  In feed-forward time-sensitive networks with Deficit Round-Robin (DRR),
worst-case delay bounds were obtained by combining Total Flow Analysis (TFA)
with the strict service curve characterization of DRR by Tabatabaee et al. The
latter is the best-known single server analysis of DRR, however the former is
dominated by Polynomial-size Linear Programming (PLP), which improves the TFA
bounds and stability region, but was never applied to DRR networks. We first
perform the necessary adaptation of PLP to DRR by computing burstiness bounds
per-class and per-output aggregate and by enabling PLP to support non-convex
service curves. Second, we extend the methodology to support networks with
cyclic dependencies: This raises further dependency loops, as, on one hand, DRR
strict service curves rely on traffic characteristics inside the network, which
comes as output of the network analysis, and on the other hand, TFA or PLP
requires prior knowledge of the DRR service curves. This can be solved by
iterative methods, however PLP itself requires making cuts, which imposes other
levels of iteration, and it is not clear how to combine them. We propose a
generic method, called PLP-DRR, for combining all the iterations sequentially
or in parallel. We show that the obtained bounds are always valid even before
convergence; furthermore, at convergence, the bounds are the same regardless of
how the iterations are combined. This provides the best-known worst-case bounds
for time-sensitive networks, with general topology, with DRR. We apply the
method to an industrial network, where we find significant improvements
compared to the state-of-the-art.
