  Flow reshaping is used in time-sensitive networks (as in the context of IEEE
TSN and IETF Detnet) in order to reduce burstiness inside the network and to
support the computation of guaranteed latency bounds. This is performed using
per-flow regulators (such as the Token Bucket Filter) or interleaved regulators
(as with IEEE TSN Asynchronous Traffic Shaping). Both types of regulators are
beneficial as they cancel the increase of burstiness due to multiplexing inside
the network. It was demonstrated, by using network calculus, that they do not
increase the worst-case latency. However, the properties of regulators were
established assuming that time is perfect in all network nodes. In reality,
nodes use local, imperfect clocks. Time-sensitive networks exist in two
flavours: (1) in non-synchronized networks, local clocks run independently at
every node and their deviations are not controlled and (2) in synchronized
networks, the deviations of local clocks are kept within very small bounds
using for example a synchronization protocol (such as PTP) or a satellite based
geo-positioning system (such as GPS). We revisit the properties of regulators
in both cases. In non-synchronized networks, we show that ignoring the timing
inaccuracies can lead to network instability due to unbounded delay in per-flow
or interleaved regulators. We propose and analyze two methods (rate and burst
cascade, and asynchronous dual arrival-curve method) for avoiding this problem.
In synchronized networks, we show that there is no instability with per-flow
regulators but, surprisingly, interleaved regulators can lead to instability.
To establish these results, we develop a new framework that captures industrial
requirements on clocks in both non-synchronized and synchronized networks, and
we develop a toolbox that extends network calculus to account for clock
imperfections.
