<pre>Independent Submission                                      M. Behringer
Request for Comments: 7980                                     A. Retana
Category: Informational                                    Cisco Systems
ISSN: 2070-1721                                                 R. White
                                                                Ericsson
                                                               G. Huston
                                                                   APNIC
                                                            October 2016


              <span class="h1">A Framework for Defining Network Complexity</span>

Abstract

   Complexity is a widely used parameter in network design, yet there is
   no generally accepted definition of the term.  Complexity metrics
   exist in a wide range of research papers, but most of these address
   only a particular aspect of a network, for example, the complexity of
   a graph or software.  While it may be impossible to define a metric
   for overall network complexity, there is a desire to better
   understand the complexity of a network as a whole, as deployed today
   to provide Internet services.  This document provides a framework to
   guide research on the topic of network complexity as well as some
   practical examples for trade-offs in networking.

   This document summarizes the work of the IRTF's Network Complexity
   Research Group (NCRG) at the time of its closure.  It does not
   present final results, but a snapshot of an ongoing activity, as a
   basis for future work.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see <a href="./rfc7841#section-2">Section&nbsp;2 of RFC 7841</a>.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   <a href="http://www.rfc-editor.org/info/rfc7980">http://www.rfc-editor.org/info/rfc7980</a>.






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Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to <a href="https://www.rfc-editor.org/bcp/bcp78">BCP 78</a> and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (<a href="http://trustee.ietf.org/license-info">http://trustee.ietf.org/license-info</a>) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.








































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Table of Contents

   <a href="#section-1">1</a>.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-4">4</a>
   <a href="#section-2">2</a>.  General Considerations  . . . . . . . . . . . . . . . . . . .   <a href="#page-5">5</a>
     <a href="#section-2.1">2.1</a>.  The Behavior of a Complex Network . . . . . . . . . . . .   <a href="#page-5">5</a>
     <a href="#section-2.2">2.2</a>.  Complex versus Complicated  . . . . . . . . . . . . . . .   <a href="#page-5">5</a>
     <a href="#section-2.3">2.3</a>.  Robust Yet Fragile  . . . . . . . . . . . . . . . . . . .   <a href="#page-6">6</a>
     <a href="#section-2.4">2.4</a>.  The Complexity Cube . . . . . . . . . . . . . . . . . . .   <a href="#page-6">6</a>
     <a href="#section-2.5">2.5</a>.  Related Concepts  . . . . . . . . . . . . . . . . . . . .   <a href="#page-6">6</a>
     <a href="#section-2.6">2.6</a>.  Technical Debt  . . . . . . . . . . . . . . . . . . . . .   <a href="#page-7">7</a>
     <a href="#section-2.7">2.7</a>.  Layering Considerations . . . . . . . . . . . . . . . . .   <a href="#page-8">8</a>
   <a href="#section-3">3</a>.  Trade-Offs  . . . . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-8">8</a>
     3.1.  Control-Plane State versus Optimal Forwarding Paths
           (Stretch) . . . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-9">9</a>
     <a href="#section-3.2">3.2</a>.  Configuration State versus Failure Domain Separation  . .  <a href="#page-10">10</a>
     3.3.  Policy Centralization versus Optimal Policy Application .  12
     3.4.  Configuration State versus Per-Hop Forwarding
           Optimization  . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-13">13</a>
     <a href="#section-3.5">3.5</a>.  Reactivity versus Stability . . . . . . . . . . . . . . .  <a href="#page-13">13</a>
   <a href="#section-4">4</a>.  Parameters  . . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-15">15</a>
   <a href="#section-5">5</a>.  Elements of Complexity  . . . . . . . . . . . . . . . . . . .  <a href="#page-16">16</a>
     <a href="#section-5.1">5.1</a>.  The Physical Network (Hardware) . . . . . . . . . . . . .  <a href="#page-16">16</a>
     <a href="#section-5.2">5.2</a>.  Algorithms  . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
     <a href="#section-5.3">5.3</a>.  State in the Network  . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
     <a href="#section-5.4">5.4</a>.  Churn . . . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
     <a href="#section-5.5">5.5</a>.  Knowledge . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
   <a href="#section-6">6</a>.  Location of Complexity  . . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
     <a href="#section-6.1">6.1</a>.  Topological Location  . . . . . . . . . . . . . . . . . .  <a href="#page-17">17</a>
     <a href="#section-6.2">6.2</a>.  Logical Location  . . . . . . . . . . . . . . . . . . . .  <a href="#page-18">18</a>
     <a href="#section-6.3">6.3</a>.  Layering Considerations . . . . . . . . . . . . . . . . .  <a href="#page-18">18</a>
   <a href="#section-7">7</a>.  Dependencies  . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-18">18</a>
     <a href="#section-7.1">7.1</a>.  Local Dependencies  . . . . . . . . . . . . . . . . . . .  <a href="#page-19">19</a>
     <a href="#section-7.2">7.2</a>.  Network-Wide Dependencies . . . . . . . . . . . . . . . .  <a href="#page-19">19</a>
     <a href="#section-7.3">7.3</a>.  Network-External Dependencies . . . . . . . . . . . . . .  <a href="#page-19">19</a>
   <a href="#section-8">8</a>.  Management Interactions . . . . . . . . . . . . . . . . . . .  <a href="#page-20">20</a>
     <a href="#section-8.1">8.1</a>.  Configuration Complexity  . . . . . . . . . . . . . . . .  <a href="#page-20">20</a>
     <a href="#section-8.2">8.2</a>.  Troubleshooting Complexity  . . . . . . . . . . . . . . .  <a href="#page-20">20</a>
     <a href="#section-8.3">8.3</a>.  Monitoring Complexity . . . . . . . . . . . . . . . . . .  <a href="#page-20">20</a>
     <a href="#section-8.4">8.4</a>.  Complexity of System Integration  . . . . . . . . . . . .  <a href="#page-21">21</a>
   <a href="#section-9">9</a>.  External Interactions . . . . . . . . . . . . . . . . . . . .  <a href="#page-21">21</a>
   <a href="#section-10">10</a>. Examples  . . . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-22">22</a>
   <a href="#section-11">11</a>. Security Considerations . . . . . . . . . . . . . . . . . . .  <a href="#page-22">22</a>
   <a href="#section-12">12</a>. Informative References  . . . . . . . . . . . . . . . . . . .  <a href="#page-22">22</a>
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-23">23</a>
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-24">24</a>






