Axioms - Networking

WORK IN PROGRESS (WIP) Revision 0.1 September 17th, 2020

In classical systems

Summary

Builds on “Axioms - Information” which may be helpful to read first.

Figure 1. Information relativity, uncertainty, and distribution in networks

Information is relative, subject to loss, noise, errors, and redundancy, and therefore, the following are uncertain:

  1. Time that an event occurred

  2. Sequence that events occurred

  3. Completeness/sufficiency (no loss, and on time)

  4. Clarity (no noise or redundancy)

  5. Accuracy (no errors and containing true statements)

  6. Topology

  7. “best” path

  8. Current topology synchronization

  9. “best” path synchronization

Networking aspires to mitigate uncertainties, in many ways, including adding information.

  • Timestamps, with and without a synchronized common reference.

  • Sequence numbering and preservation

  • Error checking

  • Topology and best path distribution

Some of the above reduce uncertainty to a greater extent than others.

  • After a topology change occurs, forwarding based on an understanding of the new topology can happen in some routers, before others, leading to micro loops.

Sometimes network architecture adds to uncertainty with respect to topology, best path, etc. by summarizing, reducing the state that is redistributed:

  1. Summarizing reachability increases uncertainty

  2. Summarizing topology increases uncertainty

N1 - The time that an event occurred is always uncertain

  1. Information is Relative

  2. The time that one router observes an event occurring will be different from another router

  3. The time that an event occurred will always be uncertain

N2 - The sequence that events occurred in is always uncertain

  1. Information is Relative

  2. The time that one router observes a sequence of events occurring will be different from another router

  3. The sequence that events occurred in is always4 uncertain

N3 - The completeness of information is always uncertain

  1. Information transmission and reception is subject to error

  2. Whether information has been lost during transmission is uncertain

  3. The completeness of information will always be uncertain

N4 - The clarity of information is always uncertain

  1. Information transmission and reception is subject to error

  2. Whether information has been added to (noise, redundancies) during transmission is uncertain

  3. The clarity of information will always be uncertain

N5 - The accuracy of information is always uncertain

  1. Information transmission and reception is subject to error

  2. Whether the copied information was accurate to begin with, and whether any inaccuracies were introduced during transmission and reception, is uncertain

  3. The accuracy of information will always be uncertain

N6 - Current topology is always uncertain

  1. Information is Relative

  2. No information function is omniscient

  3. It will always be uncertain whether a router has an accurate understanding of all distributed information

  4. The current topology will aways be uncertain, relative to any single point in the network

N7 - “best” path is always uncertain

  1. Information is Relative

  2. No information function is omniscient

  3. It will always be uncertain whether a router has an accurate understanding of all distributed information

  4. The best path will always be uncertain, relative to any single point in the network

N8 - Current topology synchronization is always uncertain

  1. Information is Relative

  2. No information function is omniscient

  3. It will always be uncertain whether each router has the accurate, and same understanding, of all distributed information

  4. Whether each router has the same understanding of the current topology, will always be uncertain

N9 - “best” path synchronization is always uncertain

  1. Information is Relative

  2. No information function is omniscient

  3. It will always be uncertain whether each router has the accurate, and same understanding, of all distributed information

