= Stationary workload supremum
{title2=$Q\overset d=\sup_{n\ge0}(\sum_{j=1}^nA_j-cn)$}
For <independent and identically distributed> arrivals with finite mean below service $c$, the <strong law of large numbers> makes the net cumulative input tend to minus infinity, so the supremum is finite <almost surely>. Applying the same formula to the past input gives a stationary solution of the <Lindley recursion>. This representation turns <queue workload> overflow into an event involving some lookback horizon.
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