We simulate queues of activity in a directed sandpile automaton in 1 + 1 dimensions by adding grains with rate r at the top row. Duration t of elementary jobs (avalanches) is given exactly by the "heavy tail" distribution P ～ t~(-3/2) for large t. In practice the durations are limited either by the system size or by dissipation at defects (concentration c). We study numerically and analytically tail behavior of the distributions of busy periods and energy dissipated in the queue. Depending on the relative ratio of driving and dissipation rates, the distribution of intermittent queue activities exhibit long-range correlations and multifractal scaling properties.
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