To provide a new representation of the flow of time, you typically implement a new clock and a time source for the clock. The clock provides the interface to the standard clock functions. The time source defines the basis of time for the clock--it is the root of the clock hierarchy that actually implements the source of the time.
A time source can be viewed as a software implementation of a set of hardware services for getting the time and implementing delays. Since it is a software implementation, it can represent any timing model.