Internet Research Task Force                              M.H. Behringer
Internet-Draft                                                     Cisco
Intended status: Informational                                 G. Huston
Expires: August 20, 2013         Asia Pacific Network Information Centre
                                                       February 18, 2013

              A Framework for Defining Network Complexity


   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.  There is a desire to define 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.

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  2
   2.  Current Understanding of Network Complexity  . . . . . . . . .  2

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     2.1.  The Behavior of a Complex Network  . . . . . . . . . . . .  2
     2.2.  Robust Yet Fragile . . . . . . . . . . . . . . . . . . . .  3
     2.3.  The Complexity Cube  . . . . . . . . . . . . . . . . . . .  3
   3.  Towards Defining Network Complexity  . . . . . . . . . . . . .  3
     3.1.  General Observations . . . . . . . . . . . . . . . . . . .  3
     3.2.  The Problem Space  . . . . . . . . . . . . . . . . . . . .  3
     3.3.  Technical Debt . . . . . . . . . . . . . . . . . . . . . .  4
     3.4.  Layering considerations  . . . . . . . . . . . . . . . . .  5
   4.  Possible Directions of Research  . . . . . . . . . . . . . . .  5
     4.1.  Definitions and Metrics  . . . . . . . . . . . . . . . . .  5
     4.2.  Comparative Analysis . . . . . . . . . . . . . . . . . . .  6
     4.3.  Containment, Control or Reduction of Complexity  . . . . .  6
     4.4.  Use Cases  . . . . . . . . . . . . . . . . . . . . . . . .  6
   5.  Security Considerations  . . . . . . . . . . . . . . . . . . .  7
   6.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . .  7
   7.  References . . . . . . . . . . . . . . . . . . . . . . . . . .  7
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . .  8

1.  Introduction

   During the design phase of a network complexity plays a key role.
   Network designers generally seek to find the simplest design that
   fulfils a set of requirements.  As no objective definition of network
   complexity exists, subjective measures are used to come to a
   conclusion.  The resulting diverging views on what constitutes
   complexity subsequently lead to conflicts in design teams.  While
   most people would agree that complexity is an important factor in
   network design, today's design decisions are made based on a rough
   estimation of the network's complexity, rather than a solid

   The goal of this document is to define a framework for network
   complexity research.  This framework describes related research and
   current understanding of the topic, as well as outlining some ways
   research could be taken forward.  Specifically, contributions are
   invited in all of the areas mentioned.

   Many references to existing research in the area of network
   complexity are listed on the Network Complexity Wiki [wiki].  That
   wiki also contains background information on previous meetings on the
   subject, previous research, etc.

2.  Current Understanding of Network Complexity

2.1.  The Behavior of a Complex Network

   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

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      a complex behaviour.
   o  Un-predictability: In a complex network, the effect of a local
      change on the behaviour of the global network may be
   o  Emergence: A network has an emergent property if a small local
      change produces a large scale, seemingly unrelated state or
   o  Non-linearity: An input into the network produces a non-linear
   o  Fragility: A small local input can break the entire system.

2.2.  Robust Yet Fragile

   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 [Doyle] 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 articulated in "The Twelve Networking Truths" RFC1925
   [RFC1925]: "Good, Fast, Cheap: Pick any two (you can't have all
   three)." 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.

2.3.  The Complexity Cube

   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 ISIS), or a human operator could calculate
   routing tables and statically configure routing.  Behringer
   [Behringer] defines these three axes of complexity as a "complexity
   cube" with three axes: Network elements, central systems, and human
   operators.  While different functions can be shifted between these
   axes of the network, the overall complexity may change.

3.  Towards Defining Network Complexity

3.1.  General Observations

   Any analysis of practical network complexity must take a wide range
   of parameters into account, also parameters which are hard to
   measure, for example the human element.  Human error constitutes in
   most cases of critical outages the trigger condition; therefore any
   analysis ignoring the human factor cannot address the full picture.
   [insert a reference that 70%(?) of critical outages have a human

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3.2.  The Problem Space

   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.  The number and algorithmical complexity of
      the protocols on network devices for example.
   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.
   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
      which are identically configured than 5 that are completely
      different configured.
   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  TCO (Total cost of ownership): TCO could be a good metric for
      network complexity, if the TCO calculation takes into accont all
      influencing factors, for example training time for staff to be
      able to maintain a network.
   o  Benchmark Unit Cost 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 are calculated can help to derive a complexity
   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 in their intended role (such as is found in the
   diferences 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.

3.3.  Technical Debt

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   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 realise 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.

