The queueing wall (M/M/1)

How it behaves

One input on the horizontal axis, the others held fixed.

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

• speculation lifts ρ from 0.90 to 0.95 → the queue factor goes from 10 to 20
• four spillers at 0.3 GB/s on a 1.5 GB/s drive: ρ = 0.8 → 5×
• ρ = 0.5 → 2 × S
• ρ = 0.8 → 5 × S
• ρ = 0.9 → 10 × S
• ρ = 0.95 → 20 × S
• ρ = 0.99 → 100 × S

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

• Physical Substrate & Performance Laws

  Why do trade-offs exist at all?

  $$R=S÷(1-\rho )$$

  Read it in place →

• Physical Substrate & Performance Laws

  Why do trade-offs exist at all?

  $$R=S/(1-\rho )$$

  Read it in place →