IMA Complex Systems Seminar

1:30, Thursday, March 4, 2004            



Multicasting and phase transitions in tree loss networks



Ilze Ziedins

Department of Statistics
The University of Auckland
Private Bag 92019
Auckland, New Zealand


We consider a generalisation of the hard-core model on regular trees that arises in statistical mechanics.  This generalisation is motivated by multicasting in queueing and loss networks.  Multicasting occurs when a transmission is made to a group of individuals from a single site, instead of just having a simple end-to-end connection.  An example of this in the loss network setting is a conference call. We analyse a model of a regular tree loss network that supports both unicast calls that require unit capacity on a single link, and multicast calls that require unit capacity on all the links emanating from a node.   At sufficiently high arrival rates for the multicast calls, the network can exhibit a phase transition, leading to unfairness due to spatial variation in the multicast blocking probabilities. The dependence of the phase transition on various parameters will be discussed, as well as the effect of simple controls within the network.  Recent work showing that the phase transitions can be nonmonotone will also be described.  This is joint work with Kavita Ramanan, Anirvan Sengupta and Brad Luen.