In this paper, we shed new light on a classical scheduling problem: given a slot-timed, constant-capacity server, what short-run scheduling decisions must be made to provide long-run service guarantees to competing flows of unit-sized tasks? We model the flows long-run guarantees as worst-case services that map each arrival vector recording a flows cumulative task arrivals to a worst-case acceptable departure vector lower-bounding its cumulative task departures. We show that these services are states that can be updated as tasks arrive and depart, introduce state-based scheduling, and find the schedulability condition that must be preserved to maintain all flows long-run guarantees. We then use this condition to identify, in each slot, all short-run scheduling decisions that preserve schedulability. To illustrate how scheduling complexity can be reduced, we additionally show that special schedules can be efficiently identified by maximizing the servers capacity slack, and that special services can be efficiently specified and updated using properties of the min-plus algebra.
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