IO Cost Model Reference Sheet
Official Formula Reference
This is your go-to guide for IO cost calculations in CS145. Stick to these formulas and notations for every problem and solution.
Quick Reference
Core Formula
IO Cost per Page:
C_r = Access Time + (Page Size ÷ Scan Speed)
C_w = Access Time + (Page Size ÷ Scan Speed)
Total IO Cost:
Total Cost = numPages × C_r (for reads)
Total Cost = numPages × C_w (for writes)
Key Variables
-
numPages: Pages to read/write
-
C_r: Time cost to read one page
-
C_w: Time cost to write one page
-
Page Size: Typically 64 MB
Device Specifications (2024)
These numbers are your baseline for problem sets and tests. Real-world figures vary by manufacturer.
| Device | Access Time | Scan Speed | C_r (64MB page) | C_w (64MB page) |
|---|---|---|---|---|
| RAM | 100 ns | 100 GB/s | 0.00064s | 0.00064s |
| SSD | 10 μs | 5 GB/s | 0.01281s | 0.01281s |
| HDD | 10 ms | 100 MB/s | 0.65s | 0.65s |
| Network | 1 μs | 10 GB/s | 0.00641s | 0.00641s |
Unit Conventions
• MB, GB = Decimal units (1000-based): 1 MB = 1,000,000 bytes, 1 GB = 1,000,000,000 bytes
• MiB, GiB = Binary units (1024-based): 1 MiB = 1,048,576 bytes, 1 GiB = 1,073,741,824 bytes
All CS145 problems use MB/GB (decimal) consistently for calculations.
• MiB, GiB = Binary units (1024-based): 1 MiB = 1,048,576 bytes, 1 GiB = 1,073,741,824 bytes
All CS145 problems use MB/GB (decimal) consistently for calculations.
This reference sheet is your constant companion for all system problems and solutions.