almost certainly have on the IP carrier industry's ability to succeed.

The rest of this document is organized as follows: The first section describes the Simplicity Principle and its implications for the design of very large systems. The remainder of the document outlines the high-level consequences of the Simplicity Principle and how it should guide large scale network architecture and design approaches.

2. Large Systems and The Simplicity Principle

The Simplicity Principle, which was perhaps first articulated by Mike O'Dell, former Chief Architect at UUNET, states that complexity is the primary mechanism which impedes efficient scaling, and as a result is the primary driver of increases in both capital expenditures (CAPEX) and operational expenditures (OPEX). The implication for carrier IP networks then, is that to be successful we must drive our architectures and designs toward the simplest possible solutions.

2.1. The End-to-End Argument and Simplicity

The end-to-end argument, which is described in [SALTZER] (as well as in RFC 1958 [RFC1958]), contends that "end-to-end protocol design should not rely on the maintenance of state (i.e., information about the state of the end-to-end communication) inside the network. Such state should be maintained only in the end points, in such a way that the state can only be destroyed when the end point itself breaks." This property has also been related to Clark's "fate-sharing" concept [CLARK]. We can see that the end-to-end principle leads directly to the Simplicity Principle by examining the so-called "hourglass" formulation of the Internet architecture [WILLINGER2002]. In this model, the thin waist of the hourglass is envisioned as the (minimalist) IP layer, and any additional complexity is added above the IP layer. In short, the complexity of the Internet belongs at the edges, and the IP layer of the Internet should remain as simple as possible.

Finally, note that the End-to-End Argument does not imply that the core of the Internet will not contain and maintain state. In fact, a huge amount coarse grained state is maintained in the Internet's core (e.g., routing state). However, the important point here is that this (coarse grained) state is almost orthogonal to the state maintained by the end-points (e.g., hosts). It is this minimization of interaction that contributes to simplicity. As a result, consideration of "core vs. end-point" state interaction is crucial when analyzing protocols such as Network Address Translation (NAT), which reduce the transparency between network and hosts.

2.2. Non-linearity and Network Complexity

Complex architectures and designs have been (and continue to be) among the most significant and challenging barriers to building cost- effective large scale IP networks. Consider, for example, the task of building a large scale packet network. Industry experience has shown that building such a network is a different activity (and hence requires a different skill set) than building a small to medium scale network, and as such doesn't have the same properties. In particular, the largest networks exhibit, both in theory and in practice, architecture, design, and engineering non-linearities which are not exhibited at smaller scale. We call this Architecture, Design, and Engineering (ADE) non-linearity. That is, systems such as the Internet could be described as highly self-dissimilar, with extremely different scales and levels of abstraction [CARLSON]. The ADE non-linearity property is based upon two well-known principles from non-linear systems theory [THOMPSON]:

2.2.1. The Amplification Principle

The Amplification Principle states that there are non-linearities which occur at large scale which do not occur at small to medium scale.

COROLLARY: In many large networks, even small things can and do cause huge events. In system-theoretic terms, in large systems such as these, even small perturbations on the input to a process can destabilize the system's output.

An important example of the Amplification Principle is non-linear resonant amplification, which is a powerful process that can transform dynamic systems, such as large networks, in surprising ways with seemingly small fluctuations. These small fluctuations may slowly accumulate, and if they are synchronized with other cycles, may produce major changes. Resonant phenomena are examples of non- linear behavior where small fluctuations may be amplified and have influences far exceeding their initial sizes. The natural world is filled with examples of resonant behavior that can produce system- wide changes, such as the destruction of the Tacoma Narrows bridge (due to the resonant amplification of small gusts of wind). Other examples include the gaps in the asteroid belts and rings of Saturn which are created by non-linear resonant amplification. Some features of human behavior and most pilgrimage systems are influenced by resonant phenomena involving the dynamics of the solar system, such as solar days, the 27.3 day (sidereal) and 29.5 day (synodic) cycles of the moon or the 365.25 day cycle of the sun.

In the Internet domain, it has been shown that increased inter- connectivity results in more complex and often slower BGP routing convergence [AHUJA]. A related result is that a small amount of inter-connectivity causes the output of a routing mesh to be significantly more complex than its input [GRIFFIN]. An important method for reducing amplification is ensure that local changes have only local effect (this is as opposed to systems in which local changes have global effect). Finally, ATM provides an excellent example of an amplification effect: if you lose one cell, you destroy the entire packet (and it gets worse, as in the absence of mechanisms such as Early Packet Discard [ROMANOV], you will continue to carry the already damaged packet).

Another interesting example of amplification comes from the engineering domain, and is described in [CARLSON]. They consider the Boeing 777, which is a "fly-by-wire" aircraft, containing as many as 150,000 subsystems and approximately 1000 CPUs. What they observe is that while the 777 is robust to large-scale atmospheric disturbances, turbulence boundaries, and variations in cargo loads (to name a few), it could be catastrophically disabled my microscopic alterations in a very few large CPUs (as the point out, fortunately this is a very rare occurrence). This example illustrates the issue "that complexity can amplify small perturbations, and the design engineer must ensure such perturbations are extremely rare." [CARLSON]

2.2.2. The Coupling Principle

The Coupling Principle states that as things get larger, they often exhibit increased interdependence between components.

COROLLARY: The more events that simultaneously occur, the larger the likelihood that two or more will interact. This phenomenon has also been termed "unforeseen feature interaction" [WILLINGER2002].

   Much of the non-linearity observed large systems is largely due to
   coupling.  This coupling has both  horizontal and vertical
   components.  In the context of networking, horizontal coupling is
   exhibited between the same protocol layer, while vertical coupling
   occurs between layers.

Coupling is exhibited by a wide variety of natural systems, including plasma macro-instabilities (hydro-magnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle effects) [NAVE], as well as various kinds of electrochemical systems (consider the custom fluorescent nucleotide synthesis/nucleic acid labeling problem [WARD]). Coupling of clock physical periodicity has also been observed [JACOBSON], as well as coupling of various types of biological cycles.

