Markov random field models of multicasting in tree networks

Ramanan, K., Sengupta, A., Ziedins, I., Mitra, P. P. (2002) Markov random field models of multicasting in tree networks. Advances in Applied Probability, 34 (1). pp. 58-84. ISSN 00018678 (ISSN)

URL: https://www.cambridge.org/core/journals/advances-i...
DOI: 10.1017/S0001867800011393

Abstract

In this paper, we analyse a model of a regular tree loss network that supports two types of calls: unicast calls that require unit capacity on a single link, and multicast calls that require unit capacity on every link emanating from a node. We study the behaviour of the distribution of calls in the core of a large network that has uniform unicast and multicast arrival rates. At sufficiently high multicast call arrival rates the network exhibits a 'phase transition', leading to unfairness due to spatial variation in the multicast blocking probabilities. We study the dependence of the phase transition on unicast arrival rates, the coordination number of the network, and the parity of the capacity of edges in the network. Numerical results suggest that the nature of phase transitions is qualitatively different when there are odd and even capacities on the links. These phenomena are seen to persist even with the introduction of nonuniform arrival rates and multihop multicast calls into the network. Finally, we also show the inadequacy of approximations such as the Erlang fixed-point approximations when multicasting is present.

Item Type: Paper
Uncontrolled Keywords: Bethe lattice Blocking probabilities Broadcasting Cayley trees Erlang fixed point approximations Hard core models Loss networks Multicasting Phase transitions Reduced load approximations Spin models Statistical mechanics Symmetry breaking Unicasting Approximation theory Mathematical models Probability Telecommunication networks Trees mathematics Markov random field models Markov processes
Subjects: physics > biophysics
organs, tissues, organelles, cell types and functions > tissues types and functions > neural networks
physics
CSHL Authors:
Communities: CSHL labs > Mitra lab
Depositing User: CSHL Librarian
Date Deposited: 02 Apr 2012 20:14
Last Modified: 06 Feb 2017 20:04
URI: http://repository.cshl.edu/id/eprint/25872

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