A spinning-mill machine and associated operational method includes a plurality of cross-winding devices arranged next to each other in a longitudinal direction along each machine side of the spinning-mill machine, wherein each cross-winding device is configured to wind yarn onto a sleeve. The cross-winding devices are arranged into a multiple number of sections along each of the machine sides. A sleeve transport device is arranged along the cross-winding devices on each machine side to supply empty sleeves to cross-winding devices. A plurality of sleeve stacks are configured to stockpile the empty sleeves. A plurality of sleeve storage devices are arranged along each machine side for distributed intermediate storage of the empty sleeves, wherein each cross-winding device is allocated with a single sleeve storage device, or the plurality of the cross-winding devices in each of the sections are allocated to a single one of the sleeve storage devices.