Some Basic Properties of Length Rate Quotient

Abstract

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). In this paper, we investigate basic properties of LRQ interleaved shapers. One is the so-called “shaping-for-free” property, which is, when an LRQ interleaved shaper is appended to a FIFO system, it does not increase the worst-case delay of the system. The other basic properties include conformance, output characterization, a sufficient and necessary condition for bounded delay, Guaranteed Rate characterization, and delay and backlog bounds for LRQ interleaved shapers as stand-alone elements. The derived properties of LRQ shed new insights on understanding interleaved shaping, which may be further exploited to achieve bounded delay in TSN/DetNet networks.