The Math of Scalability
summary
Uses math to prove counterintuitive scaling effects: traffic at Burning Man shows adding lanes slows flow, the birthday paradox gives collisions at 23 people, and Amazon EBS 2011 is cited as a real retry storms failure when replicas all rebuild simultaneously. Models applied are Universal Scalability Law, Little’s and Kingman queueing formulas; results show contention and coordination (α and β) cause sublinear or retrograde scaling, so practical fixes are lower variance, avoid coordination, and shard or time‑warp work.
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chapters (31)
- 0:00Burning Man
- 0:44The Problem
- 4:18Math is not scary
- 5:17What is scalability
- 6:24Batch vs interactive systems
- 7:14Linear scalability
- 8:52Statistics
- 10:32Law of Two Numbers
- 12:44Birthday Paradox
- 14:06Subgroup Growth
- 15:29Emerging Behavior
- 21:45Stateless
- 23:12Stateful
- 25:32Universal scalability law
- 26:52Consistency
- 28:09Confrontation
- 28:37Coordination
- 29:16Latency
- 30:11Space and Time
- 31:00Space Warp
- 31:34Time Warp
- 32:16Universal Scalability
- 33:10Congestion
- 33:29Queue
- 35:09Latency vs Utilization
- 36:45Variation
- 37:50Failures
- 39:55Failure Demand
- 40:24House Scale
- 41:16Statistical Process Control
- 42:08Math for Engineers
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