An object is to provide a network management system and the like capable of being introduced into an existing network to ascertain an instantaneous traffic variation in the network. The scheme of the present invention uses a shaping function included by each edge apparatus. The shaping function controls packet transmission in a millisecond order. The network management apparatus according to the present invention adds up the amount of transmitted packets for each control period reported by each edge apparatus and estimates this as an instantaneous traffic amount in the network. In the scheme, it is only necessary to add one network management apparatus to an existing network and to cause each edge apparatus to report the amount of transmitted packet to the network management apparatus.