Abstract
The CTM protocol permits an unlimited number of users to share a single slotted communications channel. A collision occurs when two or more users transmit messages in the same slot. Users who collide re-transmit their messages by randomly splitting into subgroups until each subgroup contains at most one message. L(n), the number of slots required to resolve a collision among n users, is a random variable whose asymptotic properties are of considerable interest. Under fairly general conditions, the asymptotic distribution of L(n) is normal. We briefly review the early research on this problem, and then present some newer results.
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References
Aldous, D. J., 1987, Ultimate instability of exponential backoff protocol for acknowledgement-based transmission control of random access communication channels, IEEE Trans. Inform. Theory, vol. IT-33, 219–223.
Bertsekas D., and Gallager, R., 1992, “Data Networks”, Second Edition, Prentice-Hall, New Jersey.
Capetanakis, J. I., 1979, Tree algorithms for packet broadcast channels, IEEE Trans. Inform. Theory, vol. IT-25, No. 5, 505–515.
Fayolle G., Flajolet P., Hofri, M, and Jacquet, P., 1985, Analysis of a stack algorithm for random multiple-access communication, IEEE Trans. Inform. Theory, vol. IT-31, 244–254.
Fayolle G., Flajolet P., and Hofri, M., 1986, On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel, Adv. Appl. Prob., vol. 18, 441–472.
Feldman P., Rachev S. T., and Rüschendorf, L, to appear, Limit theorems for recursive algorithms, J. of Computational and Applied Math.
Jacquet, P. and Regnier, M., 1988, Normal limiting distribution of the size of tries, Performance’ 87, P. J. Courtois and G. Latouche (edt.), 209–221. Elsevier Science Publ.
Rachev, S. T., 1991, “Probability Metrics and the Stability of Stochastic Models”, Wiley, Chichester, New York, 1991.
Rachev, S. T. and Rüschendorf, L., 1991, Probability metrics and recursive algorithms. Technical Report, Inst, fur Math. Stat., Univ. Munster, No. 1.
Regnier M., and Jacquet, P., 1989, New results on the size of tries, IEEE Trans. Inform. Theory, vol. 35, No. 1, 203–205.
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© 1994 Springer Science+Business Media New York
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Feldman, P.M. (1994). Asymptotic Normality of the Collision Resolution Interval for a Multiple Access Protocol. In: Anastassiou, G., Rachev, S.T. (eds) Approximation, Probability, and Related Fields. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2494-6_14
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DOI: https://doi.org/10.1007/978-1-4615-2494-6_14
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