  Packet replication and elimination functions are used by time-sensitive
networks (as in the context of IEEE TSN and IETF DetNet) to increase the
reliability of the network. Packets are replicated onto redundant paths by a
replication function. Later the paths merge again and an elimination function
removes the duplicates. This redundancy scheme has an effect on the timing
behavior of time-sensitive networks and many challenges arise from conducting
timing analyses. The replication can induce a burstiness increase along the
paths of replicates, as well as packet mis-ordering that could increase the
delays in the crossed bridges or routers. The induced packet mis-ordering could
also negatively affect the interactions between the redundancy and scheduling
mechanisms such as traffic regulators (as with per-flow regulators and
interleaved regulators, implemented by TSN asynchronous traffic shaping). Using
the network calculus framework, we provide a method of worst-case timing
analysis for time-sensitive networks that implement redundancy mechanisms in
the general use case, i.e., at end-devices and/or intermediate nodes. We first
provide a network calculus toolbox for bounding the burstiness increase and the
amount of reordering caused by the elimination function of duplicate packets.
We then analyze the interactions with traffic regulators and show that their
shaping-for-free property does not hold when placed after a packet elimination
function. We provide a bound for the delay penalty when using per-flow
regulators and prove that the penalty is not bounded with interleaved
regulators. Finally, we use an industrial use-case to show the applicability
and the benefits of our findings.
