On a sorting rule to improve computational efficiency of connection admission control algorithms for ATM networks

It is well known that the cell loss probability suffered by different connections offered to the same ATM network link is, in general, different. Therefore, most of the connection admission control (CAC) schemes proposed for ATM networks have a computational complexity depending on the number of connections offered to a link. We propose to reduce this complexity by adopting a sorting rule among connections. In particular, we compare the expected cell loss probability of a pair of different traffic sources, when they are offered to a bufferless network node along with an arbitrary background traffic. We find a necessary and sufficient condition on the source parameters which, when satisfied, guarantees that the cell loss suffered by one source always bounds the one suffered by the other, for any distribution of the background traffic. This condition defines a partial sorting on the set of traffic sources offered to a node, according to which a small set of `bounding´ connections can be defined. The CAC scheme may be then implemented to monitor only the connections belonging to this set. We show that, assuming random traffic parameters, the resulting computational complexity of the CAC scheme depends only on the logarithm of the number of connections offered to each network link