System design begins with quantitative reality. Naive estimations assuming uniformly distributed random requests collapse when deployed to real-world users, whose behavior follows heavy-tailed, Zipfian power-law distributions. In production systems, 80% to 90% of all read traffic concentrates on less than 1% to 10% of entity keys, while fan-out architectures multiply a single user interaction into hundreds of internal RPCs.
This module provides the formal mathematical and engineering foundations for modeling system workloads:
- Power Laws & Zipfian Skew: Why real workloads follow , and how skew alters cache hit rates, database partition hotspots, and connection pooling.
- Fan-Out & Amplification Factor: Quantifying write amplification, network serialization tax, and P99 tail latency degradation across multi-tier service trees.
- Headroom & Capacity Provisioning: Calculating CPU, RAM, IOPS, and network egress requirements with mathematical safety margins to survive traffic surges without cascading failures.