  We investigate the simulation problem in of dense-time system. A
specification simulates a model if the specification can match every transition
that the model can make at a time point. We also adapt the approach of Emerson
and Lei and allow for multiple strong and weak fairness assumptions in checking
the simulation relation. Furthermore, we allow for fairness assumptions
specified as either state-predicates or event-predicates. We focus on a
subclass of the problem with at most one fairness assumption for the
specification. We then present a simulation-checking algorithm for this
subclass. We propose simulation of a model by a specification against a common
environment. We present efficient techniques for such simulations to take the
common environment into consideration. Our experiment shows that such a
consideration can dramatically improve the efficiency of checking simulation.
We also report the performance of our algorithm in checking the liveness
properties with fairness assumptions.
