SN 51/1 issue (820194)—MS 028 1 Statistica Neerlandica (1997) Vol. 51, nr. 1, pp. 1–22 Limiting distribution of the collision resolution interval P. Feldman Illgen Simulation Technology, 250 Storke Road, Suite 10, Santa Barbara, CA 93117, USA, and Department of Computer Science, University of California, Santa Barbara, CA 93106, USA S. T. Rachev Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA L. Ru¨schendorf * Institut fu¨ r Mathematische Stochastik, Hebelstraße 27, 79104 Freiburg, Germany We use the theory of probability metrics to study the asymptotic normality of the collison resolution intervals in the CTM multi-access protocol under general conditions on the number of retransmitted messages and of new arrivals during the collision slots. Our main result establishes stability of the central limit theorem for the CTM algorithm. We provide extensive simulation results investigating the extent to which the mean of the collision resolution interval eventually becomes unstable for increasing values of n, the number of users who initially collide. The normal fit is numerically investigated and is shown to be quite satisfactory and stable with respect to moderate perturbations and n  50. Key Words & Phrases: multi-access problem, probability metrics, asymptotic normality. 1 Introduction The Capetanakis–Tsybakov–Mikhailov (CTM) protocol is one of the more elegant solutions to the classical multiple-access problem in which a large (actually, infinite) population of users share a single communication channel. Throughput of this protocol is close to the throughput of the slotted Aloha protocol, and the CTM protocol, unlike slotted Aloha, is inherently stable. The ‘‘tree splitting protocols’’, of which the CTM protocol is an example, pose some interesting mathematical problems, and have been the subject of intensive study in recent years (see A, Research supported by NATO, DFG and NSF grants. * rushchengalton.mathematik.uni-freiburg.de  VVS, 1997. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 238 Main Street, Cambridge, MA 02142, USA.