Several canonical examples also exist in well known network systems. Examples include the synchronization of various control loops, such as routing update synchronization and TCP Slow Start synchronization [FLOYD,JACOBSON]. An important result of these observations is that coupling is intimately related to synchronization. Injecting randomness into these systems is one way to reduce coupling.

   Interestingly, in analyzing risk factors for the Public Switched
   Telephone Network (PSTN), Charles Perrow decomposes the complexity
   problem along two related axes, which he terms "interactions" and
   "coupling" [PERROW].  Perrow cites interactions and coupling as
   significant factors in determining the reliability of a complex
   system (and in particular, the PSTN).  In this model, interactions
   refer to the dependencies between components (linear or non-linear),
   while coupling refers to the flexibility in a system.  Systems with
   simple, linear interactions have components  that affect only other
   components that are functionally downstream.  Complex system
   components interact with many other components in different and
   possibly distant parts of the system.  Loosely coupled systems are
   said to have more flexibility in time constraints, sequencing, and
   environmental assumptions than do tightly coupled systems.  In
   addition, systems with complex interactions and tight coupling are
   likely to have unforeseen failure states (of course, complex
   interactions permit more complications to develop and make the system
   hard to understand and predict); this behavior is also described in
   [WILLINGER2002].  Tight coupling also means that the system has less
   flexibility in recovering from failure states.

The PSTN's SS7 control network provides an interesting example of what can go wrong with a tightly coupled complex system. Outages such as the well publicized 1991 outage of AT&T's SS7 demonstrates the phenomenon: the outage was caused by software bugs in the switches' crash recovery code. In this case, one switch crashed due to a hardware glitch. When this switch came back up, it (plus a reasonably probable timing event) caused its neighbors to crash When the neighboring switches came back up, they caused their neighbors to crash, and so on [NEUMANN] (the root cause turned out to be a misplaced 'break' statement; this is an excellent example of cross- layer coupling). This phenomenon is similar to the phase-locking of weakly coupled oscillators, in which random variations in sequence times plays an important role in system stability [THOMPSON].

2.3. Complexity lesson from voice

In the 1970s and 1980s, the voice carriers competed by adding features which drove substantial increases in the complexity of the PSTN, especially in the Class 5 switching infrastructure. This complexity was typically software-based, not hardware driven, and therefore had cost curves worse than Moore's Law. In summary, poor margins on voice products today are due to OPEX and CAPEX costs not dropping as we might expect from simple hardware-bound implementations.

2.4. Upgrade cost of complexity

Consider the cost of providing new features in a complex network. The traditional voice network has little intelligence in its edge devices (phone instruments), and a very smart core. The Internet has smart edges, computers with operating systems, applications, etc., and a simple core, which consists of a control plane and packet forwarding engines. Adding an new Internet service is just a matter of distributing an application to the a few consenting desktops who wish to use it. Compare this to adding a service to voice, where one has to upgrade the entire core.

3. Layering Considered Harmful

There are several generic properties of layering, or vertical integration as applied to networking. In general, a layer as defined in our context implements one or more of

    Error Control:     The layer makes the "channel" more reliable
                       (e.g., reliable transport layer)
    Flow Control:      The layer avoids flooding slower peer (e.g.,
                       ATM flow control)
    Fragmentation:     Dividing large data chunks into smaller
                       pieces, and subsequent reassembly (e.g., TCP
                       MSS fragmentation/reassembly)
    Multiplexing:      Allow several higher level sessions share
                       single lower level "connection" (e.g., ATM PVC)
    Connection Setup:  Handshaking with peer (e.g., TCP three-way
                       handshake, ATM ILMI)
    Addressing/Naming: Locating, managing identifiers associated
                       with entities (e.g., GOSSIP 2 NSAP Structure

Layering of this type does have various conceptual and structuring advantages. However, in the data networking context structured layering implies that the functions of each layer are carried out completely before the protocol data unit is passed to the next layer. This means that the optimization of each layer has to be done separately. Such ordering constraints are in conflict with efficient implementation of data manipulation functions. One could accuse the layered model (e.g., TCP/IP and ISO OSI) of causing this conflict. In fact, the operations of multiplexing and segmentation both hide vital information that lower layers may need to optimize their performance. For example, layer N may duplicate lower level functionality, e.g., error recovery hop-hop versus end-to-end error recovery. In addition, different layers may need the same information (e.g., time stamp): layer N may need layer N-2 information (e.g., lower layer packet sizes), and the like [WAKEMAN]. A related and even more ironic statement comes from Tennenhouse's classic paper, "Layered Multiplexing Considered Harmful" [TENNENHOUSE]: "The ATM approach to broadband networking is presently being pursued within the CCITT (and elsewhere) as the unifying mechanism for the support of service integration, rate adaptation, and jitter control within the lower layers of the network architecture. This position paper is specifically concerned with the jitter arising from the design of the "middle" and "upper" layers that operate within the end systems and relays of multi-service networks (MSNs)."

As a result of inter-layer dependencies, increased layering can quickly lead to violation of the Simplicity Principle. Industry experience has taught us that increased layering frequently increases complexity and hence leads to increases in OPEX, as is predicted by the Simplicity Principle. A corollary is stated in RFC 1925 [RFC1925], section 2(5):

"It is always possible to agglutinate multiple separate problems into a single complex interdependent solution. In most cases this is a bad idea."

The first order conclusion then, is that horizontal (as opposed to vertical) separation may be more cost-effective and reliable in the long term.

3.1. Optimization Considered Harmful

A corollary of the layering arguments above is that optimization can also be considered harmful. In particular, optimization introduces complexity, and as well as introducing tighter coupling between components and layers.

