Towards an Erlang Theory for Flow Based Architectures

October 6, 2010
Time: 1:30pm-2:30pm
CSB 477
Hosted by: Columbia University Joint CS and EE Networking Seminar
Speaker: Professor Ravi R. Mazumdar (University of Waterloo, Canada)


File transfers compose much of the traffic of the current Internet. The main measures of the quality of service for this type of traffic are the transfer rates and duration of the file transfer. File transfers are modeled as a fluid elastic flow, whose transmission rates are adaptable depending on the network congestion or the number of other flows that share the link. There are many models for sharing the available bandwidth on a link and the most common model is that of processor sharing. Such a model assumes that the flows sharing the link are homogeneous. However, in practice, flows have different bandwidth requirements. A major concern is how to share the bandwidth at links in a network fairly when it is accessed by heterogeneous flows. A key notion of fairness that has been studied in the context of rate control of elastic flows is the notion of proportional fairness introduced by Kelly that corresponds to a Nash bargaining solution. Proportional fairness can be well approximated by using a balanced fair server bandwidth allocation scheme. Balanced fairness is a sharing policy introduced by Bonald and Proutiere and has the attractive advantage of being both tractable to flow level analysis and insensitive. Indeed it can be shown that the scaled limits (when they exist) of insensitive network models converge to proportional fair allocations. The advantage is that the resulting tractability allows us to determine performance quantities of interest in dimensioning router capacity much as in the case of the Erlang formulae in classical networks.     In the talk I will present the background on insensitive network allocations and their relation to the proportional fair allocations. The talk will focus on congestion in links that operate under a balanced fair allocation scheme for heterogeneous flows with differing maximum or peak bandwidth requirements. In particular we address how various congestion measures can be explicitly computed in large systems where the links are accessed by a large number of independent flows using ideas from local limit large deviations of convolution measures associated with multirate Erlang systems. Joint work with Thomas Bonald (Telecom ParisTech, France) and Jean-Paul Haddad (Waterloo).

Speaker Biography

The speaker was educated at the Indian Institute of Technology, Bombay (B.Tech, 1977), Imperial College, London (MSc, DIC, 1978) and UCLA (PhD, 1983). He is currently a University Research Chair Professor in the Dept. of ECE at the University of Waterloo, Ont., Canada where he has been since September 2004. Prior to this he was Professor of ECE at Purdue University, West Lafayette, USA where he continues to be an Adjunct Professor.

He is an editor of the IEEE/ACM Trans on Networking and has served as guest editor for a number of special issues of networking and applied probability related journals. He is a Fellow of the IEEE and the Royal Statistical Society. He is a recipient of the INFOCOM 2006 Best Paper Award and was runner-up for the Best Paper Award at INFOCOM 1998. His research interests are in modeling, control, and performance analysis of both wireline and wireless networks, and in applied probability and stochastic analysis with applications to queueing, filtering, and optimization.

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