Some Properties of Length Rate Quotient Shapers

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.