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1. J. Karvo, J. Virtamo, S. Aalto and O. Martikainen, Blocking of dynamic multicast connections, in the 4th INFORMS Telecommunications Conference, 1998, Boca Raton, Florida, published later in Selected Proceedings in Telecommunication Systems (bib)

   Abstract: Multicast connections have a bandwidth saving nature. This means that a multicast connection - in taking the form of a tree where streams merge at the nodes - requires much less capacity from the network links than a bunch of separate point-to-point connections providing the same connectivity. In this paper, we consider dynamic multicast connections that can be used to model, for example, TV or radio delivery on a telecommunication network, such as an ATM network with virtual circuits. The model consists of a single multicast tree, whose root is called the originating office and leaves are called users. The originating office offers the users a set of programs, called channels. The programs run independently of their subscribers, who can join and leave the channel any time. The connections that deliver a specific channel to a group of users form a dynamic subtree of the multicast tree. Because of the dynamic nature of the multicast connections, the traditional methods for calculating blocking probabilities, such as the Kaufman-Roberts recursion, are not adequate in our case. Thus, new methods are needed. Our purpose in this paper is to show how to calculate these blocking probabilities, first in a separate link, and then in the whole network. As regards the former case, we derive exact formulae for the blocking probabilities by mapping the problem to an equivalent generalized Engset system with unidentical users and generally distributed holding times. Reduced Load Approximation is used for estimating the blocking probabilities in the whole network. The accuracy of the estimation method is studied by simulations.