Network-calculus service curves of the interleaved regulator

The interleaved regulator (implemented by IEEE TSN Asynchronous Traffic Shaping) is used in time-sensitive networks for reshaping the flows with per-flow contracts. When applied to an aggregate of flows that come from a FIFO system, an interleaved regulator that reshapes the flows with their initial contracts does not increase the worst-case delay of the aggregate. This shaping-for-free property supports the computation of end-to-end latency bounds and the validation of the network's timing requirements. A common method to establish the properties of a network element is to obtain a network-calculus service-curve model. The existence of such a model for the interleaved regulator remains an open question. If a service-curve model were found for the interleaved regulator, then the analysis of this mechanism would no longer be limited to the situations where the shaping-for-free holds, which would widen its use in time-sensitive networks. In this paper, we investigate if network-calculus service curves can capture the behavior of the interleaved regulator. For an interleaved regulator that is placed outside of the shaping-for-free requirements (after a non-FIFO system), we develop Spring, an adversarial traffic generation that yields unbounded latencies. Consequently, we prove that no network-calculus service curve exists to explain the interleaved regulator's behavior. It is still possible to find non-trivial service curves for the interleaved regulator. However, their long-term rate cannot be large enough to provide any guarantee. Specifically, we prove that for the regulators that process at least four flows with the same contract, the long-term rate of any service curve is upper bounded by three times the rate of the per-flow contract.