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<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>.  Introduction</span>

   Network design can be described as the art of finding the simplest
   solution to solve a given problem.  Complexity is thus assumed in the
   design process; engineers do not ask if there should be complexity,
   but rather, how much complexity is required to solve the problem.
   The question of how much complexity assumes there is some way to
   characterize the amount of complexity present in a system.  The
   reality is, however, this is an area of research and experience
   rather than a solved problem within the network engineering space.
   Today's design decisions are made based on a rough estimation of the
   network's complexity rather than a solid understanding.

   The document begins with general considerations, including some
   foundational definitions and concepts.  It then provides some
   examples for trade-offs that network engineers regularly make when
   designing a network.  This section serves to demonstrate that there
   is no single answer to complexity; rather, it is a managed trade-off
   between many parameters.  After this, this document provides a set of
   parameters engineers should consider when attempting to either
   measure complexity or build a framework around it.  This list makes
   no claim to be complete, but it serves as a guide of known existing
   areas of investigation as well as a pointer to areas that still need
   to be investigated.

   Two purposes are served here.  The first is to guide researchers
   working in the area of complexity in their work.  The more
   researchers are able to connect their work to the concerns of network
   designers, the more useful their research will become.  This document
   may also guide research into areas not considered before.  The second
   is to help network engineers to build a better understanding of where
   complexity might be "hiding" in their networks and to be more fully
   aware of how complexity interacts with design and deployment.

   The goal of the IRTF Network Complexity Research Group (NCRG) [<a href="#ref-ncrg" title="&quot;IRTF Network Complexity Research Group (NCRG) [CONCLUDED]&quot;">ncrg</a>]
   was to define a framework for network complexity research while
   recognizing that it may be impossible to define metrics for overall
   network complexity.  This document summarizes the work of this group
   at the time of its closure in 2014.  It does not present final
   results, but rather a snapshot of an ongoing activity, as a basis for
   future work.

   Many references to existing research in the area of network
   complexity are listed on the Network Complexity Wiki [<a href="#ref-wiki" title="&quot;Network Complexity - The Wiki&quot;">wiki</a>].  This
   wiki also contains background information on previous meetings on the
   subject, previous research, etc.





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<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>.  General Considerations</span>

<span class="h3"><a class="selflink" id="section-2.1" href="#section-2.1">2.1</a>.  The Behavior of a Complex Network</span>

   While there is no generally accepted definition of network
   complexity, there is some understanding of the behavior of a complex
   network.  It has some or all of the following properties:

   o  Self-Organization: A network runs some protocols and processes
      without external control; for example, a routing process, failover
      mechanisms, etc.  The interaction of those mechanisms can lead to
      a complex behavior.

   o  Unpredictability: In a complex network, the effect of a local
      change on the behavior of the global network may be unpredictable.

   o  Emergence: The behavior of the system as a whole is not reflected
      in the behavior of any individual component of the system.

   o  Non-linearity: An input into the network produces a non-linear
      result.

   o  Fragility: A small local input can break the entire system.

<span class="h3"><a class="selflink" id="section-2.2" href="#section-2.2">2.2</a>.  Complex versus Complicated</span>

   The two terms "complex" and "complicated" are often used
   interchangeably, yet they describe different but overlapping
   properties.  The RG made the following statements about the two
   terms, but they would need further refinement to be considered formal
   definitions:

   o  A "complicated" system is a deterministic system that can be
      understood by an appropriate level of analysis.  It is often an
      externally applied attribute rather than an intrinsic property of
      a system and is typically associated with systems that require
      deep or significant levels of analysis.

   o  A "complex" system, by comparison, is an intrinsic property of a
      system and is typically associated with emergent behaviors such
      that the behavior of the system is not fully described by the sum
      of the behavior of each of the components of the system.  Complex
      systems are often associated with systems whose components exhibit
      high levels of interaction and feedback.







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<span class="h3"><a class="selflink" id="section-2.3" href="#section-2.3">2.3</a>.  Robust Yet Fragile</span>

   Networks typically follow the "robust yet fragile" paradigm: they are
   designed to be robust against a set of failures, yet they are very
   vulnerable to other failures.  Doyle [<a href="#ref-Doyle" title="&quot;The 'robust yet fragile' nature of the Internet&quot;">Doyle</a>] explains the concept
   with an example: the Internet is robust against single-component
   failure but fragile to targeted attacks.  The "robust yet fragile"
   property also touches on the fact that all network designs are
   necessarily making trade-offs between different design goals.  The
   simplest one is "Good, Fast, Cheap: Pick any two (you can't have all
   three)", as articulated in "The Twelve Networking Truths" [<a href="./rfc1925" title="&quot;The Twelve Networking Truths&quot;">RFC1925</a>].
   In real network design, trade-offs between many aspects have to be
   made, including, for example, issues of scope, time, and cost in the
   network cycle of planning, design, implementation, and management of
   a network platform.  <a href="#section-3">Section 3</a> gives some examples of trade-offs, and
   parameters are discussed in <a href="#section-4">Section 4</a>.

<span class="h3"><a class="selflink" id="section-2.4" href="#section-2.4">2.4</a>.  The Complexity Cube</span>

   Complex tasks on a network can be done in different components of the
   network.  For example, routing can be controlled by central
   algorithms and the result distributed (e.g., OpenFlow model); the
   routing algorithm can also run completely distributed (e.g., routing
   protocols such as OSPF or IS-IS), or a human operator could calculate
   routing tables and statically configure routing.  Behringer
   [<a href="#ref-Behringer" title="&quot;Classifying Network Complexity&quot;">Behringer</a>] defines these three axes of complexity as a "complexity
   cube" with the respective axes being network elements, central
   systems, and human operators.  Any function can be implemented in any
   of these three axes, and this choice likely has an impact on the
   overall complexity of the system.

