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

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4 Author(s)
Levy, H. ; Dept. of Comput. Sci., Tel Aviv Univ., Israel ; Mendelson, T. ; Sidi, M. ; Keren-Zvi, J.

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 unstable 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

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Networking, IEEE/ACM Transactions on  (Volume:7 ,  Issue: 6 )