= Lindley recursion
{c}
{title2=$W_{k+1}=(W_k+Z_{k+1})^+$}
For arrivals added before the slot's offered service, $Z_k$ is the arriving work minus that service. With independent identically distributed increments of negative mean, the stationary <queue workload> has the law $\sup_{m\geq0}\sum_{j=1}^mZ_j$. Iterating the recursion from the past gives this <supremum>; the strong law makes it finite. A different arrival/service ordering changes slot-boundary workload but requires its convention to be stated.
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