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

We introduce Pi-regulation, a new definition of traffic regulation which extends both the arrival curves of network calculus and Chang's max-plus g-regulation, and also includes new types of regulation, such as packet rate limitations. We provide a new exact equivalence between min-plus and max-plus formulations of traffic regulation. We show the existence and a max-plus representation of per-flow minimal regulators, which extends the concepts of packetized greedy shapers and minimal g-regulators. We show that any minimal regulator, placed after any arbitrary system that is FIFO for the flow of interest, does not increase the worst-case delay of the flow. We extend the theory to interleaved regulation and introduce the concept of minimal interleaved regulator. It generalizes the urgency-based shaper that was recently proposed by Specht and Samii as a simpler alternative to per-flow regulators in deterministic networks with aggregate scheduling. With this regulator, packets of multiple flows are processed in one FIFO queue and only the packet at the head of the queue is examined against the regulation constraints of its flow. We show that any minimal interleaved regulator, placed after any arbitrary FIFO system does not increase the worst-case delay of the combination.