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1. S. Aalto, J. Karvo and J. Virtamo, Calculating blocking probabilities in multicast loss systems, in Proc. SPECTS 2002, pp. 833-842, 2002, San Diego, CA (bib)

   Abstract: We study a loss network carrying multicast traffic. The multicast traffic is separated from the rest of the network, resulting in a multicast loss system, where a single server node is connected with a collection of user nodes by a network having a tree topology. A predefined set of dynamic multicast (i.e. point-to-multipoint) connections, called channels, use this network, with the server located at the root of the tree for all these channels and the users located at the leaf nodes. Earlier analytical results concerning the calculation of blocking probabilities in this kind of multicast setting have, because of their exponential complexity, been applicable only for networks with few multicast channels. Our contribution is twofold; first, we define a problem setting where the state description for the system can be simplified. This situation arises when channels can be divided into groups of statistically indistinguishable channels. Second, we present a new algorithm, making the exact calculation of the end-to-end blocking probability feasible for networks with a large number of multicast channels. The algorithm uses a new construct, called combinatorial convolution, to achieve this goal. In the best cases, our algorithm has a polynomial complexity with respect to the number of channels.