   The term "technical debt" refers to the accumulated complexity of
   sub-optimal 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.

3.4.  Layering considerations

   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 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 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.  This has lead to the perspective
   that increased layering frequently increases complexity [RFC3439].

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

4.  Possible Directions of Research

   The problem space of network complexity is very large, as many
   influencing factors contribute to the overall complexity of a
   network.  The following sections outline areas for research.

4.1.  Definitions and Metrics

   In the context of general network operations, as well as in the
   context of standardisation of protocols a common definition of the
   term "network complexity" would be useful.  It would also be useful
   to have a metric for the complexity of a protocol or network design,
   such that two candidate proposals can be objectively compared.This
   could happen in a bottom-up approach, where metrics for parts of a
   network are combined to an overall metric; or in a top-down approach
   where a global metric or vector of metrics is broken down into the
   components of a network.

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   For example, one such approach to a complexity metric is described in

      "A complexity metric could make these arguments objective.  A good
      metric would be based on quantifiable, concrete measurements of
      the system properties that induce implementation difficulties,
      complex interactions and failures, and so forth.  Many metrics are
      possible.  A perfect metric would be intuitive and easy to
      calculate, and would correlate with other, more subjective
      metrics, such as lines of code or system designers' experience.
      "We build on the observation that much of system design centers on
      issues of state - the required state must be defined and
      operations for constructing and using it must be developed - but
      in distributed systems, one state can derive from states stored on
      other nodes.  To calculate its state, a node must hear from the
      remote nodes that store the dependencies.  This adds additional
      dependencies on the network and intermediate node states required
      to relay input states to the node in question.  Thus, not only are
      a given piece of state's dependencies distributed, there are also
      more of them.
      "We conjecture that the complexity particular to networked systems
      arises from the need to ensure state is kept in sync with its
      distributed dependencies."

4.2.  Comparative Analysis

   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, if two network architectures are compared against each
   other, it may be possible to ignore the network layout and device
   hardware if those are the same in both cases.  In such specific
   comparisons it should be considerably easier to find valid metrics,
   and to compare the approaches objectively.

4.3.  Containment, Control or Reduction of Complexity

   In some disciplines such as software engineering, complexity is
   relatively well understood, as well as metrics and methods to reduce
   it.  Such approaches can be applied in the networking industry to
   achieve the same result.

4.4.  Use Cases

   While it is hard to define a universal set of metrics for network
   complexity, special use cases should be documented to serve as
   examples, and to stimulate discussion.  Such use cases could come out
   of different areas:

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   o  Documented examples of "catastrophic failure": While the cause of
      complexity is hard to understand, the result may be a catastrophic
      outage, which can be reverse-engineered to understand the root
      causes.  The knowledge from this process may give insight into
      root causes of complexity.
   o  A detailed complexity analysis of a particular network or
      protocol.  Even if this analysis may not be complete or fully
      objective, it would be useful to learn about different approaches.
   o  Analysis of existing networks, protocols or components from an
      insider point of view, discussing in detail where the perceived
      complexity in the set-up is, and how this could be changed to
      reduce complexity.
   o  Work in related areas, for example a detailled analysis of the
      total cost of ownership, and how this could be mapped into a
      complexity metric.

5.  Security Considerations

   This document does not discuss any specific security considerations.

6.  Acknowledgements

   The motivations and framework of this overview of studies into
   network complexity is 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, Jon Crowcroft, Mark
   Handley, Fred Baker, Paul Vixie, Lars Eggert, Bob Briscoe, Keith
   Jones, Bruno Klauser, Steve Youell, Joel Obstfeld.

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

7.  References

              Behringer, M.H., "Classifying Network Complexity",
              Proceedings of the ACM Re-Arch'09, December 2009.

   [Chun]     Chun, B-G., Ratnasamy, S. and E. Eddie, "NetComplex: A
              Complexity Metric for Networked System Design", 5th Usenix
              Symposium on Networked Systems Design and Implementation
              NSDI 2008, April 2008, <

   [Doyle]    Doyle, J.C., "The 'robust yet fragile' nature of the
              Internet", PNAS vol.  102 no.  41 14497-14502, October

   [RFC1925]  Callon, R., "The Twelve Networking Truths", RFC 1925,
              April 1996.

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   [RFC3439]  Bush, R. and D. Meyer, "Some Internet Architectural
              Guidelines and Philosophy", RFC 3439, December 2002.

   [wiki]     "Network Complexity Wiki", , <

Authors' Addresses

   Michael H. Behringer


   Geoff Huston
   Asia Pacific Network Information Centre


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