The network monitoring device is provided for monitoring the activity on a network carrying message packets each of which contains source and destination addresses. The monitoring device includes a network interface for sending and receiving message packets carried on the network, and a processor for collecting and processing data from the packets received by the network interface. In order to minimize processor memory requirements for the monitoring device, only randomly selected packets detected by the network interface are processed by the processor of the device. Preferably, the monitoring device is further simplified by providing a central measurement station to analyze data collected from the randomly sampled packets. As a result, the only processing required to be done by the monitoring device is the construction of collected-data packets for transmission to the central measurement station. A network monitoring system can advantageously be provided by using a number of such monitoring devices each associated with a respective logical segment of the network and each forwarding collected-data packets to a central measurement station.