<span class="h3"><a class="selflink" id="section-2.5" href="#section-2.5">2.5</a>.  Related Concepts</span>

   When discussing network complexity, a large number of influencing
   factors have to be taken into account to arrive at a full picture,
   for example:

   o  State in the Network: Contains the network elements, such as
      routers, switches (with their OS, including protocols), lines,
      central systems, etc.  This also includes the number and
      algorithmic complexity of the protocols on network devices.

   o  Human Operators: Complexity manifests itself often by a network
      that is not completely understood by human operators.  Human error
      is a primary source for catastrophic failures and therefore must
      be taken into account.





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   o  Classes/Templates: Rather than counting the number of lines in a
      configuration or the number of hardware elements, more important
      is the number of classes from which those can be derived.  In
      other words, it is probably less complex to have 1000 interfaces
      that are identically configured than 5 that are configured
      completely different.

   o  Dependencies and Interactions: The number of dependencies between
      elements, as well as the interactions between them, has influence
      on the complexity of the network.

   o  Total Cost of Ownership (TCO): TCO could be a good metric for
      network complexity if the TCO calculation takes into account all
      influencing factors, for example, training time for staff to be
      able to maintain a network.

   o  Benchmark Unit Cost (BUC): BUC is a related metric that indicates
      the cost of operating a certain component.  If calculated well, it
      reflects at least parts of the complexity of this component.
      Therefore, the way TCO or BUC is calculated can help to derive a
      complexity metric.

   o  Churn / Rate of Change: The change rate in a network itself can
      contribute to complexity, especially if a number of components of
      the overall network interact.

   Networks differ in terms of their intended purpose (such as is found
   in differences between enterprise and public carriage network
   platforms) and differences in their intended roles (such as is found
   in the differences between so-called "access" networks and "core"
   transit networks).  The differences in terms of role and purpose can
   often lead to differences in the tolerance for, and even the metrics
   of, complexity within such different network scenarios.  This is not
   necessarily a space where a single methodology for measuring
   complexity, and defining a single threshold value of acceptability of
   complexity, is appropriate.

<span class="h3"><a class="selflink" id="section-2.6" href="#section-2.6">2.6</a>.  Technical Debt</span>

   Many changes in a network are made with a dependency on the existing
   network.  Often, a suboptimal decision is made because the optimal
   decision is hard or impossible to realize at the time.  Over time,
   the number of suboptimal changes in themselves cause significant
   complexity, which would not have been there had the optimal solution
   been implemented.






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   The term "technical debt" refers to the accumulated complexity of
   suboptimal changes over time.  As with financial debt, the idea is
   that also technical debt must be repaid one day by cleaning up the
   network or software.

<span class="h3"><a class="selflink" id="section-2.7" href="#section-2.7">2.7</a>.  Layering Considerations</span>

   In considering the larger space of applications, transport services,
   network services, and media services, it is feasible to engineer
   responses for certain types of desired applications responses in many
   different ways and involving different layers of the so-called
   network protocol stack.  For example, Quality of Service (QoS) could
   be engineered at any of these layers or even in a number of
   combinations of different layers.

   Considerations of complexity arise when mutually incompatible
   measures are used in combination (such as error detection and
   retransmission at the media layer in conjunction with the use of TCP
   transport protocol) or when assumptions used in one layer are
   violated by another layer.  This results in surprising outcomes that
   may result in complex interactions, for example, oscillation, because
   different layers use different timers for retransmission.  These
   issues have led to the perspective that increased layering frequently
   increases complexity [<a href="./rfc3439" title="&quot;Some Internet Architectural Guidelines and Philosophy&quot;">RFC3439</a>].

   While this research work is focused on network complexity, the
   interactions of the network with the end-to-end transport protocols,
   application layer protocols, and media properties are relevant
   considerations here.

<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>.  Trade-Offs</span>

   Network complexity is a system-level, rather than component-level,
   problem; overall system complexity may be more than the sum of the
   complexity of the individual pieces.

   There are two basic ways in which system-level problems might be
   addressed: interfaces and continuums.  In addressing a system-level
   problem through interfaces, we seek to treat each piece of the system
   as a "black box" and develop a complete understanding of the
   interfaces between these black boxes.  In addressing a system-level
   problem as a continuum, we seek to understand the impact of a single
   change or element to the entire system as a set of trade-offs.

   While network complexity can profitably be approached from either of
   these perspectives, in this document we have chosen to approach the
   system-level impact of network complexity from the perspective of
   continuums of trade-offs.  In theory, modifying the network to



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   resolve one particular problem (or class of problems) will add
   complexity that results in the increased likelihood (or appearance)
   of another class of problems.  Discovering these continuums of trade-
   offs, and then determining how to measure each one, become the key
   steps in understanding and measuring system-level complexity in this
   view.

   The following sections describe five such continuums; more may be
   possible.

   o  Control-Plane State versus Optimal Forwarding Paths (or its
      opposite measure, stretch)

   o  Configuration State versus Failure Domain Separation

   o  Policy Centralization versus Optimal Policy Application

   o  Configuration State versus Per-Hop Forwarding Optimization

   o  Reactivity versus Stability

<span class="h3"><a class="selflink" id="section-3.1" href="#section-3.1">3.1</a>.  Control-Plane State versus Optimal Forwarding Paths (Stretch)</span>

   Control-plane state is the aggregate amount of information carried by
   the control plane through the network in order to produce the
   forwarding table at each device.  Each additional piece of
   information added to the control plane -- such as more-specific
   reachability information, policy information, additional control
   planes for virtualization and tunneling, or more precise topology
   information -- adds to the complexity of the control plane.  This
   added complexity, in turn, adds to the burden of monitoring,
   understanding, troubleshooting, and managing the network.

