How many couriers does it take to keep the backlog near zero at the default order rate? At the defaults (10 couriers, order-chance 0.4) the fleet runs near capacity: couriers are almost never idle, and waiting-orders wanders between 0 and about 30.
Try this Raise number-of-couriers from 10 to 14 and press Reset: waiting-orders stays under about 5, a courier or two is usually idle, and average-wait falls from about 65 ticks to about 30. At 8 couriers the backlog averages 20 to 30.
About this model A MathPets original about fleet sizing, built on a queueing question: how do waiting times change as demand approaches what the servers can handle? About 80 houses around a central depot place delivery orders at random, and a fleet of couriers serves them one round trip at a time.
Each tick every house without an open order places one with probability order-chance percent, stamped with the tick. Then each courier, in random order, acts on its state: an idle courier at the depot claims the nearest open order (nearest first, not first come, first served), a delivering courier moves courier-speed toward its house and on arrival records the wait (current tick minus the order's tick), and a returning courier heads back to the depot. number-of-couriers and house-density apply at setup; order-chance and courier-speed are read every tick.
Unlike a textbook open queue, each house holds at most one open order, so under overload the backlog levels off below the number of houses instead of growing without bound: a finite-source queue, like the machine-repairman model. The backlog therefore shrinks steadily as couriers are added rather than falling off a cliff; at the default order rate it reaches zero at about 14 couriers.
