  Consider a network of multiple independent stochastic linear systems where,
for each system, a scheduler collocated with the sensors arbitrates data
transmissions to a corresponding remote controller through a shared
contention-based communication network. While the systems are physically
independent, their optimal controller design problems may, in general, become
coupled, due to network contention, if the schedulers trigger transmissions
based on state-dependent events. In this article we propose a class of
probabilistic admissible schedulers for which the optimal controllers, with
respect to local standard LQG costs, have the certainty equivalence property
and can still be determined decentrally. Then, two scheduling policies within
this class are introduced; a non-event-based and an event-based, both with an
easily adjustable triggering probability at every time step. We then prove
that, for each closed-loop system, the event-based scheduler and its optimal
controller outperforms the closed-loop system with the non-event-based
scheduler and its associated optimal controller. Moreover, we show that, for
each closed-loop system, the optimal state estimators for both scheduling
policies follows a linear iteration. Finally, we provide a method to regulate
the triggering probabilities of the schedulers by maximizing a network utility
function.