An important and related effect of optimization is described by the Law of Diminishing Returns, which states that if one factor of production is increased while the others remain constant, the overall returns will relatively decrease after a certain point [SPILLMAN]. The implication here is that trying to squeeze out efficiency past that point only adds complexity, and hence leads to less reliable systems.

3.2. Feature Richness Considered Harmful

While adding any new feature may be considered a gain (and in fact frequently differentiates vendors of various types of equipment), but there is a danger. The danger is in increased system complexity.

3.3. Evolution of Transport Efficiency for IP

The evolution of transport infrastructures for IP offers a good example of how decreasing vertical integration has lead to various efficiencies. In particular,

    | IP over ATM over SONET  -->
    | IP over SONET over WDM  -->
    | IP over WDM
   Decreasing complexity, CAPEX, OPEX

The key point here is that layers are removed resulting in CAPEX and OPEX efficiencies.

3.4. Convergence Layering

Convergence is related to the layering concepts described above in that convergence is achieved via a "convergence layer". The end state of the convergence argument is the concept of Everything Over Some Layer (EOSL). Conduit, DWDM, fiber, ATM, MPLS, and even IP have all been proposed as convergence layers. It is important to note that since layering typically drives OPEX up, we expect convergence will as well. This observation is again consistent with industry experience.

There are many notable examples of convergence layer failure. Perhaps the most germane example is IP over ATM. The immediate and most obvious consequence of ATM layering is the so-called cell tax: First, note that the complete answer on ATM efficiency is that it depends upon packet size distributions. Let's assume that typical Internet type traffic patterns, which tend to have high percentages of packets at 40, 44, and 552 bytes. Recent data [CAIDA] shows that about 95% of WAN bytes and 85% of packets are TCP. Much of this traffic is composed of 40/44 byte packets.

Now, consider the case of a a DS3 backbone with PLCP turned on. Then the maximum cell rate is 96,000 cells/sec. If you multiply this value by the number of bits in the payload, you get: 96000 cells/sec * 48 bytes/cell * 8 = 36.864 Mbps. This, however, is unrealistic since it
assumes perfect payload packing. There are two other things that contribute to the ATM overhead (cell tax): The wasted padding and the 8 byte SNAP header.

It is the SNAP header which causes most of the problems (and you can't do anything about this), forcing most small packets to consume two cells, with the second cell to be mostly empty padding (this interacts really poorly with the data quoted above, e.g., that most packets are 40-44 byte TCP Ack packets). This causes a loss of about another 16% from the 36.8 Mbps ideal throughput.

So the total throughput ends up being (for a DS3):

             DS3 Line Rate:              44.736
             PLCP Overhead              - 4.032
             Per Cell Header:           - 3.840
             SNAP Header & Padding:     - 5.900
                                         30.960 Mbps

Result: With a DS3 line rate of 44.736 Mbps, the total overhead is about 31%.

Another way to look at this is that since a large fraction of WAN traffic is comprised of TCP ACKs, one can make a different but related calculation. IP over ATM requires:

IP data (40 bytes in this case)
8 bytes SNAP
8 bytes AAL5 stuff
5 bytes for each cell
+ as much more as it takes to fill out the last cell

On ATM, this becomes two cells - 106 bytes to convey 40 bytes of information. The next most common size seems to be one of several sizes in the 504-556 byte range - 636 bytes to carry IP, TCP, and a 512 byte TCP payload - with messages larger than 1000 bytes running third.

One would imagine that 87% payload (556 byte message size) is better than 37% payload (TCP Ack size), but it's not the 95-98% that customers are used to, and the predominance of TCP Acks skews the average.

3.4.1. Note on Transport Protocol Layering

Protocol layering models are frequently cast as "X over Y" models. In these cases, protocol Y carries protocol X's protocol data units (and possibly control data) over Y's data plane, i.e., Y is a "convergence layer". Examples include Frame Relay over ATM, IP over ATM, and IP over MPLS. While X over Y layering has met with only marginal success [TENNENHOUSE,WAKEMAN], there have been a few notable instances where efficiency can be and is gained. In particular, "X over Y efficiencies" can be realized when there is a kind of "isomorphism" between the X and Y (i.e., there is a small convergence layer). In these cases X's data, and possibly control traffic, are "encapsulated" and transported over Y. Examples include Frame Relay over ATM, and Frame Relay, AAL5 ATM and Ethernet over L2TPv3 [L2TPV3]; the simplifying factors here are that there is no requirement that a shared clock be recovered by the communicating end points, and that control-plane interworking is minimized. An alternative is to interwork the X and Y's control and data planes; control-plane interworking is discussed below.

3.5. Second Order Effects

IP over ATM provides an excellent example of unanticipated second order effects. In particular, Romanov and Floyd's classic study on TCP good-put [ROMANOV] on ATM showed that large UBR buffers (larger than one TCP window size) are required to achieve reasonable performance, that packet discard mechanisms (such as Early Packet Discard, or EPD) improve the effective usage of the bandwidth and that more elaborate service and drop strategies than FIFO+EPD, such as per VC queuing and accounting, might be required at the bottleneck to ensure both high efficiency and fairness. Though all studies clearly indicate that a buffer size not less than one TCP window size is required, the amount of extra buffer required naturally depends on the packet discard mechanism used and is still an open issue.

Examples of this kind of problem with layering abound in practical networking. Consider, for example, the effect of IP transport's implicit assumptions of lower layers. In particular:

  • Packet loss: TCP assumes that packet losses are indications of congestion, but sometimes losses are from corruption on a wireless link [RFC3115].
  • Reordered packets: TCP assumes that significantly reordered packets are indications of congestion. This is not always the case [FLOYD2001].
  • Round-trip times: TCP measures round-trip times, and assumes that the lack of an acknowledgment within a period of time based on the measured round-trip time is a packet loss, and therefore an indication of congestion [KARN].
  • Congestion control: TCP congestion control implicitly assumes that all the packets in a flow are treated the same by the network, but this is not always the case [HANDLEY].

