Stochastic Analysis of a Modified First Fit Decreasing Packing

We make a stochastic analysis 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 µ on [0, 1], and independent random variables X1, ', Xn distributed according to µ. Let Rn = RX1, ', Xn be the number of unit size bins that mFFD needs to pack items of size X1, ', Xn. We prove that cµ = limn→∞ERn/n exists and that the random variable Rn-ncµ/√n converges in distribution. The main tools are deterministic inequalities concerning mFFD, that might be of independent interest.