   Removing control-plane state, however, is not always a net positive
   gain for the network as a system; removing control-plane state almost
   always results in decreased optimality in the forwarding and handling
   of packets traveling through the network.  This decreased optimality
   can be termed "stretch", which is defined as the difference between
   the absolute shortest (or best) path traffic could take through the
   network and the path the traffic actually takes.  Stretch is
   expressed as the difference between the optimal and actual path.  The
   figure below provides an example of this trade-off.









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                                +---R1---+
                                |        |
        (aggregate: 192.0.2/24) R2       R3 (aggregate: 192.0.2/24)
                                |        |
                                R4-------R5
                                |
       (announce: 192.0.2.1/32) R6

   Assume each link is of equal cost in this figure and that R6 is
   advertising 192.0.2.1/32.

   For R1, the shortest path to 192.0.2.1/32, advertised by R6, is along
   the path [R1,R2,R4,R6].

   Assume, however, the network administrator decides to aggregate
   reachability information at R2 and R3, advertising 192.0.2.0/24
   towards R1 from both of these points.  This reduces the overall
   complexity of the control plane by reducing the amount of information
   carried past these two routers (at R1 only in this case).

   Aggregating reachability information at R2 and R3, however, may have
   the impact of making both routes towards 192.0.2.1/32 appear as equal
   cost paths to R1; there is no particular reason R1 should choose the
   shortest path through R2 over the longer path through R3.  This, in
   effect, increases the stretch of the network.  The shortest path from
   R1 to R6 is 3 hops, a path that will always be chosen before
   aggregation is configured.  Assuming half of the traffic will be
   forwarded along the path through R2 (3 hops), and half through R3 (4
   hops), the network is stretched by ((3+4)/2) - 3), or .5, a "half a
   hop".

   Traffic engineering through various tunneling mechanisms is, at a
   broad level, adding control-plane state to provide more optimal
   forwarding (or network utilization).  Optimizing network utilization
   may require detuning stretch (intentionally increasing stretch) to
   increase overall network utilization and efficiency; this is simply
   an alternate instance of control-plane state (and hence, complexity)
   weighed against optimal forwarding through the network.

<span class="h3"><a class="selflink" id="section-3.2" href="#section-3.2">3.2</a>.  Configuration State versus Failure Domain Separation</span>

   A failure domain, within the context of a network control plane, can
   be defined as the set of devices impacted by a change in the network
   topology or configuration.  A network with larger failure domains is
   more prone to cascading failures, so smaller failure domains are
   normally preferred over larger ones.





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   The primary means used to limit the size of a failure domain within a
   network's control plane is information hiding; the two primary types
   of information hidden in a network control plane are reachability
   information and topology information.  An example of aggregating
   reachability information is summarizing the routes 192.0.2.1/32,
   192.0.2.2/32, and 192.0.2.3/32 into the single route 192.0.2.0/24,
   along with the aggregation of the metric information associated with
   each of the component routes.  Note that aggregation is a "natural"
   part of IP networks, starting with the aggregation of individual
   hosts into a subnet at the network edge.  An example of topology
   aggregation is the summarization of routes at a link-state flooding
   domain boundary, or the lack of topology information in a distance-
   vector protocol.

   While limiting the size of failure domains appears to be an absolute
   good in terms of network complexity, there is a definite trade-off in
   configuration complexity.  The more failure domain edges created in a
   network, the more complex configuration will become.  This is
   particularly true if redistribution of routing information between
   multiple control-plane processes is used to create failure domain
   boundaries; moving between different types of control planes causes a
   loss of the consistent metrics most control planes rely on to build
   loop-free paths.  Redistribution, in particular, opens the door to
   very destructive positive feedback loops within the control plane.
   Examples of control-plane complexity caused by the creation of
   failure domain boundaries include route filters, routing aggregation
   configuration, and metric modifications to engineer traffic across
   failure domain boundaries.

   Returning to the network described in the previous section,
   aggregating routing information at R2 and R3 will divide the network
   into two failure domains: (R1, R2, R3) and (R2, R3, R4, R5).  A
   failure at R5 should have no impact on the forwarding information at
   R1.

   A false failure domain separation occurs, however, when the metric of
   the aggregate route advertised by R2 and R3 is dependent on one of
   the routes within the aggregate.  For instance, if the metric of the
   192.0.2.0/24 aggregate is derived from the metric of the component
   192.0.2.1/32, then a failure of this one component will cause changes
   in the forwarding table at R1 -- in this case, the control plane has
   not truly been separated into two distinct failure domains.  The
   added complexity in the illustration network would be the management
   of the configuration required to aggregate the control-plane
   information, and the management of the metrics to ensure the control
   plane is truly separated into two distinct failure domains.





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   Replacing aggregation with redistribution adds the complexity of
   managing the feedback of routing information redistributed between
   the failure domains.  For instance, if R1, R2, and R3 were configured
   to run one routing protocol while R2, R3, R4, R5, and R6 were
   configured to run another protocol, R2 and R3 could be configured to
   redistribute reachability information between these two control
   planes.  This can split the control plane into multiple failure
   domains (depending on how, specifically, redistribution is
   configured) but at the cost of creating and managing the
   redistribution configuration.  Further, R3 must be configured to
   block routing information redistributed at R2 towards R1 from being
   redistributed (again) towards R4 and R5.

<span class="h3"><a class="selflink" id="section-3.3" href="#section-3.3">3.3</a>.  Policy Centralization versus Optimal Policy Application</span>

   Another broad area where control-plane complexity interacts with
   optimal network utilization is QoS.  Two specific actions are
   required to optimize the flow of traffic through a network: marking
   and Per Hop Behaviors (PHBs).  Rather than examining each packet at
   each forwarding device in a network, packets are often marked, or
   classified, in some way (typically through Type of Service bits) so
   they can be handled consistently at all forwarding devices.

