The authors study an adaptive or greedy policy for sequentially and equitably packing I (I≥2) bins, or equivalently, for scheduling jobs for the service of I processors. The connection between bin-packing and makespan scheduling is described in Coffman and Lueker. It is shown that the suitably normalized bin contents become nearly jointly, but degenerately, Gaussian if the Poisson arrival rate of jobs of independent, identically distributed magnitudes becomes large. Explicit simple parameter characterizations are given; the asymptotic results are compared with simulations. The advantage of the greedy ‘shortest line next’ policy over a laissez-faire policy of equal access is quantified, and seen to depend on the square root of the number of bins.
