RAID — levels 0, 1, 5, 6, 10 — trade-offs

4.2.39 · Coding › Operating Systems

WHY does RAID exist?

Core tension: tum capacity, speed, aur reliability teeno ko ek saath maximize nahi kar sakte. Apna trade-off chuno.

HOW parity works (derive it from scratch)

Derivation. Maano data blocks hain $D_{1}, D_{2}, \dots, D_{n - 1}$ alag $n - 1$ disks par. Parity define karo: $P = D_{1} \oplus D_{2} \oplus \dots \oplus D_{n - 1}$ Maano disk $k$ khatam ho jaata hai. Hum baaki saare $D_{i}$ aur $P$ jaante hain. Jo kuch bhi hamare paas hai uska XOR karo: $D_{1} \oplus \dots \oplus D_{k - 1} \oplus D_{k + 1} \oplus \dots \oplus P$ $P$ substitute karo aur $\oplus$ properties use karo: $x \oplus x = 0$ aur $x \oplus 0 = x$ . Har surviving block $P$ ke andar apni copy ko cancel karta hai, bas ye bachta hai: $= D_{k}$

RAID 6 ke liye hum ek doosra, independent parity $Q$ add karte hain jo Reed–Solomon ka use karta hai Galois field $GF (2^{8})$ par: $Q = ⨁_{i} g^{i} \cdot D_{i}$ Do independent equations ( $P$ aur $Q$ ) tumhe do unknowns solve karne dete hain → 2 disk failures survive ho jaati hain.

The five levels

Figure — RAID — levels 0, 1, 5, 6, 10 — trade-offs

The write penalty (WHY RAID 5/6 writes are slow)

Worked examples

Common mistakes (steel-manned)

Recall Feynman: 12-saal-ke-bachche ko samjhao

Socho tum aur tumhare doston ne ek comic ki ek-ek page copy ki. RAID 0: sab alag-alag pages rakhte hain — ek saath padhne mein super fast, lekin agar ek dost apna page kho de toh comic barbad. RAID 1: do doston ke paas same pages hain, isliye agar ek chhoot jaaye toh doosre ke paas hai. RAID 5: har dost ek magic "summary number" bhi likhta hai taaki agar koi ek dost gayab ho jaaye, baaki log missing page summary se rebuild kar sakein. RAID 6: do magic summaries, isliye agar do dost bhi gayab ho jaayein tum theek ho. RAID 10: dosto ko backups ke roop mein pair karo, phir comic ko pairs mein split karo — fast aur safe.

Active recall

RAID ka full form kya hai?

Redundant Array of Independent Disks.

Kaunsa RAID level zero redundancy rakhta hai?

RAID 0 (pure striping).

n disks ke saath RAID 5 ki usable capacity?

(n − 1) disks ke barabar.

n disks ke saath RAID 6 ki usable capacity?

(n − 2) disks ke barabar.

RAID 6 kitne disk failures survive karta hai?

Do simultaneous failures.

Khoye hue block D_k ke liye parity recovery formula?

D_k = P ⊕ (saare surviving data blocks ka XOR).

XOR parity exactly ek disk kyun recover karta hai?

XOR self-inverse hai (x⊕x=0); ek parity = ek equation = ek unknown solve ho sakta hai.

Ek chhote RAID 5 write ke liye kitne I/Os lagte hain, aur kyun?

4 — read old data, read old parity, write new data, write new parity.

Chhote write par parity update karne ka formula?

P_new = P_old ⊕ D_old ⊕ D_new.

RAID 10 aur RAID 0+1 mein kya fark hai?

RAID 10 = mirror phir stripe (zyada failure-tolerant); 0+1 = stripe phir mirror.

RAID 6 doosre XOR P ki jagah doosra parity Q kyun use karta hai?

XOR ki do copies same equation deti hain; Q GF(2^8) coding use karta hai independent hone ke liye, jisse do unknowns solve ho sakein.

Kya RAID backups ka substitute hai?

Nahi — ye disk failure se bachata hai, deletion/corruption/ransomware se nahi.

Write-heavy database ke liye kaunsa level best hai?

RAID 10 (fast writes + redundancy); chhote random writes ke liye parity levels avoid karo.

Connections

XOR and Boolean Algebra — parity ke peeche ka math.
Galois Fields GF(2^n) — RAID 6 ke doosre parity ka basis.
Disk Scheduling — striping throughput kaise improve karta hai.
Reliability and MTBF — failure tolerance quantify karna.
Backups vs Redundancy — RAID ≠ backup kyun.
File Systems — RAID filesystem layer ke neeche rehta hai.