Diffusion approximation to a queueing system with time-dependent arrival and service rates

A time nonhomogeneous diffusion approximation to a single server-single queue service system is obtained. Under various assumptions on the time-dependent functions appearing in the infinitesimal moments, transient and steady-state behaviour are analyzed. In particular, a diffusion approximation characterized by space-linear and time-varying moments is studied. The density of the busy period and the probability for the busy period to terminate are obtained. Finally, estimates of the goodness of the diffusion approximation are given.