This paper deals with the sizing of end buffers in ATM networks for sessions subject to constant bit rate (CBR) traffic. Our objective is to predict the cell-loss rate at the end buffer as a function of the system parameters. We introduce the D+G/D/1 queue as a generic model to represent exit buffers in telecommunications networks under constant rate traffic, and use it to model the end buffer. This is a queue whose arrival rate is equal to its service rate and whose arrivals are generated at regular intervals and materialize after a generally distributed random amount of time. We reveal that under the infinite buffer assumption, the system possesses rather intriguing properties: on the one hand, the system is instable in the sense that the buffer content is monotonically nondecreasing as a function of time. On the other hand, the likelihood that the buffer contents will exceed certain level B by time t diminishes with B. Improper simulation of such systems may therefore lead to false results. We turn to analyze this system under finite buffer assumption and derive bounds on the cell-loss rates. The bounds are expressed in terms of simple formulae of the system parameters. We carry out the analysis for two major types of networks: 1) datagram networks, where the packets (cells) traverse the network via independent paths and 2) virtual circuit networks, where all cells of a connection traverse the same path. Numerical examination of ATM-like examples show that the bounds are very good for practical prediction of cell loss and the selection of buffer size.