  We consider a communication network over which transmissions must fulfill the
so-called token bucket traffic specification, with a rollout (i.e., predictive)
controller that both schedules transmissions and computes the corresponding
control values. In the token bucket specification, a transmission is allowed if
the current level of tokens is above a certain threshold. Recently, it has been
shown that having a full bucket at the time of a set point change significantly
improves the control performance as compared to when the bucket level is low.
In this work, we develop mechanisms that guarantee that the bucket fills up
after the controlled plant has converged to a set point. To do this, we
consider two different setups. First, we consider that all transmissions over
the network must fulfill the token bucket specification and show convergence to
the upper sector of the bucket by adding a slight terminal cost on the bucket
level. Afterwards, we consider a modified network which additionally features a
direct link over which transmissions need not fulfill the token bucket
specification. In this setup, we prove convergence of the bucket level exactly
to the upper rim. These mechanisms enable a similar level of flexibility as
event-triggered control: In converged state, little communication is used while
in precarious operating conditions, a burst of transmissions is possible. Other
than event-triggered approaches, the proposed methods allow to specify the
network traffic beforehand by means of the token bucket. Lastly, we validate
the proposed approaches in a numerical example.
