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:
Time that an event occurred
Sequence that events occurred
Completeness/sufficiency (no loss, and on time)
Clarity (no noise or redundancy)
Accuracy (no errors and containing true statements)
Topology
“best” path
Current topology synchronization
“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:
Summarizing reachability increases uncertainty
Summarizing topology increases uncertainty
N1 - The time that an event occurred is always uncertain
The time that one router observes an event occurring will be different from another router
The time that an event occurred will always be uncertain
N2 - The sequence that events occurred in is always uncertain
The time that one router observes a sequence of events occurring will be different from another router
The sequence that events occurred in is always4 uncertain
N3 - The completeness of information is always uncertain
Information transmission and reception is subject to error
Whether information has been lost during transmission is uncertain
The completeness of information will always be uncertain
N4 - The clarity of information is always uncertain
Information transmission and reception is subject to error
Whether information has been added to (noise, redundancies) during transmission is uncertain
The clarity of information will always be uncertain
N5 - The accuracy of information is always uncertain
Information transmission and reception is subject to error
Whether the copied information was accurate to begin with, and whether any inaccuracies were introduced during transmission and reception, is uncertain
The accuracy of information will always be uncertain
N6 - Current topology is always uncertain
It will always be uncertain whether a router has an accurate understanding of all distributed information
The current topology will aways be uncertain, relative to any single point in the network
N7 - “best” path is always uncertain
It will always be uncertain whether a router has an accurate understanding of all distributed information
The best path will always be uncertain, relative to any single point in the network
N8 - Current topology synchronization is always uncertain
It will always be uncertain whether each router has the accurate, and same understanding, of all distributed information
Whether each router has the same understanding of the current topology, will always be uncertain
N9 - “best” path synchronization is always uncertain
It will always be uncertain whether each router has the accurate, and same understanding, of all distributed information
Whether each router has the same understanding of the “best” path, will always be uncertain
N10 - Summarizing reachability increases uncertainty
Summarizing reachability increases uncertainty
N11 - Summarizing topology increases uncertainty
Summarizing topology increases uncertainty
Appendix A - If Networks were Infinite
A network control plane could transmit, store, and process any amount of state (information)
There would be no scale-drivers for using address aggregation/summarization
There would be no scale-drivers for dividing networks into areas
There would be no capacity-drivers for Quality of Service, ECMP, or Traffic engineering
A network could power and cool any amount of equipment, at any load
Some amount of policy could be eliminated
Many resource saving approaches and mechanisms would not be required
However, networks are not infinite, they are finite
Appendix B - Definitions
Storage: information at rest
Networking: information in relative motion
Compute: adding, deleting, updating information
Dense graph: number of edges is close to maximum number of edges
Sparse graph: number of edges is NOT close to maximum number of edges
Regular graph: each node/vertex has the same number of neighbors/degrees
Latency: total time it takes for a desired outcome to be achieved
Link latency: total time it takes a single bit to travel from start to finish of a link
Reachability: the ability to get from one node to another in a network/graph
Serialization delay: time to encode a single bit on to a communications channel.
Internet Protocol (IP) router: forwarding based on IP addressing information
Internet Protocol (IP) switch: IP router that limits capabilities to maximize port density and switching capacity
Ethernet switch: forwarding based on Ethernet addressing information
IP control plane: routing protocols that determine topology and/or paths based on IP addressing
IP/MPLS: IP control plane & label distribution protocols with a MPLS data plane
Segment Routing: IP control plane with MPLS or IP data plane
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.
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
Networks allow value to be combined and exchanged, over distance
The value of a network is proportional to the number & frequency of exchanges
In small networks: square of connected users (n-squared). Metcalfe’s law, network effects.
In large networks: search, directories, and other approaches to discovering and exchanging value impacts the value of a network.
In economic and time sensitive systems, reducing latency increases value.
In economic and time sensitive systems, reducing errors increases value.
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
Copy information from a source to intended destination(s)
Information that is sufficient, clear, and accurate
Copy information without subtraction, addition, or modification
Clarify when events occur and the sequence of events
Appendix E - Complexity
Information / information complexity cannot be reduced below necessary information
Information complexity will be equivalent for equivalent functions
Choice is a form of complexity
Added information for control is a form of complexity
Added mechanisms for error detection, mitigation and/or recovery are a form of complexity
The number of network nodes in a control plane is a form of complexity
The interdependence between different processes is a form of complexity
The understandability of a topology is a form of complexity
The understandability of network operation is a form of complexity
Guaranteed capacity and delivery creates additional complexity
Appendix F - Networks are finite
See also: Network Architecture: Why Choices Must Be Made
Resources are finite
Externalities are finite
The speed of information is finite
Because networks are finite, choices & tradeoffs are required.
The more “infinite” network resources are relative to use, the fewer choices, tradeoffs, and additional capabilities are required.
Appendix G - Finite Network Resources
Information
Compute
Storage
Links
Switching
Energy
Cooling
Space
People
Appendix H - Quality
Packet and TDM switched networks replace guaranteed capacity/delivery with probabilistic
A change in quality can shift a demand curve
To guarantee capacity & delivery, additional information/complexity is added
Appendix I - Choices & tradeoffs in networks
See also: A Network Is Always A Tradeoff
Designing / constructing a network is a decision to make tradeoffs
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.
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.
There are often tradeoffs between network complexity and operational complexity.
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.
Some tradeoffs may be mitigated by changing topology and/or adding capacity.
Complexity often comes with the need to make choices.
Choice itself is an additional complexity.
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.
Choices can shift profit from one profit pool to another.
Appendix J - Topology
Topologies that are economically, technologically, and/or aesthetically challenging, will decay, and likely be replaced.
Appendix K - Time & Delay
Time is how long it takes light to travel a measured distance
Measured time changes, if measured distance changes, relative to observation
Time and sequence of events is relative to the frame of reference
We add complexity, time stamps / time protocols / sync, to improve the agreement of when events occurred, and their sequence
For a single bit of information, the latency will often be larger than the serialization delay.
For a large quantity of information, the serialization delay will often be larger than the latency.