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Suppose requests to store files arrive at a storage facility in a Poisson stream at rate 1. Each file is allocated storage space on arrival and each remains independently for an exponential time with mean l/p. The lengths of the files are assumed to be independent with common distribution F. Each file is placed in the lowest addressed contiguous sequence of locations large enough to accommodate the fre at its arrival time. This is the so-called first-fit storage discipline. We conjecture that first-fit is asymptotically optimal in the sense that the ratio of expected empty space to expected occupied space tends to zero as p → 0, i.e., as the occupied space tends to ∞. This conjecture seems very hard to prove, but it has been proved for constant file lengths , i.e., when F degenerates. We are unable to prove the conjecture but give a graphic display of the results of a Monte Carlo simulation which makes it very convincing.