   Packet-marking policies must be configured on specific forwarding
   devices throughout the network.  Distributing marking closer to the
   edge of the network necessarily means configuring and managing more
   devices, but it produces optimal forwarding at a larger number of
   network devices.  Moving marking towards the network core means
   packets are marked for proper handling across a smaller number of
   devices.  In the same way, each device through which a packet passes
   with the correct PHBs configured represents an increase in the
   consistency in packet handling through the network as well as an
   increase in the number of devices that must be configured and managed
   for the correct PHBs.  The network below is used for an illustration
   of this concept.

                              +----R1----+
                              |          |
                           +--R2--+   +--R3--+
                           |      |   |      |
                           R4     R5  R6     R7

   In this network, marking and PHB configuration may be configured on
   any device, R1 through R7.

   Assume marking is configured at the network edge; in this case, four
   devices (R4, R5, R6, R7) must be configured, including ongoing
   configuration management, to mark packets.  Moving packet marking to



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   R2 and R3 will halve the number of devices on which packet-marking
   configuration must be managed, but at the cost of inconsistent packet
   handling at the inbound interfaces of R2 and R3 themselves.

   Thus, reducing the number of devices that must have managed
   configurations for packet marking will reduce optimal packet flow
   through the network.  Assuming packet marking is actually configured
   along the edge of this network, configuring PHBs on different devices
   has this same trade-off of managed configuration versus optimal
   traffic flow.  If the correct PHBs are configured on R1, R2, and R3,
   then packets passing through the network will be handled correctly at
   each hop.  The cost involved will be the management of PHB
   configuration on three devices.  Configuring a single device for the
   correct PHBs (R1, for instance), will decrease the amount of
   configuration management required at the cost of less than optimal
   packet handling along the entire path.

<span class="h3"><a class="selflink" id="section-3.4" href="#section-3.4">3.4</a>.  Configuration State versus Per-Hop Forwarding Optimization</span>

   The number of PHBs configured along a forwarding path exhibits the
   same complexity versus optimality trade-off described in the section
   above.  The more classes (or queues) traffic is divided into, the
   more fine-grained traffic will be managed as it passes through the
   network.  At the same time, each class of service must be managed,
   both in terms of configuration and in its interaction with other
   classes of service configured in the network.

<span class="h3"><a class="selflink" id="section-3.5" href="#section-3.5">3.5</a>.  Reactivity versus Stability</span>

   The speed at which the network's control plane can react to a change
   in configuration or topology is an area of widespread study.
   Control-plane convergence can be broken down into four essential
   parts:

   o  Detecting the change

   o  Propagating information about the change

   o  Determining the best path(s) through the network after the change

   o  Changing the forwarding path at each network element along the
      modified paths

   Each of these areas can be addressed in an effort to improve network
   convergence speeds; some of these improvements come at the cost of
   increased complexity.





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   Changes in network topology can be detected much more quickly through
   faster echo (or hello) mechanisms, lower-layer physical detection,
   and other methods.  Each of these mechanisms, however, can only be
   used at the cost of evaluating and managing false positives and high
   rates of topology change.

   If the state of a link change can be detected in 10 ms, for instance,
   the link could theoretically change state 50 times in a second -- it
   would be impossible to tune a network control plane to react to
   topology changes at this rate.  Injecting topology change information
   into the control plane at this rate can destabilize the control
   plane, and hence the network itself.  To counter this, most
   techniques that quickly detect link-down events include some form of
   dampening mechanism; configuring and managing these dampening
   mechanisms increases complexity.

   Changes in network topology must also be propagated throughout the
   network so each device along the path can compute new forwarding
   tables.  In high-speed network environments, propagation of routing
   information changes can take place in tens of milliseconds, opening
   the possibility of multiple changes being propagated per second.
   Injecting information at this rate into the control plane creates the
   risk of overloading the processes and devices participating in the
   control plane as well as creating destructive positive feedback loops
   in the network.  To avoid these consequences, most control-plane
   protocols regulate the speed at which information about network
   changes can be transmitted by any individual device.  A recent
   innovation in this area is using exponential backoff techniques to
   manage the rate at which information is advertised into the control
   plane; the first change is transmitted quickly, while subsequent
   changes are transmitted more slowly.  These techniques all control
   the destabilizing effects of rapid information flows through the
   control plane through the added complexity of configuring and
   managing the rate at which the control plane can propagate
   information about network changes.

   All control planes require some form of algorithmic calculation to
   find the best path through the network to any given destination.
   These algorithms are often lightweight but they still require some
   amount of memory and computational power to execute.  Rapid changes
   in the network can overwhelm the devices on which these algorithms
   run, particularly if changes are presented more quickly than the
   algorithm can run.  Once a device running these algorithms becomes
   processor or memory bound, it could experience a computational
   failure altogether, causing a more general network outage.  To
   prevent computational overloading, control-plane protocols are
   designed with timers limiting how often they can compute the best
   path through a network; often these timers are exponential in nature



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   and thus allow the first computation to run quickly while delaying
   subsequent computations.  Configuring and managing these timers is
   another source of complexity within the network.

   Another option to improve the speed at which the control plane reacts
   to changes in the network is to precompute alternate paths at each
   device and possibly preinstall forwarding information into local
   forwarding tables.  Additional state is often needed to precompute
   alternate paths, and additional algorithms and techniques are often
   configured and deployed.  This additional state, and these additional
   algorithms, add some amount of complexity to the configuration and
   management of the network.

   In some situations (for some topologies), a tunnel is required to
   pass traffic around a network failure or topology change.  These
   tunnels, while not manually configured, represent additional
   complexity at the forwarding and control planes.

<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>.  Parameters</span>

   In <a href="#section-3">Section 3</a>, we describe a set of trade-offs in network design to
   illustrate the practical choices network operators have to make.  The
   amount of parameters to consider in such trade-off scenarios is very
   large, and thus a complete listing may not be possible.  Also, the
   dependencies between the various metrics themselves is very complex
   and requires further study.  This document attempts to define a
   methodology and an overall high-level structure.

