Little's Law

Biological Parallel

Little's Law states that inventory equals arrival rate times processing time (L = λW). Biology obeys this relationship with mathematical precision across every scale. The human circulatory system demonstrates this perfectly: 5 liters of blood (inventory) equals 5 liters per minute cardiac output (arrival rate) times 1 minute transit time (processing time). Change any variable and the others adjust to maintain the equation. Increase heart rate and blood transits faster; decrease it and the same 5 liters spends more time in circulation. Neurotransmitter dynamics at synapses follow identical mathematics. Synaptic vesicles (inventory) equal vesicle arrival rate from the cell body times synaptic residence time before reuptake or degradation. Fast-spiking neurons require higher arrival rates to maintain vesicle inventory during rapid firing. Digestive tracts apply the same principle: food volume in the intestine equals ingestion rate times digestion time. Deer with multi-chamber stomachs have enormous gut inventory precisely because they have slow processing times for cellulose breakdown, while carnivores process protein quickly and maintain lower gut inventory. Little's Law reveals why systems break under load. If arrival rate increases but processing time stays constant, inventory must grow. Kidney filtration demonstrates this: glomerular filtration rate (arrival) times tubular processing time determines fluid inventory in nephrons. When processing slows (disease), fluid accumulates—edema. Cells face the same constraint with protein synthesis: ribosome count (inventory) equals mRNA arrival rate times translation time. When cells need more protein but can't speed translation, they build more ribosomes. The law is inescapable: speed processing, reduce inventory, or build capacity. Biology has no other options.