understanding software engineering with equations
TRANSCRIPT
Why this talk?
• Hard!
• Non-intuitive
• Misunderstood
• Seen as black-art done by amateurs
Software engineering is:
I’m not a mathematician
Mental models, rather than
precise calculations
Why do systems get so
complicated?
Handing complexity with
𝒏 𝒏 − 𝟏
𝟐
10
1
2
34
5
𝒏 𝒏 − 𝟏
𝟐
66
12
3
4
5
67
8
9
10
11
12
Complexity is caused by:
quadratic increase in
connections
How do we reduce complexity?
4
44 3
15!1
2
3
4
5
6
7
8
9
10
11
12
Org structure
or
Code structure?
Design reduces dependencies
Summary:
What is the effect of messy
code?
Go slow to go fast with
𝑻 𝒏 = 𝑶(𝒏)
0
50
100
150
200
250
300
10 20 30 40 50 60 70 80 90 100
TIM
E+
RIS
K T
O M
AK
E C
HA
NG
E
FEATURES BUILT
CODE CHANGE COMPLEXITY
O(n) O(n2)
Clean Code gives
• Easy to read
• SOLID design
• Boy scout refactoring
• Self-testing
• TDD
𝑶(𝒏)
Messy code gives
• Manual regression testing
• Spaghetti dependencies
• Hart to understand
𝑶(𝒏𝟐)
Your algorithm of work
determines order of time
complexity
In summary
We’re so busy! Why don’t we get
stuff done?
Credit: http://www.autoevolution.com/
Maximise efficiency with
𝑭𝒍𝒐𝒘 = 𝑺𝒑𝒆𝒆𝒅 . 𝑫𝒆𝒏𝒔𝒊𝒕𝒚
𝑽𝒆𝒉𝒊𝒄𝒍𝒆𝒔
𝑯𝒐𝒖𝒓=
𝑴𝒆𝒕𝒆𝒓𝒔
𝑯𝒐𝒖𝒓.𝑽𝒆𝒉𝒊𝒄𝒍𝒆𝒔
𝑴𝒆𝒕𝒆𝒓
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0
20
40
60
80
100
120
140
50 100 150 200 250 300 350 400 450 500
FL
OW
RA
TE
(V
EH
ICLE
S/H
OU
R)
SP
EE
D (
KIL
OM
ET
ER
/HO
UR
)
DENSITY (VEHICLES/KILOMETER)
OPTIMAL FLOW
Speed (Km/h) Flow (Vehicles/h)
UnstableStable
Speed decreases as
density increases.
This is not intuitive.
Optimum flow at
speed 60 and
density 250.
Neither MAXED!
Speed = (1 – Density . JamDens) . MaxSpeed
How does this apply to software?
• 𝐹𝑙𝑜𝑤 = 𝑆𝑝𝑒𝑒𝑑. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦
• Velocity = Throughput = Flow (avg # features delivered per week)• WIP = Density (avg # features started but not completed)
• 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒 =1
𝑆𝑝𝑒𝑒𝑑(avg time it takes to complete a feature)
• 𝑇ℎ𝑜𝑢𝑔ℎ𝑝𝑢𝑡 =𝑊𝐼𝑃
𝐶𝑦𝑐𝑙𝑒 𝑇𝑖𝑚𝑒(aka Little’s Law)
𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 =𝑨𝒗𝒈 𝒇𝒆𝒂𝒕𝒖𝒓𝒆𝒔 𝒊𝒏 𝒑𝒓𝒐𝒈𝒓𝒆𝒔𝒔
𝑨𝒗𝒈 𝒕𝒊𝒎𝒆 𝒕𝒐 𝒄𝒐𝒎𝒑𝒍𝒆𝒕𝒆 𝒂 𝒇𝒆𝒂𝒕𝒖𝒓𝒆
In summary
Improve continuously with
𝑨 = 𝑷𝒆𝒓𝒕
http://jamesclear.com/marginal-gains
• r = -1% per week (decay rate)
• t = 104 weeks/2 years (time in weeks)
This gives us
• 34% of original
• Degraded 66% over 2 years!
Is this how technical debt behaves?
𝒆𝒓𝒕
• r = 1% per week (improvement rate)
• t = 104 weeks/2 years (time in weeks)
This gives us
• 294% improvement over 2 years!
𝑰𝒎𝒑𝒓𝒐𝒗𝒆𝒎𝒆𝒏𝒕 = 𝒆𝒓𝒕
In summary
Simplify by removing dependencies
Go slow to go fast
Remove congestion to flow
Continuous improvement compounds
Other equations
• Entropy
• Bayesian Inference
• The software engineering equation
• Yours?