  4. Whether each router has the same understanding of the “best” path, will always be uncertain

N10 - Summarizing reachability increases uncertainty

  1. Summarization reduces information

  2. Summarization reduces certainty

  3. Summarizing reachability increases uncertainty

N11 - Summarizing topology increases uncertainty

  1. Summarization reduces information

  2. Summarization reduces certainty

  3. Summarizing topology increases uncertainty

Appendix A - If Networks were Infinite

  1. A network control plane could transmit, store, and process any amount of state (information)

  2. There would be no scale-drivers for using address aggregation/summarization

  3. There would be no scale-drivers for dividing networks into areas

  4. There would be no capacity-drivers for Quality of Service, ECMP, or Traffic engineering

  5. A network could power and cool any amount of equipment, at any load

  6. Some amount of policy could be eliminated

  7. Many resource saving approaches and mechanisms would not be required

  8. However, networks are not infinite, they are finite

Appendix B - Definitions

  1. Storage: information at rest

  2. Networking: information in relative motion

  3. Compute: adding, deleting, updating information

  4. Dense graph: number of edges is close to maximum number of edges

  5. Sparse graph: number of edges is NOT close to maximum number of edges

  6. Regular graph: each node/vertex has the same number of neighbors/degrees

  7. Latency: total time it takes for a desired outcome to be achieved

  8. Link latency: total time it takes a single bit to travel from start to finish of a link

  9. Reachability: the ability to get from one node to another in a network/graph

  10. Serialization delay: time to encode a single bit on to a communications channel.

  11. Internet Protocol (IP) router: forwarding based on IP addressing information

  12. Internet Protocol (IP) switch: IP router that limits capabilities to maximize port density and switching capacity

  13. Ethernet switch: forwarding based on Ethernet addressing information

  14. IP control plane: routing protocols that determine topology and/or paths based on IP addressing

  15. IP/MPLS: IP control plane & label distribution protocols with a MPLS data plane

  16. Segment Routing: IP control plane with MPLS or IP data plane

  17. Automation: is the increase in productivity that comes from repetitive execution of a known process, in a shorter amount of time, with less errors, than a person would, over a significant population of tasks.

  18. Autonomy: is the increase in productivity that comes from responding to an environment, quicker than a person would, with the same or better responses.

Appendix C - Value of Networks

  1. Networks allow value to be combined and exchanged, over distance

  2. The value of a network is proportional to the number & frequency of exchanges

    1. In small networks: square of connected users (n-squared). Metcalfe’s law, network effects.

    2. In large networks: search, directories, and other approaches to discovering and exchanging value impacts the value of a network.

  3. In economic and time sensitive systems, reducing latency increases value.

  4. In economic and time sensitive systems, reducing errors increases value.

  5. When link latency, serialization, and queuing delays far exceed computation & storage access delays, there will be a tendency to move information and computation / storage as close as possible.

Appendix D - Network goals

  1. Copy information from a source to intended destination(s)

  2. Information that is sufficient, clear, and accurate

  3. Copy information without subtraction, addition, or modification

  4. Clarify when events occur and the sequence of events

Appendix E - Complexity

  1. Information / information complexity cannot be reduced below necessary information

  2. Information complexity will be equivalent for equivalent functions

  3. Choice is a form of complexity

  4. Added information for control is a form of complexity

  5. Added mechanisms for error detection, mitigation and/or recovery are a form of complexity

  6. The number of network nodes in a control plane is a form of complexity

  7. The interdependence between different processes is a form of complexity

  8. The understandability of a topology is a form of complexity

  9. The understandability of network operation is a form of complexity

  10. Guaranteed capacity and delivery creates additional complexity

Appendix F - Networks are finite

See also: Network Architecture: Why Choices Must Be Made

  1. Resources are finite

  2. Externalities are finite

  3. The speed of information is finite

  4. Because networks are finite, choices & tradeoffs are required.

  5. The more “infinite” network resources are relative to use, the fewer choices, tradeoffs, and additional capabilities are required.

Appendix G - Finite Network Resources

  1. Information

  2. Compute

  3. Storage

  4. Links

  5. Switching

  6. Energy

  7. Cooling

  8. Space

  9. People

Appendix H - Quality

  1. Packet and TDM switched networks replace guaranteed capacity/delivery with probabilistic

  2. A change in quality can shift a demand curve

  3. To guarantee capacity & delivery, additional information/complexity is added

Appendix I - Choices & tradeoffs in networks

See also: A Network Is Always A Tradeoff

  1. Designing / constructing a network is a decision to make tradeoffs

  2. As topologies approach structures that are economically, technologically, and aesthetically challenging, they will tend towards new topology/networking that addresses those challenges. Failure to do so will likely inhibit growth.

  3. Aesthetically unpleasing topologies will likely change, because they may also be hard to understand, and therefore operationally complex, all things being equal, for example approaches to tools and management.

  4. There are often tradeoffs between network complexity and operational complexity.

  5. Tradeoffs are often between the cost of adding a capability and the cost/consequence of not adding a capability, for a given topology and given capacity.

  6. Some tradeoffs may be mitigated by changing topology and/or adding capacity.

  7. Complexity often comes with the need to make choices.

  8. Choice itself is an additional complexity.

  9. A network designer’s role extends beyond the network itself, and deeply into operations. An additional and/or alternative observation is that operations tools and methods may expand topology optionality.

  10. Choices can shift profit from one profit pool to another.

Appendix J - Topology

  1. Topologies that are economically, technologically, and/or aesthetically challenging, will decay, and likely be replaced.

Appendix K - Time & Delay

  1. Time is how long it takes light to travel a measured distance

  2. Measured time changes, if measured distance changes, relative to observation

  3. Time and sequence of events is relative to the frame of reference

  4. We add complexity, time stamps / time protocols / sync, to improve the agreement of when events occurred, and their sequence

  5. For a single bit of information, the latency will often be larger than the serialization delay.

  6. For a large quantity of information, the serialization delay will often be larger than the latency.