A system, and associated components and methodology, that automatically acquires data representative of the space left in each of a series of containers (32) in which one or more articles have been placed for packaging, and dispenses a controlled amount of dunnage material based on that data from a selected one of a plurality of dunnage dispensers (12). The system includes void volume data acquisition apparatus (11) for acquiring void volume data for the containers sequentially supplied thereto and for associating the sequentially acquired void volume data with the container. The system also includes a plurality of dunnage dispensers remotely located relative to the void volume data acquisition apparatus to dispense a controlled amount of dunnage material for insertion into one of the containers selectively transported to that dispenser from the void volume data acquisition apparatus.