PNSol's Chief Scientist introduces blockchains and how their performance issues can be addressed using ∆Q

1. © Predictable Network Solutions Ltd 2017 www.pnsol.com
Using the ∆Q calculus to model
blockchain scalability
Neil Davies, Predictable Network Solutions / Input Output HK
neil.davies@pnsol.com
neil.davies@iohk.io

2. © Predictable Network Solutions Ltd 2017 www.pnsol.com
Brief introduction to blockchains

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What is a blockchain?
● Public distributed ledger
○ In full public purview
● Becomes increasingly immutable
○ Each ‘block’ references the previous block
■ Using cryptographic functions (signatures, hashes etc.)
○ A record of ‘history’ that is hard to change
■ Changing a block becomes harder the more time that passes - all subsequent
blocks would also have to be changed
● Blocks hold records of ‘transactions’
○ Whose validity can be checked by anybody

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4Structure of blockchain growth
A new block is added (‘mined’ or ‘minted’)
by a ‘leader’, chosen either by:
● A race (e.g. to solve a hard problem),
or
● Random selection by consensus
This new block has to be communicated to the next
leader so that it can be referenced by the next block
● The next leader could be anybody, so the
block has to be ‘diffused’ to everybody
● This has to happen before the next block is
due to be added
(end of) block
arrived too late
Chain continues
to grow - but
reduces
performance

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5Key performance metrics
Incorporate
new block
Mint
block
diffuse
transactions
Key performance metrics
• Time to “immutablity”
• Inclusion in block
• Chain growth of 2 to 10 blocks
• Transaction rate / work measures
• transactions per cycle
• Total data per cycle
• Cycle time
Exact number
depends on
use case

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Extracting the performance - ∆Q

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7Cycle of behaviour (expanded)
Mint
Block
Incorporate
Block
Diffuse
Send
Block
Receive
Block
“mempool”
local database
of blocks and
outstanding
transactions
Every20seconds
Need to get to
>99% of
(potential) slot
leaders “in time”

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Diffusion - robustness and performance
• No hegemony
• No central decision making or control authority
• Have to assume “bad actors” exist
• And will exercise any influence that they can muster
• No fixed topology
• Participants changing over time (hourly, weekly etc)
• Nodes come and go, stake distribution changes etc
• Randomness needed to resist attacks by bad actors
• Standard routing approaches too restrictive
• They create (single) points of failure - overly reduce connectivity
• Too slow to converge after change - single BGP hop recovery is many slot intervals
• Too easy to disrupt through adversarial attack

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9Implications - need more visibility and control
A B
D
H
I
J
G
F
E
C D
A
F
C
B
E
I
J
G
H

10. © Predictable Network Solutions Ltd 2017 www.pnsol.com
10Network topology
D
A
F
C
B
E
I
J
G
H
Multiple (potential) next-hops, “randomly” chosen

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11Network topography
D
A FC
B
E
I
J
G
H
Topology does not
capture all essential
properties needed
for robustness and
performance - can’t
ignore geographical
effects.

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12Network topography - global scale
D
A FC
B
E
I
J
G
H

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13
∆QG→D
∆QE→D
∆QF→E
∆QE→C
∆QE→F
∆QC→E
∆QH→G
∆QG→H
∆QF→J
∆QJ→F
∆QG→F
∆QF→G
∆QB→J
∆QJ→B
∆QJ→I
∆QI→J
∆QH→I
∆QI→H
∆QI→A
∆QA→I
∆QH→A
∆QA→H
∆QD→C
∆QC→D
∆QA→B
∆QB→A
∆QC→B
∆QB→C
Topography = Topology + ∆Q
D
A
F
C
B
E
I
J
G
H
Adding in the salient effects of the real world
∆QD→G
∆QD→E

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14Outcome-focused first-hop route choice
∆QA→I
∆QI→J
∆QJ→F
A
F
I
J
G
H
∆QA→H
∆QH→G
∆QG→F
∆QI→H
Which is the best first-hop from A to get to F for a block (of a given
size)?
- Four routes - two first hops
- There is both a ∆Q|G and a ∆Q|S component
Shortest number of hops does not imply earliest time to delivery
from A→F
Simplified for
illustration (third
first hop ignored)
∆QH→I

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15
Global understanding from local
measurement
From/To A B C D ...
A B: 112/35 B: 199/77 H: 365/148 ...
B A: 112/35 - C: 87/42 C: 92/75 ...
C B: 199/77 B: 87/42 - D: 5/33 ...
D G: 365/148 E: 108/103 E: 21/71 - ...
... ... ... ... ... ...
Direct connects as measured
- Exploits ∆Q measurement
approach
Indirectly connected calculated
- Exploits ∆Q convolution
- First hop is chosen on basis of
best diffusion outcome
Resolves several existing issues, e.g
- Appropriate use of multiple paths
- Asymmetric bearersOptimum first hop for block may be dependent on actual block size:
- lower ∆Q|G / higher ∆Q|S link (e.g. DSL)
could be outperformed by
- higher ∆Q|G / lower ∆Q|S link (e.g. 3G/4G)
when diffusing larger block sizes
firsthop: G (ms) / S (µs/o)
[ one way - end to end]Indicative based on
measurement
Simple delay
measures not
sufficient

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16Cooperative performance optimisation
Nodes calculate
per hop ∆Q
[local “measure”]
Nodes share this
information
regularly
Each node calculates
its own ∆Q matrix
[local “manage”]
Nodes change
“best first hop”
(with hysteresis)
[local “manipulate”]
Each iteration round this loop
can improve the performance of
the data diffusion.
Can be used to
assure / monitor
system health

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Summary
• Using ∆Q (+ other maths) to do system performance design and analysis
• Using real time real world measurements to application outcome
performance
• As well as ongoing system integrity
• This creates basis for high integrity distributed systems with strong
performance assurances.
• Enables new ways of thinking about using the underlying network
resources