  Length Rate Quotient (LRQ) is the first algorithm of interleaved shaping -- a
novel concept proposed to provide per-flow shaping for a flow aggregate without
per-flow queuing. This concept has been adopted by Time-Sensitive Networking
(TSN) and Deterministic Networking (DetNet). An appealing property of
interleaved shaping is that, when an interleaved shaper is appended to a FIFO
system, it does not increase the worst-case delay of the system. Based on this
"shaping-for-free" property, an approach has been introduced to deliver bounded
end-to-end latency. Specifically, at each output link of a node, class-based
aggregate scheduling is used together with one interleaved shaper per-input
link and per-class, and the interleaved shaper re-shapes every flow to its
initial traffic constraint. In this paper, we investigate other properties of
interleaved LRQ shapers, particularly as stand-alone elements. In addition,
under per-flow setting, we also investigate per-flow LRQ based flow aggregation
and derive its properties. The analysis focuses directly on the timing of
operations, such as shaping and scheduling, in the network. This timing based
method can be found in the Guaranteed Rate (GR) server model and more generally
the max-plus branch of network calculus. With the derived properties, we not
only show that an improved end-to-end latency bound can be obtained for the
current approach, but also demonstrate with two examples that new approaches
may be devised. End-to-end delay bounds for the three approaches are derived
and compared. As a highlight, the two new approaches do not require different
node architectures in allocating (shaping / scheduling) queues, which implies
that they can be readily adapted for use in TSN and DetNet. This together with
the derived properties of LRQ shed new insights on providing the TSN / DetNet
qualities of service.
