Sizing exit buffers in ATM networks: An intriguing coexistence of instability and tiny cell loss rates

This paper deals with the sizing of end buffers in ATM: networks for sessio ns subject to constant bit rate (CBR) traffic. Our objective is to predict the cell-lossrate 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 buffer s 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 s ervice rate and whose arrivals are generated at regular intervals and mater ialize after a generally distributed random amount of time. We reveal that under the infinite buffer assumption, the system possesses rather intriguin g 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 th e other hand, the likelihood that the buffer contents will exceed certain l evel 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 fini te buffer assumption and derive bounds on the cell-loss rates. The bounds a re expressed in terms of simple formulae of the system parameters. We carry out the analysis for two major types of networks: 1) datagram networks, wh ere the packets (cells) traverse the network via independent paths and 2) v irtual circuit networks, where all cells of a connection traverse the same path. Numerical examination of ATM-like examples show that the bounds are v ery good for practical prediction of cell loss and the selection of buffer size.