3.6. Instantiating the EOSL Model with IP

While IP is being proposed as a transport for almost everything, the base assumption, that Everything over IP (EOIP) will result in OPEX and CAPEX efficiencies, requires critical examination. In particular, while it is the case that many protocols can be efficiently transported over an IP network (specifically, those protocols that do not need to recover synchronization between the communication end points, such as Frame Relay, Ethernet, and AAL5 ATM), the Simplicity and Layering Principles suggest that EOIP may not represent the most efficient convergence strategy for arbitrary services. Rather, a more CAPEX and OPEX efficient convergence layer might be much lower (again, this behavior is predicted by the Simplicity Principle).

An example of where EOIP would not be the most OPEX and CAPEX efficient transport would be in those cases where a service or protocol needed SONET-like restoration times (e.g., 50ms). It is not hard to imagine that it would cost more to build and operate an IP network with this kind of restoration and convergence property (if that were even possible) than it would to build the SONET network in the first place.

4. Avoid the Universal Interworking Function

While there have been many implementations of Universal Interworking unction (UIWF), IWF approaches have been problematic at large scale. his concern is codified in the Principle of Minimum Intervention BRYANT]:

"To minimise the scope of information, and to improve the efficiency of data flow through the Encapsulation Layer, the payload should, where possible, be transported as received without modification."

4.1. Avoid Control Plane Interworking

This corollary is best understood in the context of the integrated solutions space. In this case, the architecture and design frequently achieves the worst of all possible worlds. This is due to the fact that such integrated solutions perform poorly at both ends of the performance/CAPEX/OPEX spectrum: the protocols with the least switching demand may have to bear the cost of the most expensive, while the protocols with the most stringent requirements often must make concessions to those with different requirements. Add to this the various control plane interworking issues and you have a large opportunity for failure. In summary, interworking functions should be restricted to data plane interworking and encapsulations, and these functions should be carried out at the edge of the network.

   As described above, interworking models have been successful in those
   cases where there is a kind of "isomorphism" between the layers being
   interworked.  The trade-off here, frequently described as the
   "Integrated vs.  Ships In the Night trade-off" has been examined at
   various times and  at various protocol layers.  In general, there are
   few cases in which such integrated solutions have proven efficient.
   Multi-protocol BGP [RFC2283] is a subtly different but notable
   exception.  In this case, the control plane is  independent of the
   format of the control data.  That is, no control plane data
   conversion is required, in contrast with control plane interworking
   models such as the ATM/IP interworking envisioned by some soft-switch
   manufacturers, and the so-called "PNNI-MPLS SIN" interworking

5. Packet versus Circuit Switching: Fundamental Differences

Conventional wisdom holds that packet switching (PS) is inherently more efficient than circuit switching (CS), primarily because of the efficiencies that can be gained by statistical multiplexing and the fact that routing and forwarding decisions are made independently in a hop-by-hop fashion [[MOLINERO2002]. Further, it is widely assumed that IP is simpler that circuit switching, and hence should be more economical to deploy and manage [MCK2002]. However, if one examines these and related assumptions, a different picture emerges (see for example [ODLYZKO98]). The following sections discuss these assumptions.

5.1. Is PS is inherently more efficient than CS?

It is well known that packet switches make efficient use of scarce bandwidth [BARAN]. This efficiency is based on the statistical multiplexing inherent in packet switching. However, we continue to be puzzled by what is generally believed to be the low utilization of

   Internet backbones.  The first question we might ask is what is the
   current average utilization of Internet backbones, and how does that
   relate to the utilization of long distance voice networks?  Odlyzko
   and Coffman [ODLYZKO,COFFMAN] report that the average utilization of
   links in the IP networks was in the range between 3% and 20%
   (corporate intranets run in the 3% range, while commercial Internet
   backbones run in the 15-20% range).  On the other hand, the average
   utilization of long haul voice lines is about 33%.  In addition, for
   2002, the average utilization of optical networks (all services)
   appears to be hovering at about 11%, while the historical average is
   approximately 15% [ML2002].  The question then becomes why we see
   such utilization levels, especially in light of the assumption that
   PS is inherently more efficient than CS.  The reasons cited by
   Odlyzko and Coffman include:
      (i).   Internet traffic is extremely asymmetric and bursty, but
             links are symmetric and of fixed capacity (i.e., don't know
             the traffic matrix, or required link capacities);

(ii). It is difficult to predict traffic growth on a link, so

operators tend to add bandwidth aggressively;

(iii). Falling prices for coarser bandwidth granularity make it

appear more economical to add capacity in large increments.

Other static factors include protocol overhead, other kinds of equipment granularity, restoration capacity, and provisioning lag time all contribute to the need to "over-provision" [MC2001].

5.2. Is PS simpler than CS?

The end-to-end principle can be interpreted as stating that the complexity of the Internet belongs at the edges. However, today's Internet backbone routers are extremely complex. Further, this complexity scales with line rate. Since the relative complexity of circuit and packet switching seems to have resisted direct analysis, we instead examine several artifacts of packet and circuit switching as complexity metrics. Among the metrics we might look at are software complexity, macro operation complexity, hardware complexity, power consumption, and density. Each of these metrics is considered below.

5.2.1. Software/Firmware Complexity

One measure of software/firmware complexity is the number of instructions required to program the device. The typical software image for an Internet router requires between eight and ten million instructions (including firmware), whereas a typical transport switch requires on average about three million instructions [MCK2002].

This difference in software complexity has tended to make Internet routers unreliable, and has notable other second order effects (e.g., it may take a long time to reboot such a router). As another point of comparison, consider that the AT&T (Lucent) 5ESS class 5 switch, which has a huge number of calling features, requires only about twice the number of lines of code as an Internet core router [EICK].

