A RDF is a lattice of substates, each substate represents either the on state or the off state, and has a particular number (see Figure 1). The connections are only among substates of different states. A simulation of an on-off trajectory from a RDF is made with a generalized Gillespie algorithm, where here a random jumping time is first taken from density functions that are (usually) not exponential using the rejection method, and then the specific next substate is chosen according to the jumping probabilities that are determined from the jumping time probability density functions. A RDF can have irreversible connections, yet, it generates an on-off trajectory that has the property of microscopic reversibility, meaning that the physical system fluctuates around equilibrium.