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This paper examines the allocative efficiency of two popular non-price allocation mechanisms — the lottery (random allocation) and the waiting-line auction (queue system) — for the cases where consumers possess identical time costs (the homogeneous case), and where time costs are correlated with time valuations (the heterogeneous case). We show that the relative efficiency of the two mechanisms depends critically on the scarcity factor (measured by the ratio of the number of objects available for allocation over the number of participants) and on the shape of the distribution of valuations. We obtain a set of analytical results showing that the lottery generally dominates the waiting-line auction unless the there are very few high-valuation individuals and the scarcity factor is sufficiently high. We further demonstrate that while consumer heterogeneity may improve the relative allocative efficiency of the waiting-line auction, this is usually not significant enough to reverse the general dominance of the lottery.

The General Dominance of Lottery over Waiting-Line Auction