Finally, since routers are as much or more software than hardware devices, another result of the code complexity is that the cost of routers benefits less from Moore's Law than less software-intensive devices. This causes a bandwidth/device trade-off that favors bandwidth more than less software-intensive devices.

5.2.2. Macro Operation Complexity

An Internet router's line card must perform many complex operations, including processing the packet header, longest prefix match, generating ICMP error messages, processing IP header options, and buffering the packet so that TCP congestion control will be effective (this typically requires a buffer of size proportional to the line rate times the RTT, so a buffer will hold around 250 ms of packet data). This doesn't include route and packet filtering, or any QoS or VPN filtering.

On the other hand, a transport switch need only to map ingress time- slots to egress time-slots and interfaces, and therefore can be considerably less complex.

5.2.3. Hardware Complexity

One measure of hardware complexity is the number of logic gates on a line card [MOLINERO2002]. Consider the case of a high-speed Internet router line card: An OC192 POS router line card contains at least 30 million gates in ASICs, at least one CPU, 300 Mbytes of packet buffers, 2 Mbytes of forwarding table, and 10 Mbytes of other state memory. On the other hand, a comparable transport switch line card has 7.5 million logic gates, no CPU, no packet buffer, no forwarding table, and an on-chip state memory. Rather, the line-card of an electronic transport switch typically contains a SONET framer, a chip to map ingress time-slots to egress time-slots, and an interface to the switch fabric.

5.2.4. Power

Since transport switches have traditionally been built from simpler hardware components, they also consume less power [PMC].

5.2.5. Density

The highest capacity transport switches have about four times the capacity of an IP router [CISCO,CIENA], and sell for about one-third as much per Gigabit/sec. Optical (OOO) technology pushes this complexity difference further (e.g., tunable lasers, MEMs switches. e.g., [CALIENT]), and DWDM multiplexers provide technology to build extremely high capacity, low power transport switches.

A related metric is physical footprint. In general, by virtue of their higher density, transport switches have a smaller "per-gigabit" physical footprint.

5.2.6. Fixed versus variable costs

Packet switching would seem to have high variable cost, meaning that it costs more to send the n-th piece of information using packet switching than it might in a circuit switched network. Much of this advantage is due to the relatively static nature of circuit switching, e.g., circuit switching can take advantage of of pre- scheduled arrival of information to eliminate operations to be performed on incoming information. For example, in the circuit switched case, there is no need to buffer incoming information, perform loop detection, resolve next hops, modify fields in the packet header, and the like. Finally, many circuit switched networks combine relatively static configuration with out-of-band control planes (e.g., SS7), which greatly simplifies data-plane switching. The bottom line is that as data rates get large, it becomes more and more complex to switch packets, while circuit switching scales more or less linearly.

5.2.7. QoS

While the components of a complete solution for Internet QoS, including call admission control, efficient packet classification, and scheduling algorithms, have been the subject of extensive research and standardization for more than 10 years, end-to-end signaled QoS for the Internet has not become a reality. Alternatively, QoS has been part of the circuit switched infrastructure almost from its inception. On the other hand, QoS is usually deployed to determine queuing disciplines to be used when there is insufficient bandwidth to support traffic. But unlike voice traffic, packet drop or severe delay may have a much more serious effect on TCP traffic due to its congestion-aware feedback loop (in particular, TCP backoff/slow start).

5.2.8. Flexibility

A somewhat harder to quantify metric is the inherent flexibility of the Internet. While the Internet's flexibility has led to its rapid growth, this flexibility comes with a relatively high cost at the edge: the need for highly trained support personnel. A standard rule of thumb is that in an enterprise setting, a single support person suffices to provide telephone service for a group, while you need ten computer networking experts to serve the networking requirements of the same group [ODLYZKO98A]. This phenomenon is also described in [PERROW].

5.3. Relative Complexity

The relative computational complexity of circuit switching as compared to packet switching has been difficult to describe in formal terms [PARK]. As such, the sections above seek to describe the complexity in terms of observable artifacts. With this in mind, it is clear that the fundamental driver producing the increased complexities outlined above is the hop-by-hop independence (HBHI) inherent in the IP architecture. This is in contrast to the end to end architectures such as ATM or Frame Relay.

[WILLINGER2002] describes this phenomenon in terms of the robustness requirement of the original Internet design, and how this requirement has the driven complexity of the network. In particular, they describe a "complexity/robustness" spiral, in which increases in complexity create further and more serious sensitivities, which then requires additional robustness (hence the spiral).

The important lesson of this section is that the Simplicity Principle, while applicable to circuit switching as well as packet switching, is crucial in controlling the complexity (and hence OPEX and CAPEX properties) of packet networks. This idea is reinforced by the observation that while packet switching is a younger, less mature discipline than circuit switching, the trend in packet switches is toward more complex line cards, while the complexity of circuit switches appears to be scaling linearly with line rates and aggregate capacity.

5.3.1. HBHI and the OPEX Challenge

As a result of HBHI, we need to approach IP networks in a fundamentally different way than we do circuit based networks. In particular, the major OPEX challenge faced by the IP network is that debugging of a large-scale IP network still requires a large degree of expertise and understanding, again due to the hop-by-hop independence inherent in a packet architecture (again, note that this hop-by-hop independence is not present in virtual circuit networks such as ATM or Frame Relay). For example, you may have to visit a large set of your routers only to discover that the problem is external to your own network. Further, the debugging tools used to diagnose problems are also complex and somewhat primitive. Finally, IP has to deal with people having problems with their DNS or their mail or news or some new application, whereas this is usually not the case for TDM/ATM/etc. In the case of IP, this can be eased by improving automation (note that much of what we mention is customer facing). In general, there are many variables external to the network that effect OPEX.

Finally, it is important to note that the quantitative relationship between CAPEX, OPEX, and a network's inherent complexity is not well understood. In fact, there are no agreed upon and quantitative metrics for describing a network's complexity, so a precise relationship between CAPEX, OPEX, and complexity remains elusive.

