In this paper we analyze the performance of a congestion control scheme of the type adopted by CCITT Recommendations I. 15X. In this scheme, a reactive type of congestion control is applied at both the network and the user Network Interface (UNI) levels in an integrated services network of the ATM (Asynchronous Transfer Mode) type. Depending on the user type (loss or delay sensitive) the user will either lose or delay some cells so as to meet a certain network performance criteria. The numbers of users and qualities of each type admitted to the network are controlled by the statistical multiplexer. This together with a mechanism to subclassify users of each type according to their quality (or priority) and the user specified control constitute the combined quality/congestion control in ATM based networks.