Cell Loss Probabilities in a Statistical Multiplexer in an ATM Network
In this paper we evaluate the loss probability of cells generated by a burst/silence source which is mixed with a superposition of M independent identical burst/silence traffic streams in a statistical multiplexer with a finite buffer capacity. The model incorporates the main stochastic characteristics of the system, namely the periodicity of an active source and the modulation effect produced by the alternation between active and silent periods of each source. The resulting queueing system is a discrete-time Markov chain and the queue length distribution seen by an arriving cell of the tagged source is evaluated. The loss probability of a string of consecutive cells of this source is computed, together with the conditional loss probability of such a string, given that the first cell was lost. Numerical results show that, although the tagged source has a small single cell loss probability, it may experience a high conditional loss of a string of consecutive cells, and hence may suffer from a quality of service degradation. The impact of the buffer size of the multiplexer, the burst length of sources and the load of the system on this conditional loss probability is studied.
KeywordsATM Statistical Multiplexing Loss Probabilities Quality of Service.
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- P. Brown and A. Simonian, Perturbation of a periodic flow in a synchronous server, In: Proc. Performance ‘87, Brussels, P.-J. Courtois and G. Latouche, Eds., North-Holland, 1988, pp. 89–112Google Scholar
- J.N. Daigle and J.D. Langford, Models for analysis of packet voice communications systems, IEEE J. Select. Areas Commun., Vol. SAC-4, No 6, September 1986, pp. 926–937Google Scholar
- H. Kroner, Statistical multiplexing of sporadic sources-Exact and approximate performance analysis, paper to be presented at the 13-th ITC, Copenhagen, June 1991Google Scholar
- H. Kroner, T. Theimer, and U. Briem, Queueing Models for ATM Systems A Comparison, Proceedings of the 7th ITC Specialist Seminar, Morristown, USA, 1990Google Scholar
- G. Latouche, A study of deterministic cycles in packet queues subject ot periodic traffic, Technical Report T.R.89/1, October 1989Google Scholar
- V. Ramaswami and G. Latouche, Modeling packet arrivals from asynchronous input lines, Proceedings of the ITC 12, 1988, Paper 3.1B.3Google Scholar
- V. Ramaswami, Traffic performance modeling for packet communication whence, where and whither, Keynote Adress, Third Australian Teletraffic Seminar, November, 1988Google Scholar
- V. Ramaswami and W. Willinger, Efficient traffic performance strategies for packet multiplexers, ITC Specialist Seminar, Adelaide, September 1989Google Scholar
- Y.C. Yenq, Approximation for voice traffic in statistical multiplexer, Proc. IEEE IN-FOCOM, April 1984, pp. 256–259Google Scholar