Back-of-Envelope Estimation

1// ============================================
2// Back-of-Envelope Estimation — Practice Examples
3// ============================================
4
5// ---------- Example 1: Twitter-like Feed Service ----------
6
7function estimateTwitterScale() {
8  // Step 1: Users
9  const monthlyActiveUsers = 500_000_000; // 500M MAU
10  const dailyActiveUsers = monthlyActiveUsers * 0.4; // 200M DAU (40% MAU)
11
12  // Step 2: Activity per user
13  const tweetsPerUserPerDay = 2;           // Average (most users read, few tweet)
14  const feedRefreshesPerUserPerDay = 20;   // Users scroll feed often
15  const followsPerUser = 200;              // Average followings
16
17  // Step 3: QPS (Queries Per Second)
18  const secondsInDay = 86_400;             // Round to ~100K for quick math
19  const tweetWriteQPS = (dailyActiveUsers * tweetsPerUserPerDay) / secondsInDay;
20  // = (200M * 2) / 86400 ≈ 4,630 writes/sec
21
22  const feedReadQPS = (dailyActiveUsers * feedRefreshesPerUserPerDay) / secondsInDay;
23  // = (200M * 20) / 86400 ≈ 46,300 reads/sec
24
25  const peakMultiplier = 3; // Peak hours = ~3x average
26  const peakReadQPS = feedReadQPS * peakMultiplier;
27  // ≈ 139,000 reads/sec at peak
28
29  // Step 4: Storage
30  const avgTweetSize = 300;    // bytes (280 chars + metadata)
31  const tweetsPerDay = dailyActiveUsers * tweetsPerUserPerDay;
32  // = 400M tweets/day
33
34  const dailyStorage = tweetsPerDay * avgTweetSize;
35  // = 400M * 300 bytes = 120 GB/day
36
37  const yearlyStorage = dailyStorage * 365;
38  // = 120 GB * 365 ≈ 43.8 TB/year (text only, no media)
39
40  // Step 5: Media storage (images/videos)
41  const percentWithMedia = 0.2;            // 20% of tweets have media
42  const avgMediaSize = 500_000;            // 500 KB average
43  const dailyMediaStorage = tweetsPerDay * percentWithMedia * avgMediaSize;
44  // = 400M * 0.2 * 500KB = 40 TB/day ← THIS is why CDNs exist!
45
46  return {
47    tweetWriteQPS: Math.round(tweetWriteQPS),
48    feedReadQPS: Math.round(feedReadQPS),
49    peakReadQPS: Math.round(peakReadQPS),
50    dailyStorageGB: Math.round(dailyStorage / 1e9),
51    yearlyStorageTB: Math.round(yearlyStorage / 1e12),
52    dailyMediaStorageTB: Math.round(dailyMediaStorage / 1e12),
53  };
54}
55
56// ---------- Example 2: Estimating Cache Size ----------
57
58function estimateCacheRequirements() {
59  // Rule: Cache the hottest 20% of data (Pareto principle: 80/20 rule)
60
61  const totalDailyRequests = 10_000_000_000; // 10B requests/day
62  const uniqueURLs = 1_000_000_000;          // 1B unique URLs
63  const avgResponseSize = 500;               // 500 bytes
64
65  // 20% of URLs serve 80% of traffic
66  const hotURLs = uniqueURLs * 0.2;          // 200M URLs to cache
67  const cacheSize = hotURLs * avgResponseSize;
68  // = 200M * 500 bytes = 100 GB ← fits in a single Redis cluster!
69
70  // How many Redis nodes?
71  const redisMemoryPerNode = 64 * 1e9;       // 64 GB per node
72  const nodesNeeded = Math.ceil(cacheSize / redisMemoryPerNode);
73  // = ceil(100GB / 64GB) = 2 nodes (with replication: 4-6 nodes)
74
75  return {
76    hotURLs,
77    cacheSizeGB: Math.round(cacheSize / 1e9),
78    redisNodes: nodesNeeded,
79    withReplication: nodesNeeded * 3, // 3x for replication factor
80  };
81}
82
83// ---------- Example 3: Bandwidth Estimation ----------
84
85function estimateBandwidth() {
86  // Video streaming service like Netflix
87  const concurrentViewers = 10_000_000;      // 10M concurrent
88  const avgBitrateBytes = 5_000_000;         // 5 Mbps = ~625 KB/s per stream
89  const totalBandwidth = concurrentViewers * avgBitrateBytes;
90  // = 10M * 5MB/s = 50 TB/s ← This is why Netflix uses CDNs globally
91
92  // Convert to Gbps
93  const bandwidthGbps = (totalBandwidth * 8) / 1e9;
94  // = 400,000 Gbps = 400 Tbps
95
96  return {
97    totalBandwidthTBps: Math.round(totalBandwidth / 1e12),
98    bandwidthGbps: Math.round(bandwidthGbps),
99  };
100}
101
102console.log("Twitter estimates:", estimateTwitterScale());
103console.log("Cache estimates:", estimateCacheRequirements());
104console.log("Bandwidth estimates:", estimateBandwidth());