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

We define the minimal interleaved regulator, which generalizes the Urgency Based Shaper that was recently proposed by Specht and Samii as a simpler alternative to per-flow reshaping in deterministic networks with aggregate scheduling. With this regulator, packets of multiple flows are processed in one FIFO queue; the packet at the head of the queue is examined against the regulation constraints of its flow; it is released at the earliest time at which this is possible without violating the constraints. Packets that are not at the head of the queue are not examined until they reach the head of the queue. This regulator thus possibly delays the packet at the head of the queue but 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 case delay of the combination is not increased. This shaping-for-free property is well-known with per-flow shapers; surprisingly, it continues to hold here. To derive this property, we introduce a new definition of traffic regulator, the minimal Pi-regulator, which extends both the greedy shaper of network calculus and Chang's max-plus regulator and also includes new types of regulators such as packet rate limiters. Incidentally, we provide a new insight on the equivalence between min-plus and max-plus formulations of regulators and shapers.