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We define the minimal interleaved regulator, which generalizes the UrgencyBased Shaper that was recently proposed by Specht and Samii as a simpleralternative to per-flow reshaping in deterministic networks with aggregatescheduling. With this regulator, packets of multiple flows are processed in oneFIFO queue; the packet at the head of the queue is examined against theregulation constraints of its flow; it is released at the earliest time atwhich this is possible without violating the constraints. Packets that are notat the head of the queue are not examined until they reach the head of thequeue. This regulator thus possibly delays the packet at the head of the queuebut also all following packets, which typically belong to other flows. However,we show that, when it is placed after an arbitrary FIFO system, the worst casedelay of the combination is not increased. This shaping-for-free property iswell-known with per-flow shapers; surprisingly, it continues to hold here. Toderive this property, we introduce a new definition of traffic regulator, theminimal Pi-regulator, which extends both the greedy shaper of network calculusand Chang's max-plus regulator and also includes new types of regulators suchas packet rate limiters. Incidentally, we provide a new insight on theequivalence between min-plus and max-plus formulations of regulators andshapers.

A Theory of Traffic Regulators for Deterministic Networks with Application to Interleaved Regulators