The one-to-plural communication system for realizing the time slot allocation control method of the invention comprises the terminal-side apparatus 800˜830 provided with the buffer 801, the Queue length report function 802, and the output control function 803, and the network-side apparatus 840 provided with the necessary buffer capacity reduction type time slot allocation control function 141. The necessary buffer capacity reduction type time slot allocation control function 141, by using the Queue length information reported from the Queue report function 802, allocates time slots so that Queue lengths in the buffer 801 may become constant as nearly as possible among the terminal-side apparatus 800˜830, and reports the results to the output control circuit 803 which controls the output of cells from the buffer 801. Thus, this invention provides, in dynamic time slot allocation control, a time slot allocation control method for reducing the necessary buffer capacity of each terminal-side apparatus, and also a one-to-plural media shared type communication system for realizing it.