Hierarchical Reactive Monitoring of Multicast Membership Size

Knowing the number of active receivers in a multicast group is very important and useful for many applications. Retaining an exact count of the multicast group size is a very difficult task. Fortunately, estimating the group size rather than finding it exactly may be sufficient for applications like pricing. In particular, it may suffice to know at any given moment that the number of receivers in the group is between some predefined bounds, thresholds. This estimation is disseminated to the multicast ISPs worldwide. The ISPs then locally compute the price of transmitting a unit of bandwidth to the group, and present this price to senders in their domain. This paper concentrates on the algorithmic aspects of retaining multicast group size estimation for the purposes of accounting and pricing. We suggest novel network-level algorithms that combine a hierarchical control structure with a reactive (event-driven) monitoring mechanism in order to conserve network traffic and cope with the problem of feedback implosion. We provide a rigorous definition of the problem, theoretically analyze our algorithms, and investigate their relative performance using extensive simulation studies. We show that on real Internet traces that our algorithms reduce the overhead monitoring traffic by a factor of 2-10 depending on the required accuracy and a specific behavior of the group size.