   To analyze trade-offs it is necessary to formalize them.  The list of
   parameters for such trade-offs is long, and the parameters can be
   complex in themselves.  For example, "cost" can be a simple
   unidimensional metric, but "extensibility" and "optimal forwarding
   state" are harder to define in detail.

   A list of parameters to trade off contains metrics such as:

   o  State: How much state needs to be held in the control plane,
      forwarding plane, configuration, etc.?

   o  Cost: How much does the network cost to build and run (i.e.,
      capital expenditure (capex) and operating expenses (opex))?

   o  Bandwidth/Delay/Jitter: Traffic characteristics between two points
      (average, max, etc.)

   o  Configuration Complexity: How hard is it to configure and maintain
      the configuration?




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   o  Susceptibility to Denial of Service: How easy is it to attack the
      service?

   o  Security (Confidentiality/Integrity): How easy is it to
      sniff/modify/insert the data flow?

   o  Scalability: To what size can I grow the network/service?

   o  Stability: How stable is the network under the influence of local
      change?

   o  Reactivity: How fast does the network converge or adapt to new
      situations?

   o  Extensibility: Can I use the network for other services in the
      future?

   o  Ease of Troubleshooting: Are failure domains separated?  How hard
      is it to find and correct problems?

   o  Optimal Per-Hop Forwarding Behavior

   o  Predictability: If I change a parameter, what will happen?

   o  Clean Failure: When a problem arises, does the root cause lead to
      deterministic failure?

<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>.  Elements of Complexity</span>

   Complexity can be found in various elements in a networked system.
   For example, the configuration of a network element reflects some of
   the complexity contained in this system, or an algorithm used by a
   protocol may be more or less complex.  When classifying complexity,
   "WHAT is complex?" is the first question to ask.  This section offers
   a method to answer this question.

<span class="h3"><a class="selflink" id="section-5.1" href="#section-5.1">5.1</a>.  The Physical Network (Hardware)</span>

   The set of network devices and wiring contains a certain complexity.
   For example, adding a redundant link between two locations increases
   the complexity of the network but provides more redundancy.  Also,
   network devices can be more or less modular, which has impact on
   complexity trading off against ease of maintenance, availability, and
   upgradability.







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<span class="h3"><a class="selflink" id="section-5.2" href="#section-5.2">5.2</a>.  Algorithms</span>

   The behavior of the physical network is not only defined by the
   hardware but also by algorithms that run on network elements and in
   central locations.  Every algorithm has a certain intrinsic
   complexity, which is the subject of research on software complexity.

<span class="h3"><a class="selflink" id="section-5.3" href="#section-5.3">5.3</a>.  State in the Network</span>

   The way a network element treats traffic is defined largely by the
   state in the network, in form of configuration, routing state,
   security measures, etc.  <a href="#section-3.1">Section 3.1</a> shows an example where more
   control-plane state allows for a more precise forwarding.

<span class="h3"><a class="selflink" id="section-5.4" href="#section-5.4">5.4</a>.  Churn</span>

   The rate of change itself is a parameter in complexity and needs to
   be weighed against other parameters.  <a href="#section-3.5">Section 3.5</a> explains a trade-
   off between the speed of communicating changes through the network
   and the stability of the network.

<span class="h3"><a class="selflink" id="section-5.5" href="#section-5.5">5.5</a>.  Knowledge</span>

   Certain complexity parameters have a strong link to the human aspect
   of networking.  For example, the more options and parameters a
   network protocol has, the harder it is to configure and troubleshoot.
   Therefore, there is a trade-off between the knowledge to be
   maintained by operational staff and desired functionality.  The
   required knowledge of network operators is therefore an important
   part in complexity considerations.

<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>.  Location of Complexity</span>

   The previous section discussed in which form complexity may be
   perceived.  This section focuses on where this complexity is located
   in a network.  For example, an algorithm can run centrally,
   distributed, or even in the head of a network administrator.  In
   classifying the complexity of a network, the location of a component
   may have an impact on overall complexity.  This section offers a
   methodology to find WHERE the complex component is located.

<span class="h3"><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a>.  Topological Location</span>

   An algorithm can run distributed; for example, a routing protocol
   like OSPF runs on all routers in a network.  But, it can also be in a
   central location such as the Network Operations Center (NOC).  The
   physical location has an impact on several other parameters, such as
   availability (local changes might be faster than going through a



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   remote NOC) and ease of operation, because it might be easier to
   understand and troubleshoot one central entity rather than many
   remote ones.

   The example in <a href="#section-3.3">Section 3.3</a> shows how the location of state (in this
   case configuration) impacts the precision of the policy enforcement
   and the corresponding state required.  Enforcement closer to the edge
   requires more network-wide state but is more precise.

<span class="h3"><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a>.  Logical Location</span>

   Independent of its physical location, the logical location also may
   make a difference to complexity.  A controller function, for example,
   can reside in a NOC and also on a network element.  Generally,
   organizing a network in separate logical entities is considered
   positive because it eases the understanding of the network, thereby
   making troubleshooting and configuration easier.  For example, a BGP
   route reflector is a separate logical entity from a BGP speaker, but
   it may reside on the same physical node.

<span class="h3"><a class="selflink" id="section-6.3" href="#section-6.3">6.3</a>.  Layering Considerations</span>

   Also, the layer of the TCP/IP stack in which a function is
   implemented can have an impact on the complexity of the overall
   network.  Some functions are implemented in several layers in
   slightly different ways; this may lead to unexpected results.

   As an example, a link failure is detected on various layers: L1, L2,
   the IGP, BGP, and potentially more.  Since those have dependencies on
   each other, different link failure detection times can cause
   undesired effects.  Dependencies are discussed in more detail in the
   next section.

<span class="h2"><a class="selflink" id="section-7" href="#section-7">7</a>.  Dependencies</span>

   Dependencies are generally regarded as related to overall complexity.
   A system with less dependencies is generally considered less complex.
   This section proposes a way to analyze dependencies in a network.

