The principal investigator will develop on-line statistical techniques for the operations and management of ATM networks. The statistical techniques include: estimating the quality of service, estimating the spare resources, and improving network operations. The motivation for this work is: 1) user-network contracts specify a quality of service that is difficult to verify and 2) the network needs to monitor its performance in real time to improve its operations. Some users will want to monitor the QoS that the network provides. For instance, if the user is a service reseller, he may want to protect himself against complaints from subscribers. Similarly, the network will use such monitoring for quality control and also for improving its operations. Given the likely penetration of ATM networks, improving the operations and management of these networks is an important objective. The statistical properties of quality of service estimators are difficult to analyze on realistic models. Consequently, this research will combine analysis, simulation, and actual experiments to develop the on-line techniques.