Skip to main content
PureBuild Logo
PureBuild.xyz
TOOLSBLOGGLOSSARYCOMPARE
About Maker
  1. Home
  2. Blog
  3. The Knee in the Curve
BACK TO LOGS
2025-12-28 • PureBuild • 2 min read

The Knee in the Curve

Why systems don't fail linearly. The mathematics of Queueing Theory and the 80% utilization trap.

Share:
Advertisement

80% is 100%

A common mistake in capacity planning is assuming you can run a server or a database at 99% CPU utilization. Intuition suggests that if you have 100 requests per second capacity, and you are receiving 90 requests, you are fine. Queueing Theory (Little's Law) proves you are dead.

The Hockey Stick Graph

Response time does not increase linearly with utilization. It stays flat until about 70-80% utilization, and then it goes vertical (asymptotes to infinity). Why? Because variability exists. Requests don't arrive in perfectly spaced intervals. They arrive in bursts.

At high utilization, a tiny burst creates a queue. Because the CPU is busy, it can't clear the queue faster than new requests arrive. The queue grows infinitely.

Vertical vs Horizontal Scaling

  • Vertical: Buy a bigger server. Easy, but has a hard limit.
  • Horizontal: Add more servers behind a load balancer. Harder architecture (statelessness required), but infinite scale.

The Thundering Herd

A classic failure mode:

  1. Database slows down (high CPU).
  2. Web servers time out waiting for DB.
  3. Users refresh the page (retries).
  4. Web servers send more requests to the dying DB.
  5. Total Collapse.

To prevent this, you need Circuit Breakers and Exponential Backoff.

Use the Capacity Planner to visualize where your breaking point is. It's always sooner than you think.

Sponsored

Try these related tools:

Capacity Planner
Tools for Founders
Sponsored
StripePopular

Payment infrastructure for the internet

Start accepting payments in minutes. No setup fees, no monthly fees.

Start Free
BrexPopular

The AI-powered spend platform

Corporate card with 10-20x higher limits. No personal guarantee required.

Get Started
AWS Activate

Build on AWS

Up to $100k in AWS credits for startups. Plus training and support.

Apply Now
Vercel

Develop. Preview. Ship.

Deploy your Next.js app with zero configuration. Free tier available.

Deploy Free
Notion

All-in-one workspace

Write, plan, and organize. Free for startups with up to 1000 users.

Try Free

Related Articles

2025-12-28

Capital Table Logic

2025-12-28

The Mathematics of Founder Equity

2025-12-28

The Price of Your Time

Stay Updated

500+ founders

New tools, deep dives, and startup insights. No spam, unsubscribe anytime.

Join the discussion

Have thoughts on this? Ping me on Twitter.

@yewlne7
Share:

Tools

  • View All Tools →
  • Equity Calculator
  • Dilution Simulator
  • Runway Calculator
  • Unit Economics

More Tools

  • Hourly Rate
  • Net Revenue
  • API Cost Estimator
  • Capacity Planner
  • Viral Coefficient
  • Launch Timing ✦

Resources

  • All Resources →
  • Blog & Guides
  • Startup Glossary
  • FAQ
  • Tool Comparisons
  • For Founders
  • For Employees
  • RSS Feed

Connect

  • Twitter

No spam. Unsubscribe anytime.

© 2026 PureBuild • Crafted with logic, not AI

HomeBlogSitemap