   For example, [<a href="#ref-Chun" title="&quot;NetComplex: A Complexity Metric for Networked System Designs&quot;">Chun</a>] states: "We conjecture that the complexity
   particular to networked systems arises from the need to ensure state
   is kept in sync with its distributed dependencies."

   In this document, we distinguish three types of dependencies: local
   dependencies, network-wide dependencies, and network-external
   dependencies.





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<span class="h3"><a class="selflink" id="section-7.1" href="#section-7.1">7.1</a>.  Local Dependencies</span>

   Local dependencies are relative to a single node in the network.  For
   example, an interface on a node may have an IP address; this address
   may be used in other parts of the configuration.  If the interface
   address changes, the dependent configuration parts have to change as
   well.

   Similar dependencies exist for QoS policies, access-control lists,
   names and numbers of configuration parts, etc.

<span class="h3"><a class="selflink" id="section-7.2" href="#section-7.2">7.2</a>.  Network-Wide Dependencies</span>

   Routing protocols, failover protocols, and many others have
   dependencies across the network.  If one node is affected by a
   problem, this may have a ripple effect through the network.  These
   protocols are typically designed to deal with unexpected consequences
   and thus are unlikely to cause an issue on their own.  But,
   occasionally a number of complexity issues come together (for
   example, different timers on different layers), resulting in
   unexpected behavior.

<span class="h3"><a class="selflink" id="section-7.3" href="#section-7.3">7.3</a>.  Network-External Dependencies</span>

   Some dependencies are on elements outside the actual network, for
   example, on an external NTP clock source or an Authentication,
   Authorization, and Accounting (AAA) server.  Again, a trade-off is
   made: in the example of AAA used for login authentication, we reduce
   the configuration (state) on each node (in particular, user-specific
   configuration), but we add an external dependency on a AAA server.
   In networks with many administrators, a AAA server is clearly the
   only manageable way to track all administrators.  But, it comes at
   the cost of this external dependency with the consequence that admin
   access may be lost for all devices at the same time when the AAA
   server is unavailable.

   Even with the external dependency on a AAA server, the advantage of
   centralizing the user information (and logging) still has significant
   value over distributing user information across all devices.  To
   solve the problem of the central dependency not being available,
   other solutions have been developed -- for example, a secondary
   authentication mode with a single root-level password in case the AAA
   server is not available.








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<span class="h2"><a class="selflink" id="section-8" href="#section-8">8</a>.  Management Interactions</span>

   A static network generally is relatively stable; conversely, changes
   introduce a degree of uncertainty and therefore need to be examined
   in detail.  Also, the troubleshooting of a network exposes
   intuitively the complexity of the network.  This section proposes a
   methodology to classify management interactions with regard to their
   relationship to network complexity.

<span class="h3"><a class="selflink" id="section-8.1" href="#section-8.1">8.1</a>.  Configuration Complexity</span>

   Configuration can be seen as distributed state across network devices
   where the administrator has direct influence on the operation of the
   network.  Modifying the configuration can improve the network
   behavior overall or negatively affect it.  In the worst case, a
   single misconfiguration could potentially bring down the entire
   network.  Therefore, it is important that a human administrator can
   manage the complexity of the configuration well.

   The configuration reflects most of the local and global dependencies
   in the network, as explained in <a href="#section-7">Section 7</a>.  Tracking those
   dependencies in the configuration helps in understanding the overall
   network complexity.

<span class="h3"><a class="selflink" id="section-8.2" href="#section-8.2">8.2</a>.  Troubleshooting Complexity</span>

   Unexpected behavior can have a number of sources: the configuration
   may contain errors, the operating system (algorithms) may have bugs,
   and the hardware may be faulty, which includes anything from broken
   fibers to faulty line cards.  In serious problems, a combination of
   causes could result in a single visible condition.  Tracking the root
   causes of an error condition may be extremely difficult, pointing to
   the complex nature of a network.

   Being able to find the source of a problem requires, therefore, a
   solid understanding of the complexity of a network.  The
   configuration complexity discussed in the previous section represents
   only a part of the overall problem space.

<span class="h3"><a class="selflink" id="section-8.3" href="#section-8.3">8.3</a>.  Monitoring Complexity</span>

   Even in the absence of error conditions, the state of the network
   should be monitored to detect error conditions ideally before network
   services are affected.  For example, a single link-down event may not
   cause a service disruption in a well-designed network, but the
   problem needs to be resolved quickly to restore redundancy.





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   Monitoring a network has itself a certain complexity.  Issues are in
   scale; variations of devices to be monitored; variations of methods
   used to collect information; the inevitable loss of information as
   reporting is aggregated centrally; and the knowledge required to
   understand the network, the dependencies, and the interactions with
   users and other external inputs.

<span class="h3"><a class="selflink" id="section-8.4" href="#section-8.4">8.4</a>.  Complexity of System Integration</span>

   A network doesn't just consist of network devices but includes a vast
   array of backend and support systems.  It also interfaces a large
   variety of user devices, and a number of human interfaces, both to
   the user/customer as well as to administrators of the network.  A
   system integration job is required in order to make sure the overall
   network provides the overall service expected.

   All those interactions and systems have to be modeled to understand
   the interdependencies and complexities in the network.  This is a
   large area of future research.

<span class="h2"><a class="selflink" id="section-9" href="#section-9">9</a>.  External Interactions</span>

   A network is not a self-contained entity, but it exists to provide
   connectivity and services to users and other networks, both of which
   are outside the direct control of a network administrator.  The user
   experience of a network also illustrates a form of interaction with
   its own complexity.

