A spatial and temporal numerical simulation has been carried out of a pulsed (100% modulated), rf inductively coupled plasma discharge in argon, connected to an additional (ballast) diffusion chamber of much larger volume. It is demonstrated that during the active phase, the presence of the large ballast volume has a small impact on the parameters of the plasma in the smaller discharge chamber. In this case the plasma parameters in the discharge chamber can be estimated separately from the diffusion chamber by a standard method using the characteristic ambipolar diffusion time (for example, using a global model). However, during the afterglow phase, the situation is changed significantly. In the afterglow, the densities of charged particles in the discharge chamber become lower than in the large ballast chamber due to more rapid diffusion loss. As a result, the reverse of the active phase situation occurs, namely, the plasma does not flow from the small to the large chamber, but in the opposite direction, from diffusive to discharge volume, and both the plasma density gradient and the self-consistent ambipolar electric field in the small chamber change directions. This phenomenon leads to new effects in the discharge volume, in particular a decreasing rate of decay of densities of charged particles and electron temperature. Thus, in the afterglow the presence of a large additional ballast volume has a significant impact on the plasma transport. In this case, a simple treatment of the plasma in the discharge chamber in the framework of a spatially averaged model (for example, the global model) is inadequate.