In an ATM exchange, a cell transmission control section transmits an ATM cell to a transmission path of an ATM network. A traffic monitor monitors traffic of the cell transmissions. A statistical process section performs a temporal statistical process on the result of the traffic monitoring using a clock and a memory. A CAC produces an instruction for traffic control over a transmission terminal based on the result of the statistical process. A UPC controls traffic of a transmission path from the transmission terminal in accordance with the instruction.