   External interactions fall into the following categories:

   o  User Interactions: Users need a way to request a service, to have
      their problems resolved, and potentially to get billed for their
      usage.  There are a number of human interfaces that need to be
      considered, which depend to some extent on the network, for
      example, for troubleshooting or monitoring usage.

   o  Interactions with End Systems: The network also interacts with the
      devices that connect to it.  Typically, a device receives an IP
      address from the network and information on how to resolve domain
      names, plus potentially other services.  While those interactions
      are relatively simple, the vast amount of end-device types makes
      this a complicated space to track.

   o  Internetwork Interactions: Most networks connect to other
      networks.  Also, in this case, there are many interactions between
      networks, both technical (for example, running a routing protocol)
      as well as non-technical (for example, tracing problems across
      network boundaries).



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   For a fully operational network providing services to users, the
   external interactions and dependencies also form an integral part of
   the overall complexity of the network service.  A specific example
   are the root DNS servers, which are critical to the function of the
   Internet.  Practically all Internet users have an implicit dependency
   on the root DNS servers, which explains why those are frequent
   targets for attacks.  Understanding the overall complexity of a
   network includes understanding all those external dependencies.  Of
   course, in the case of the root DNS servers, there is little a
   network operator can influence.

<span class="h2"><a class="selflink" id="section-10" href="#section-10">10</a>.  Examples</span>

   In the foreseeable future, it is unlikely to define a single,
   objective metric that includes all the relevant aspects of
   complexity.  In the absence of such a global metric, a comparative
   approach could be easier.

   For example, it is possible to compare the complexity of a
   centralized system where algorithms run centrally and the results are
   distributed to the network nodes with a distributed algorithm.  The
   type of algorithm may be similar, but the location is different, and
   a different dependency graph would result.  The supporting hardware
   may be the same and thus could be ignored for this exercise.  Also,
   layering is likely to be the same.  The management interactions,
   though, would significantly differ in both cases.

   The classification in this document also makes it easier to survey
   existing research with regards to which area of complexity is
   covered.  This could help in identifying open areas for research.

<span class="h2"><a class="selflink" id="section-11" href="#section-11">11</a>.  Security Considerations</span>

   This document does not discuss any specific security considerations.

<span class="h2"><a class="selflink" id="section-12" href="#section-12">12</a>.  Informative References</span>

   [<a id="ref-Behringer">Behringer</a>] Behringer, M., "Classifying Network Complexity",
               Proceedings of the 2009 Workshop on Re-architecting the
               Internet (Re-Arch '09), ACM, DOI 10.1145/1658978.1658983,
               December 2009.

   [<a id="ref-Chun">Chun</a>]      Chun, B-G., Ratnasamy, S., and E. Eddie, "NetComplex: A
               Complexity Metric for Networked System Designs",
               Proceedings of the 5th USENIX Symposium on Networked
               Systems Design and Implementation (NSDI '08), pp.
               393-406, April 2008, &lt;<a href="http://usenix.org/events/nsdi08/tech/full_papers/chun/chun.pdf">http://usenix.org/events/nsdi08/</a>
               <a href="http://usenix.org/events/nsdi08/tech/full_papers/chun/chun.pdf">tech/full_papers/chun/chun.pdf</a>&gt;.



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   [<a id="ref-Doyle">Doyle</a>]     Doyle, J., Anderson, D., Li, L., Low, S., Roughnan, M.,
               Shalunov, S., Tanaka, R., and W. Willinger, "The 'robust
               yet fragile' nature of the Internet", Proceedings of the
               National Academy of Sciences of the United States of
               America (PNAS), Volume 102, Number 41,
               DOI 10.1073/pnas.0501426102, October 2005.

   [<a id="ref-ncrg">ncrg</a>]      IRTF, "IRTF Network Complexity Research Group (NCRG)
               [CONCLUDED]", &lt;<a href="https://irtf.org/concluded/ncrg">https://irtf.org/concluded/ncrg</a>&gt;.

   [<a id="ref-RFC1925">RFC1925</a>]   Callon, R., "The Twelve Networking Truths", <a href="./rfc1925">RFC 1925</a>,
               DOI 10.17487/RFC1925, April 1996,
               &lt;<a href="http://www.rfc-editor.org/info/rfc1925">http://www.rfc-editor.org/info/rfc1925</a>&gt;.

   [<a id="ref-RFC3439">RFC3439</a>]   Bush, R. and D. Meyer, "Some Internet Architectural
               Guidelines and Philosophy", <a href="./rfc3439">RFC 3439</a>,
               DOI 10.17487/RFC3439, December 2002,
               &lt;<a href="http://www.rfc-editor.org/info/rfc3439">http://www.rfc-editor.org/info/rfc3439</a>&gt;.

   [<a id="ref-wiki">wiki</a>]      "Network Complexity - The Wiki",
               &lt;<a href="http://networkcomplexity.org/">http://networkcomplexity.org/</a>&gt;.

Acknowledgements

   The motivations and framework of this overview of studies into
   network complexity are the result of many meetings and discussions
   with too many people to provide a full list here.  However, key
   contributions have been made by John Doyle, Dave Meyer, Jon
   Crowcroft, Mark Handley, Fred Baker, Paul Vixie, Lars Eggert, Bob
   Briscoe, Keith Jones, Bruno Klauser, Stephen Youell, Joel Obstfeld,
   and Philip Eardley.

   The authors would like to acknowledge the contributions of Rana
   Sircar, Ken Carlberg, and Luca Caviglione in the preparation of this
   document.
















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Authors' Addresses

   Michael H. Behringer
   Cisco Systems
   Building D, 45 Allee des Ormes
   Mougins  06250
   France

   Email: mbehring@cisco.com


   Alvaro Retana
   Cisco Systems
   7025 Kit Creek Rd.
   Research Triangle Park, NC  27709

   United States of America
   Email: aretana@cisco.com


   Russ White
   Ericsson
   144 Warm Wood Lane
   Apex, NC   27539
   United States of America

   Email: russ@riw.us
   URI:   <a href="http://www.ericsson.com">http://www.ericsson.com</a>


   Geoff Huston
   Asia Pacific Network Information Centre
   6 Cordelia St
   South Brisbane, QLD  4101
   Australia

   Email: gih@apnic.net
   URI:   <a href="http://www.apnic.net">http://www.apnic.net</a>













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