Server Load Response Latency (Computer Science) Solution

Part 1: Dominance Filtering

For large $N$, the quadratic terms $N^2$ grow much faster than linear terms $N$ or constants.

• Dominant numerator term: $12N^2$
• Dominant denominator term: $3N^2$

Part 2: Analytical Limit Calculation

Divide every term by the highest denominator power $N^2$:

As $N \to \infty$, the reciprocal terms approach zero:

Part 3: Horizontal Asymptote & Systems Architecture Conclusion

• Horizontal Asymptote: $y = 4$
• System SLA Impact: As the cluster scales indefinitely, the average request latency levels off at a deterministic floor of $4\text{ ms}$. This informs cloud engineers that infrastructure latency will not degrade beyond $4\text{ ms}$ under heavy node concurrency, satisfying strict real-time user experience guarantees.