  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.