6. The Myth of Over-Provisioning

As noted in [MC2001] and elsewhere, much of the complexity we observe in today's Internet is directed at increasing bandwidth utilization. As a result, the desire of network engineers to keep network utilization below 50% has been termed "over-provisioning". However, this use of the term over-provisioning is a misnomer. Rather, in modern Internet backbones the unused capacity is actually protection capacity. In particular, one might view this as "1:1 protection at the IP layer". Viewed in this way, we see that an IP network provisioned to run at 50% utilization is no more over-provisioned than the typical SONET network. However, the important advantages that accrue to an IP network provisioned in this way include close to speed of light delay and close to zero packet loss [FRALEIGH]. These benefits can been seen as a "side-effect" of 1:1 protection provisioning.

There are also other, system-theoretic reasons for providing 1:1-like protection provisioning. Most notable among these reasons is that packet-switched networks with in-band control loops can become unstable and can experience oscillations and synchronization when congested. Complex and non-linear dynamic interaction of traffic means that congestion in one part of the network will spread to other parts of the network. When routing protocol packets are lost due to congestion or route-processor overload, it causes inconsistent routing state, and this may result in traffic loops, black holes, and lost connectivity. Thus, while statistical multiplexing can in theory yield higher network utilization, in practice, to maintain consistent performance and a reasonably stable network, the dynamics of the Internet backbones favor 1:1 provisioning and its side effects to keep the network stable and delay low.

7. The Myth of Five Nines

Paul Baran, in his classic paper, "SOME PERSPECTIVES ON NETWORKS-- PAST, PRESENT AND FUTURE", stated that "The tradeoff curves between cost and system reliability suggest that the most reliable systems might be built of relatively unreliable and hence low cost elements, if it is system reliability at the lowest overall system cost that is at issue" [BARAN77].

Today we refer to this phenomenon as "the myth of five nines". Specifically, so-called five nines reliability in packet network elements is consider a myth for the following reasons: First, since 80% of unscheduled outages are caused by people or process errors [SCOTT], there is only a 20% window in which to optimize. Thus, in order to increase component reliability, we add complexity (optimization frequently leads to complexity), which is the root cause of 80% of the unplanned outages. This effectively narrows the 20% window (i.e., you increase the likelihood of people and process failure). This phenomenon is also characterized as a "complexity/robustness" spiral [WILLINGER2002], in which increases in complexity create further and more serious sensitivities, which then requires additional robustness, and so on (hence the spiral).

The conclusion, then is that while a system like the Internet can reach five-nines-like reliability, it is undesirable (and likely impossible) to try to make any individual component, especially the most complex ones, reach that reliability standard.

8. Architectural Component Proportionality Law

As noted in the previous section, the computational complexity of packet switched networks such as the Internet has proven difficult to describe in formal terms. However, an intuitive, high level definition of architectural complexity might be that the complexity of an architecture is proportional to its number of components, and that the probability of achieving a stable implementation of an architecture is inversely proportional to its number of components. As described above, components include discrete elements such as hardware elements, space and power requirements, as well as software, firmware, and the protocols they implement.

Stated more abstractly:

         A   be a representation of architecture A,

|A| be number of distinct components in the service

delivery path of architecture A,

         w   be a monotonically increasing function,
         P   be the probability of a stable implementation of an
             architecture, and let
         Complexity(A) = O(w(|A|))
         P(A)          = O(1/w(|A|))
       O(f) = {g:N->R | there exists c > 0 and n such that g(n)
       < c*f(n)}

[That is, O(f) comprises the set of functions g for which there exists a constant c and a number n, such that g(n) is smaller or equal to c*f(n) for all n. That is, O(f) is the set of all functions that do not grow faster than f, disregarding constant factors]

Interestingly, the Highly Optimized Tolerance (HOT) model [HOT] attempts to characterize complexity in general terms (HOT is one recent attempt to develop a general framework for the study of complexity, and is a member of a family of abstractions generally termed "the new science of complexity" or "complex adaptive systems"). Tolerance, in HOT semantics, means that "robustness in complex systems is a constrained and limited quantity that must be carefully managed and protected." One focus of the HOT model is to characterize heavy-tailed distributions such as Complexity(A) in the above example (other examples include forest fires, power outages, and Internet traffic distributions). In particular, Complexity(A) attempts to map the extreme heterogeneity of the parts of the system (Internet), and the effect of their organization into highly structured networks, with hierarchies and multiple scales.

8.1. Service Delivery Paths

The Architectural Component Proportionality Law (ACPL) states that the complexity of an architecture is proportional to its number of components.

COROLLARY: Minimize the number of components in a service delivery path, where the service delivery path can be a protocol path, a software path, or a physical path.

This corollary is an important consequence of the ACPL, as the path between a customer and the desired service is particularly sensitive to the number and complexity of elements in the path. This is due to the fact that the complexity "smoothing" that we find at high levels of aggregation [ZHANG] is missing as you move closer to the edge, as well as having complex interactions with backoffice and CRM systems. Examples of architectures that haven't found a market due to this effect include TINA-based CRM systems, CORBA/TINA based service architectures. The basic lesson here was that the only possibilities for deploying these systems were "Limited scale deployments (such) as in Starvision can avoid coping with major unproven scalability issues", or "Otherwise need massive investments (like the carrier- grade ORB built almost from scratch)" [TINA]. In other words, these systems had complex service delivery paths, and were too complex to be feasibly deployed.

