This project is concerned with the allocation of network resources, specifically buffer and bandwidth, to users and to virtual paths in an Asynchronous Transfer Mode network. The research concentrates on developing a framework for analysis of this resource allocation probelm. Users are assumed to receive benefit as a function of their quality of service. measured by cell loss probability and completion time for real-time services. Network usage is measured using effective bandwidth and buffer occupancy. The paradigm of price and demand is used to represent the minimal required information transfer between user and network. These prices are considered purely as internal network indicators for the purpose of resource allocation; what users are actually charged by their service provider is a separate issue not considered here. The goal is to allocate bandwidth and buffer so as to make as many users happy as possible, and to do so efficiently. Furthermore, it is desirable that any such mechanism be distributed both hierarchically and geographically. The P.I. proposes to develop this framework to jointly allocate buffer and bandwidth, to study the use of priorities to replace explicit reservation of resources, and to analyze the resulting network dynamics.