Stochastic analysis of a modified First Fit Decreasing packing

A stochastic analysis is made of a modified version mFFD of First Fit Decreasing, in which each bin is closed after it receives its first fallback item. Consider a probability measure on , and independent random variables distributed according to. Let be the number of unit size bins that mFFD needs to pack items of size . It is proven that exists and that the random variable converges in distribution. The main tools are deterministic inequalities concerning mFFD, that might be of independent interest.