Scalability: free-recall review
Free-recall prompts across the scalability unit. Answer each in your own words first — including the arithmetic — then reveal the model answer and compare.
Retrieval beats re-reading. For each prompt, say or write a full answer from memory — including the arithmetic — before you open the model answer. The effort of reconstruction is what makes Little’s Law, the queueing curve, and the latency numbers stick.
Reconstruct the unit’s spine without looking back: why throughput and latency are different axes, why latency goes vertical near a resource’s limit, what vertical and horizontal scaling each cost, how to estimate a system on a napkin, and which latency numbers reject a design on sight.
- 01State Little's Law, define each term, and use it to find a throughput ceiling.
- 02Why does latency go vertical near a resource's limit, and what utilization do you target?
- 03Compare vertical and horizontal scaling, and state what the USL adds beyond Amdahl's law.
- 04Walk a back-of-envelope estimate and name the two cheat sheets and two rounding rules.
- 05List the latency hierarchy and two designs the numbers let you reject in a sentence.
If you could reconstruct each answer from memory, you hold the unit’s spine: Little’s Law (λ = L/W) gives a throughput ceiling from concurrency and latency; the queueing curve (W = 1/(μ−λ)) makes the tail go vertical near a resource’s limit, so you keep 30–40% headroom; vertical scaling is simple but capped, costly, and a SPOF while horizontal is elastic but needs statelessness and pays the USL coordination tax (α plateaus, β goes retrograde); back-of-envelope estimation (four quantities, two cheat sheets, round to one figure, size for the peak) finds which resource breaks first; and the latency hierarchy (RAM ~100 ns to cross-region ~150 ms) lets you reject a disk-per-request, cross-region, or N+1 design in a sentence. The thread tying them together: at this depth, scaling is arithmetic and physics you reason about up front, not behavior you discover in production.
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