9. Conclusions

This document attempts to codify long-understood Internet architectural principles. In particular, the unifying principle described here is best expressed by the Simplicity Principle, which states complexity must be controlled if one hopes to efficiently scale a complex object. The idea that simplicity itself can lead to some form of optimality has been a common theme throughout history, and has been stated in many other ways and along many dimensions. For example, consider the maxim known as Occam's Razor, which was formulated by the medieval English philosopher and Franciscan monk William of Ockham (ca. 1285-1349), and states "Pluralitas non est ponenda sine neccesitate" or "plurality should not be posited without necessity." (hence Occam's Razor is sometimes called "the principle of unnecessary plurality" and " the principle of simplicity"). A perhaps more contemporary formulation of Occam's Razor states that the simplest explanation for a phenomenon is the one preferred by nature. Other formulations of the same idea can be found in the KISS (Keep It Simple Stupid) principle and the Principle of Least Astonishment (the assertion that the most usable system is the one that least often leaves users astonished). [WILLINGER2002] provides a more theoretical discussion of "robustness through simplicity", and in discussing the PSTN, [KUHN87] states that in most systems, "a trade-off can be made between simplicity of interactions and looseness of coupling".

   When applied to packet switched network architectures, the Simplicity
   Principle has implications that some may consider heresy, e.g., that
   highly converged approaches are likely to be less efficient than
   "less converged" solutions.  Otherwise stated, the "optimal"
   convergence layer may be much lower in the protocol stack that is
   conventionally believed.  In addition, the analysis above leads to
   several conclusions that are contrary to the conventional wisdom
   surrounding  packet networking.  Perhaps most significant is the
   belief that packet switching is simpler than circuit switching.  This
   belief has lead to conclusions such as "since packet is simpler than
   circuit, it must cost less to operate".  This study finds to the
   contrary.  In particular, by examining the metrics described above,
   we find that packet switching is more complex than circuit switching.
   Interestingly, this conclusion is borne out by the fact that
   normalized OPEX for data networks is typically significantly greater
   than for voice networks [ML2002].

Finally, the important conclusion of this work is that for packet networks that are of the scale of today's Internet or larger, we must strive for the simplest possible solutions if we hope to build cost effective infrastructures. This idea is eloquently stated in [DOYLE2002]: "The evolution of protocols can lead to a robustness/complexity/fragility spiral where complexity added for robustness also adds new fragilities, which in turn leads to new and thus spiraling complexities". This is exactly the phenomenon that the Simplicity Principle is designed to avoid.

10. Security Considerations

   This document does not directly effect the security of any existing
   Internet protocol.  However, adherence to the Simplicity Principle
   does have a direct affect on our ability to implement secure systems.
   In particular, a system's complexity grows, it becomes  more
   difficult to model and analyze, and hence it becomes more difficult

to find and understand the security implications inherent in its architecture, design, and implementation.

11. Acknowledgments

Many of the ideas for comparing the complexity of circuit switched and packet switched networks were inspired by conversations with Nick McKeown. Scott Bradner, David Banister, Steve Bellovin, Steward Bryant, Christophe Diot, Susan Harris, Ananth Nagarajan, Andrew Odlyzko, Pete and Natalie Whiting, and Lixia Zhang made many helpful comments on early drafts of this document.

