{
  "slug": "little-law",
  "term": "Little's law",
  "aliases": [
    "L = lambda W"
  ],
  "definition": "Little's law relates time-averaged occupancy L to the operation rate lambda and mean residence time W within the same system boundary.",
  "note": "L = lambda x W uses a time average for occupancy, a count per time for rate and an arithmetic mean over operations for residence time [little1961] [little2011]. For ordinary benchmark estimates, use a stable population and account for unfinished operations crossing the measurement window. An empty-to-empty finite trace also permits an exact occupancy-area identity without constant load. Hesela's arithmetic example, 10,000 operations/s x 0.002 s/operation = 20 average outstanding operations, is not a hardware measurement [hesela-accounting]. In Hesela's two-request cropped-window example, time-averaged occupancy is 1.2 while the completion rate multiplied by full mean completed-request residence gives 0.6; pre-window and unfinished work explain the mismatch [hesela-accounting].",
  "status": "shipping",
  "advantages": [],
  "limitations": [
    {
      "text": "Substituting p99 latency or a configured queue limit changes the quantities in the law; it does not predict required concurrency or attainable device IOPS.",
      "citationIds": [
        "little2011",
        "hesela-accounting"
      ]
    }
  ],
  "related": [
    "queue-depth",
    "iops",
    "latency-storage",
    "open-loop-load",
    "closed-loop-load"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "citations": [
    {
      "id": "little1961",
      "title": "John D. C. Little. A Proof for the Queuing Formula: L = lambda W. Operations Research 9(3), 383-387 (1961). DOI: 10.1287/opre.9.3.383.",
      "url": "https://doi.org/10.1287/opre.9.3.383",
      "accessed": "2026-10-13"
    },
    {
      "id": "little2011",
      "title": "John D. C. Little. Little's Law as Viewed on Its 50th Anniversary. Operations Research 59(3), 536-549 (2011), pp. 537-539. DOI: 10.1287/opre.1110.0940.",
      "url": "https://people.cs.umass.edu/~emery/classes/cmpsci691st/readings/OS/Littles-Law-50-Years-Later.pdf",
      "accessed": "2026-10-13"
    },
    {
      "id": "hesela-accounting",
      "title": "Hesela: IOPS, bytes and average occupancy; synthetic accounting examples.",
      "url": "https://hesela.com/analyses/storage-latency-coordinated-omission/#io-accounting",
      "accessed": "2026-10-13"
    }
  ],
  "updated": "2026-10-13"
}