hesela.devLittle's law
Little's law relates time-averaged occupancy L to the operation rate lambda and mean residence time W within the same system boundary.
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 [1] [2]. 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 [3]. 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 [3].
Relations
- related
- queue-depth, iops, latency-storage, open-loop-load, closed-loop-load
Limitations
- Substituting p99 latency or a configured queue limit changes the quantities in the law; it does not predict required concurrency or attainable device IOPS. [2, 3]
Citations
- 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.
- 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.
- Hesela: IOPS, bytes and average occupancy; synthetic accounting examples.