12. References

   [AHUJA]         "The Impact of Internet Policy and Topology on
                   Delayed Routing Convergence", Labovitz, et. al.
                   Infocom, 2001.
   [ATMMPLS]       "ATM-MPLS Interworking Migration Complexities Issues
                   and Preliminary Assessment", School of
                   Interdisciplinary Computing and Engineering,
                   University of Missouri-Kansas City, April 2002
   [BARAN]         "On Distributed Communications", Paul Baran, Rand
                   Corporation Memorandum RM-3420-PR,
         ", August,
                   FUTURE", Paul Baran,  Information Processing 77,
                   North-Holland Publishing Company, 1977,
   [BRYANT]        "Protocol Layering in PWE3", Bryant et al, Work in
   [CARLSON]       "Complexity and Robustness", J.M. Carlson and John
                   Doyle, Proc. Natl. Acad. Sci. USA, Vol. 99, Suppl. 1,
                   2538-2545, February 19, 2002.
   [CIENA]         "CIENA Multiwave CoreDiretor",
   [CLARK]         "The Design Philosophy of the DARPA Internet
                   Protocols", D. Clark, Proc. of the ACM SIGCOMM, 1988.
   [COFFMAN]       "Internet Growth: Is there a 'Moores Law' for Data
                   Traffic", K.G. Coffman and A.M. Odlyzko, pp. 47-93,
                   Handbook of Massive Data Stes, J. Elli, P. M.
                   Pardalos, and M. G. C. Resende, Editors. Kluwer,
   [DOYLE2002]     "Robustness and the Internet: Theoretical
                   Foundations", John C. Doyle, et. al. Work in
   [EICK]          "Visualizing Software Changes", S.G. Eick, et al,
                   National Institute of Statistical Sciences, Technical
                   Report 113, December 2000.
   [MOLINERO2002]  "TCP Switching: Exposing Circuits to IP", Pablo
                   Molinero-Fernandez and Nick McKeown, IEEE January,
   [FLOYD]         "The Synchronization of Periodic Routing Messages",
                   Sally Floyd and Van Jacobson, IEEE ACM Transactions
                   on Networking, 1994.
   [FLOYD2001]     "A Report on Some Recent Developments in TCP
                   Congestion Control, IEEE Communications Magazine, S.
                   Floyd, April 2001.
   [FRALEIGH]      "Provisioning IP Backbone Networks to Support Delay-
                   Based Service Level Agreements", Chuck Fraleigh,
                   Fouad Tobagi, and Christophe Diot, 2002.
   [GRIFFIN]       "What is the Sound of One Route Flapping", Timothy G.
                   Griffin,  IPAM Workshop on Large-Scale Communication
                   Networks: Topology, Routing, Traffic, and Control,
                   March, 2002.
   [HANDLEY]       "On Inter-layer Assumptions (A view from the
                   Transport Area), slides from a presentation at the
                   IAB workshop on Wireless Internetworking", M.
                   Handley,  March 2000.
   [HOT]           J.M. Carlson and John Doyle, Phys. Rev. E 60, 1412-
                   1427, 1999.
   [ISO10589]      "Intermediate System to Intermediate System
                   Intradomain Routing Exchange Protocol (IS-IS)".
   [JACOBSON]      "Congestion Avoidance and Control", Van Jacobson,
                   Proceedings of ACM Sigcomm 1988, pp. 273-288.
   [KARN]          "TCP vs Link Layer Retransmission" in P. Karn et al.,
                   Advice for Internet Subnetwork Designers, Work in
   [KUHN87]        "Sources of Failure in the Public Switched Telephone
                   Network", D. Richard Kuhn, EEE Computer, Vol. 30, No.
                   4, April, 1997.
   [L2TPV3]        Lan, J., et. al., "Layer Two Tunneling Protocol
                   (Version 3) -- L2TPv3", Work in Progress.
   [MC2001]        "U.S Communications Infrastructure at A Crossroads:
                   Opportunities Amid the Gloom", McKinsey&Company for
                   Goldman-Sachs, August 2001.
   [MCK2002]       Nick McKeown, personal communication, April, 2002.
   [ML2002]        "Optical Systems", Merril Lynch Technical Report,
                   April, 2002.
   [NAVE]          "The influence of mode coupling on the non-linear
                   evolution of tearing modes", M.F.F. Nave, et al, Eur.
                   Phys. J. D 8, 287-297.
   [NEUMANN]       "Cause of AT&T network failure", Peter G. Neumann,
   [ODLYZKO]       "Data networks are mostly empty for good reason",
                   A.M. Odlyzko, IT Professional 1 (no. 2), pp. 67-69,
                   Mar/Apr 1999.
   [ODLYZKO98A]    "Smart and stupid networks: Why the Internet is like
                   Microsoft".  A. M. Odlyzko, ACM Networker, 2(5),
                   December, 1998.
   [ODLYZKO98]     "The economics of the Internet: Utility, utilization,
                   pricing, and Quality of Service", A.M. Odlyzko, July,
   [PARK]          "The Internet as a Complex System: Scaling,
                   Complexity and Control", Kihong Park and Walter
                   Willinger, AT&T Research, 2002.
   [PERROW]        "Normal Accidents: Living with High Risk
                   Technologies", Basic Books, C. Perrow, New York,
   [PMC]           "The Design of a 10 Gigabit Core Router
                   Architecture", PMC-Sierra, http://www.pmc-
   [RFC1629]       Colella, R., Callon, R., Gardner, E. and Y. Rekhter,
                   "Guidelines for OSI NSAP Allocation in the Internet",
                   RFC 1629, May 1994.
   [RFC1925]       Callon, R., "The Twelve Networking Truths", RFC 1925,
                   1 April 1996.
   [RFC1958]       Carpenter, B., Ed., "Architectural principles of the
                   Internet", RFC 1958, June 1996.
   [RFC2283]       Bates, T., Chandra, R., Katz, D. and Y. Rekhter,
                   "Multiprotocol Extensions for BGP4", RFC 2283,
                   February 1998.
   [RFC3155]       Dawkins, S., Montenegro, G., Kojo, M. and N. Vaidya,
                   "End-to-end Performance Implications of Links with
                   Errors", BCP 50, RFC 3155, May 2001.
   [ROMANOV]       "Dynamics of TCP over ATM Networks", A. Romanov, S.
                   Floyd, IEEE JSAC, vol. 13, No 4, pp.633-641, May
   [SALTZER]       "End-To-End Arguments in System Design", J.H.
                   Saltzer, D.P. Reed, and D.D. Clark, ACM TOCS, Vol 2,
                   Number 4, November 1984, pp 277-288.
   [SCOTT]         "Making Smart Investments to Reduce Unplanned
                   Downtime", D. Scott, Tactical Guidelines, TG-07-4033,
                   Gartner Group Research Note, March 1999.
   [SPILLMAN]      "The Law of Diminishing Returns:, W. J. Spillman and
                   E. Lang, 1924.
   [STALLINGS]     "Data and Computer Communications (2nd Ed)", William
                   Stallings, Maxwell Macmillan, 1989.
   [TENNENHOUSE]   "Layered multiplexing considered harmful", D.
                   Tennenhouse, Proceedings of the IFIP Workshop on
                   Protocols for High-Speed Networks, Rudin ed., North
                   Holland Publishers, May 1989.
   [THOMPSON]      "Nonlinear Dynamics and Chaos". J.M.T. Thompson and
                   H.B. Stewart, John Wiley and Sons, 1994, ISBN
   [TINA]          "What is TINA and is it useful for the TelCos?",
                   Paolo Coppo, Carlo A. Licciardi, CSELT, EURESCOM
                   Participants in P847 (FT, IT, NT, TI)
   [WAKEMAN]       "Layering considered harmful", Ian Wakeman, Jon
                   Crowcroft, Zheng Wang, and Dejan Sirovica, IEEE
                   Network, January 1992, p. 7-16.
   [WARD]          "Custom fluorescent-nucleotide synthesis as an
                   alternative method for nucleic acid labeling",
                   Octavian Henegariu*, Patricia Bray-Ward and David C.
                   Ward, Nature Biotech 18:345-348 (2000).

[WILLINGER2002] "Robustness and the Internet: Design and evolution",

Walter Willinger and John Doyle, 2002.

   [ZHANG]         "Impact of Aggregation on Scaling Behavior of
                   Internet Backbone Traffic", Sprint ATL Technical
                   Report TR02-ATL-020157 Zhi-Li Zhang, Vinay Ribeiroj,
                   Sue Moon, Christophe Diot, February, 2002.

13. Authors' Addresses

Randy Bush

David Meyer

14. Full Copyright Statement

Copyright © The Internet Society (2002). All Rights Reserved.

This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into languages other than English.

The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assigns.



Funding for the RFC Editor function is currently provided by the Internet Society.